U.S. patent application number 10/519577 was filed with the patent office on 2007-08-23 for method and apparatus for detecting multiple optical wave lengths.
Invention is credited to MartinF Fay, Daniel Levner, Jingming Xu.
Application Number | 20070196047 10/519577 |
Document ID | / |
Family ID | 35996305 |
Filed Date | 2007-08-23 |
United States Patent
Application |
20070196047 |
Kind Code |
A9 |
Levner; Daniel ; et
al. |
August 23, 2007 |
Method and apparatus for detecting multiple optical wave
lengths
Abstract
Optical gratings that perform a number of functions at various
wavelengths are formed by various methods that preserve spectral
information within a wavelength band, the functions including:
coupling radiation from one waveguide to another, controllable
gratings that operate on different wavelengths in response to
external control signals.
Inventors: |
Levner; Daniel; (Toronto,
CA) ; Fay; MartinF; (Waltham, MA) ; Xu;
Jingming; (Providence, RI) |
Correspondence
Address: |
DORSEY & WHITNEY LLP;INTELLECTUAL PROPERTY DEPARTMENT
SUITE 3400
1420 FIFTH AVENUE
SEATTLE
WA
98101
US
|
Prior
Publication: |
|
Document Identifier |
Publication Date |
|
US 20060051022 A1 |
March 9, 2006 |
|
|
Family ID: |
35996305 |
Appl. No.: |
10/519577 |
Filed: |
June 27, 2003 |
PCT Filed: |
June 27, 2003 |
PCT NO: |
PCT/US03/20237 |
371 Date: |
December 27, 2004 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
10188530 |
Jul 3, 2002 |
|
|
|
10519577 |
Dec 27, 2004 |
|
|
|
60392306 |
Jun 27, 2002 |
|
|
|
60393209 |
Jul 1, 2002 |
|
|
|
60302904 |
Jul 3, 2001 |
|
|
|
Current U.S.
Class: |
385/37 ;
385/50 |
Current CPC
Class: |
G02B 6/12007 20130101;
G02F 1/3132 20130101; G02B 6/02147 20130101; G02B 6/29322 20130101;
G02F 2203/585 20130101; G02B 5/1828 20130101; G02B 6/29334
20130101; G02B 6/29311 20130101; G02F 1/2955 20130101; G02B 6/4215
20130101; G02F 2202/13 20130101; G02F 2203/055 20130101; G02B
6/29323 20130101; G02F 2201/305 20130101; G02F 1/0955 20130101;
G02F 2203/48 20130101; G02B 6/29383 20130101; G02F 2202/32
20130101; G02B 2006/1213 20130101; G02B 6/02133 20130101; H01S
3/0675 20130101; G02B 6/2932 20130101 |
Class at
Publication: |
385/037 ;
385/050 |
International
Class: |
G02B 6/34 20060101
G02B006/34 |
Claims
1. An optical device comprising at least two waveguides in at least
one propagation layer of grating material, a first one of said
waveguides adapted for transporting input radiation from a first
input port to output radiation exiting from a first output port and
a second one of said waveguides transporting input radiation from a
second input port to output radiation exiting from a second-output
port, and a one- or two-dimensional (binary) supergtating in a
modulation layer of grating material for coupling input radiation
propagating from one of said first and second input ports along a
corresponding waveguide to the other of said first and second
waveguides
2. A device according to claim 1, in which said one- or
two-dimensional supergrating couples input radiation in said first
waveguide traveling in a first direction to said second waveguide
traveling in a second direction substantially parallel to said
first direction.
3. A device according to claim 1, in which said one- or
two-dimensional supergrating couples input radiation in said first
waveguide travelling in a first direction to said second waveguide,
traveling in a second direction substantially opposite to said
first direction.
4. A device according to claim 1, in which said first and second
waveguides are symmetric and said one- or two-dimensional
supergrating comprises a central portion between said first and
second waveguides having a first pattern of high and low values of
index of refraction and first and second outer portions having a
second pattern of high and low values of index of refraction having
the opposite sense to said first pattern, whereby said one- or
two-dimensional supergrating suppresses back reflection in said
first and second waveguides.
5. A device according to claim 1, in which said two dimensional
supergrating comprises an array of controllable means, responsive
to a set of control signals, for altering the modal index of
refraction value in corresponding pixels in said array in at least
two modes including a first mode in which said device couples input
radiation in said first waveguide travelling in a first direction
to said second waveguide traveling in a second direction
substantially parallel to said first direction and a second mode in
which said device couples input radiation in said first waveguide
travelling in a first direction to said second waveguide traveling
in a second direction substantially opposite to said first
direction.
6. A device according to claim 5, in which said one- or
two-dimensional supergrating comprises an array of controllable
means responsive to a set of control signals that are adapted to
switch radiation of any of N different wavelengths between said
first and second-waveguides in said first and second modes in
response to corresponding values of said control signal, whereby
said device may be controlled to pass radiation in any one of N
wavelengths from any of said input ports to any of said output
ports, thereby forming a wavelength-dependent supergrating
2.times.2 coupler.
7. A device according to claim 1, in which said one- or
two-dimensional supergrating comprises an array of controllable
means, responsive to a set of control signals, for altering the
index of refraction value in corresponding pixels in said array in
at least two modes including a first mode in which said device
couples input radiation in said first waveguide to said second
waveguide and a second mode in which said device couples input
radiation in said second waveguide to said first waveguide.
8. A device according to claim 7, in which said one- or
two-dimensional supergrating comprises an array of controllable
means responsive to a set of control signals that are adapted to
switch radiation of any of N different wavelengths between said
first and second waveguides in said first and second modes in
response to corresponding values of said control signal, whereby
said device may be controlled to pass radiation in any: one of N
wavelengths from any of said input ports to any of said output
ports, thereby forming a wavelength-dependent supergrating
2.times.2 coupler.
9. An N.times.M system for controllably directing radiation of a
selected wavelength from any one of N input ports to any one of M
output ports comprising a set of wavelength dependent supergrating
couplers arranged to accept incoming radiation in an input
wavelength range and to couple radiation entering in any of said N
input ports to any of said M output ports, comprising a first row
of N/2 input couplers, a final row of M/2 couplers and a set of
intermediate mixing couplers that couple radiation from one or more
couplers in a preceding row to one or more couplers in the next
row.
10. A device according to claim 9, in which said one- or
two-dimensional supergrating comprises an array of controllable
means responsive to a set of control signals that are adapted to
switch radiation of any of N different wavelengths between said
first and second waveguides in response to corresponding values of
said control signal, whereby said device may be controlled to pass
radiation in any one of N wavelengths from any of said input ports
to any of said output ports, thereby forming a wavelength-dependent
supergrating cross-bar coupler.
11. A device for receiving optical radiation of N input wavelengths
and dividing it into N physically separate channels, comprising: an
input channel, a set of wavelength dependent supergrating couplers
connected in series to said input channel, each of said set of
couplers being adapted to couple radiation in a radiation band from
said input channel to an output channel.
12. A device according to claim 11, in which each of said couplers
processes a single one of said N channels of radiation.
13. A device according to claim 11, in which at least some of said
couplers process a range of channels of radiation and following
couplers complete the process of separating each of said N
channels.
14. A device for receiving optical radiation of N input wavelengths
and dividing it into N physically separate channels, comprising: an
input channel, a two dimensional wavelength dependent supergrating
adapted for deflecting radiation of different wavelengths and
directing the deflected radiation toward a set of output
channels.
15. A device according to claim 14, in which the one- or
two-dimensional wavelength dependent supergrating deflects
radiation away from the input direction of travel at angles that
depend on the wavelength and focus that radiation into a set of
waveguides for each wavelength channel.
16. A device for processing optical radiation in a set of
wavelengths comprising a set of waveguides having at least one
input port and at least one output port, in which an input beam of
radiation traveling on an input waveguide passes through at least
one wavelength dependent supergrating coupler that couples a
selected wavelength band in or out of the input waveguide, so that
the remaining optical beam in the input waveguide has a wavelength
range that has been added to or subtracted from by the selected
wavelength band.
17. A device according to claim 16, in which said wavelength
dependent supergrating coupler adds radiation from a second input
port to said input beam.
18. A device according to claim 16, in which said wavelength
dependent supergrating coupler subtracts radiation in a wavelength
subtraction range from said input beam.
19. A device according to claim 16, in which at least two
supergrating couplers are connected in series, with a first
supergrating coupler controlling a first wavelength range and a
second supergrating coupler controlling a second wavelength
range.
20. A device for monitoring the strength of radiation in a
waveguide comprising: An input waveguide containing radiation in a
selected wavelength range; and A wavelength dependent supergrating
coupler intercepting said radiation and deflecting a portion of
said radiation out of said waveguide and onto a radiation meter
responsive to the power of radiation impinging thereon, whereby the
magnitude of deflected radiation is a measure of the magnitude of
radiation traveling in the waveguide.
21. An optical device for altering the incoming power spectrum of
an incoming beam and converting said incoming beam to an outgoing
beam having an outgoing power spectrum comprising: A set of N
controllable wavelength sensitive power removal modules for
removing a controllable amount of power in a wavelength range from
said incoming beam, whereby said incoming power spectrum is
converted to said outgoing power spectrum by subtracting power from
selected wavelength ranges.
22. An optical amplifier comprising a gain medium for receiving an
input beam having an input power spectrum and increasing the energy
thereof, thereby forming an output beam having an output power
spectrum: Comprising a power control unit for removing a
controllable amount of power in at least one wavelength range from
said incoming beam, whereby said input power spectrum may be
adjusted such that said output power spectrum has a desired
profile.
23. An array of waveguides arranged in a grid comprising a set of
input waveguides for receiving multiplexed inputs comprising at
least one wavelength crossing a set of output waveguides, each of
the input waveguides having a series of wavelength dependent
supergrating couplers that each couple radiation of a selected
output wavelength range to a corresponding output waveguide,
whereby radiation entering with a number of wavelengths on input
waveguides is sorted into a set of output waveguides, each carrying
an output wavelength range.
24. A device according to claim 23, in which at least some of said
output wavelength ranges cover a single wavelength channel.
25. An optical device for receiving an input beam having an input
wavelength dependent group delay spectrum and applying a
compensating group delay spectrum, thereby generating an output
beam, comprising: An input port for receiving said input beam; at
least one wavelength dependent supergrating for imposing a
compensating wavelength dependent delay on radiation traveling
therethrough; and an output port.
26. A device according to claim 25, in which said input port is
connected to an optical circulator that couples input radiation to
a reflective supergrating that reflects back radiation into said
circulator with said wavelength dependent delay impressed
thereon.
27. A device according to claim 25, in which said input port is a
first end of a first waveguide having a transmissive supergrating
that passes radiation therethrough out a second end of said first
waveguide with said wavelength dependent delay impressed
thereon.
28. A device according to claim 25, in which said input port is
connected to a reflective supergrating that couples input radiation
in said first waveguide travelling in a first direction to a second
waveguide and traveling in a second direction substantially
opposite to said first direction with said wavelength dependent
delay impressed thereon.
29. A device according to claim 25, in which said input port is
connected to a transmissive supergrating that couples input
radiation in said first waveguide traveling in a first direction to
a second waveguide traveling in a second direction substantially
parallel to said first direction with said wavelength dependent
delay impressed thereon.
30. An optical device comprising an input port for receiving
incident radiation and directing the radiation on an array of
pixels comprising a supergrating, each pixel having a modal index
of refraction selected from a set of index values, the array of
pixels collectively processing the incident radiation and directing
at least one beam of output radiation to at least one output port,
in which at least some of the array of pixels are connected to
control means for controllably setting the value of the modal index
of refraction of the corresponding pixels in response to a control
signal, so that the process applied to the incident radiation may
be determined by the control signals applied to the control
means.
31. A laser comprising a gain medium, pumping means for
establishing an inversion in said gain medium and means for
resonating optical radiation in said gain medium, in which: said
means for resonating radiation in said gain medium comprises at
least one array of pixels comprising a supergrating, each pixel
having a modal index of refraction selected from a set of index
values, the array of pixels collectively processing the incident
radiation, in which at least some of the array: of pixels are
connected to control means for controllably setting the value of
the index of refraction of the corresponding pixels in response to
a control signal, so that the process applied to the incident
radiation may be determined by the control signals applied to the
control means.
32. A laser according to claim 31, in which said supergrating
resonates radiation in at least two wavelength ranges with a
respective loss set by said control signals, thereby establishing a
power spectrum determined by said control signals.
33. A laser according to claim 31, in which said supergrating is
located outside said gain medium.
34. A laser according to claim 31, in which said supergrating is
located inside said gain medium.
35. A laser according to claim 31, in which said supergrating is
located inside said gain medium and said supergrating directs
radiation of different wavelengths along different paths through
said gain medium, thereby establishing a wavelength dependent
length through said resonator.
36. A device for receiving optical radiation of at least two input
wavelengths on at least one physically separate channels and
combining it into a single output channel, comprising: a least two
input channels; a one- or two-dimensional wavelength dependent
supergrating adapted for deflecting radiation of different
wavelengths and directing the deflected radiation toward said
output channel.
37. A device according to claim 36, in which the one- or
two-dimensional wavelength dependent supergrating deflects
radiation away from the input directions of travel at angles that
depend on the wavelength and focus that radiation into a waveguide
for the output wavelength channel.
38. An optical device comprising at least one input port and at
least one output port connected by asymmetric optical means having
different attenuation in opposite directions, further comprising a
supergrating coupling radiation within a pass band from the input
port to the output port.
39. A device according to claim 38, in which the supergrating
couples radiation traveling in a first direction from a first
waveguide to radiation traveling in the first direction in a second
waveguide.
40. A device according to claim 38, in which the supergrating
couples radiation traveling in a first direction in an input
waveguide to radiation traveling in a second direction opposite to
the first direction in an output waveguide.
41. A device according to claim 40, in which the input waveguide
and the output waveguide are the same.
42. A device according to claim 40, in which the input waveguide
and the output waveguide are physically separated.
43. An optical device comprising at least one input port and at
least one output port connected by asymmetric optical means having
different attenuation in opposite directions, further comprising a
supergrating>coupling radiation within a pass band from an input
port to the next port in sequence.
44. An optical device comprising an input port and an output port
disposed along an optical axis and connected by a supergrating
coupling radiation within a pass band from the input port to the
output port, further comprising a set of lateral pixels extending
in two lateral directions that represent an analog profile that
forms a design set of wave fronts.
45. An optical device according to claim 45, in which a set of
pixels of said supergrating are controlled by controllable means,
responsive to a set of control signals, for altering the index of
refraction value in corresponding pixels in said array.
46. A three-dimensional optical device comprising at least one
waveguide in a first propagation layer of grating material for
transporting input radiation from a first input port to output
radiation exiting from a first output port, and a two dimensional
supergrating in a modulation layer of grating material for coupling
input radiation propagating from said first port out of said first
propagation layer to at least one other propagation layer disposed
along a third dimensional axis at a different location from said
first propagation layer and having quantized pixels formed therein
for processing said radiation; and means for directing processed
radiation toward said first output port.
47. A material comprising a layer of optically propagating material
in a reference plane that transmits radiation in a wavelength
range, the material-being impressed with a pattern of index of
refraction change such that propagation in the reference plane is
suppressed, the pattern of index of refraction change being
digitized from an analog index of refraction profile.
48. A material according to claim 47, in which the pattern of index
of refraction change is modified to permit propagation of radiation
in the wavelength range within a restricted area and in a
restricted direction.
49. A material according to claim 47, that is disposed on a
substrate of photo-electric material, whereby propagation of
radiation that impinges on the photo-electric material is
facilitated compared with propagation of radiation that does not
impinge on the photoelectric material.
50. A material according to claim 47, that is capable of laser
action at a laser wavelength and has at least one localized area
permitting propagation of radiation at the laser wavelength,
whereby stimulated emission at the laser wavelength is confined to
resonate within the localized area.
51. A material according to claim 47, that contains a waveguide
that within which the pattern of index of refraction change is
absent, such that radiation propagates within the waveguide, in
which material the waveguide follows a curve having a radius of
curvature less than a reference value.
52. A material according to claim 47, that contains two waveguides
with a separation region therebetween, the separation region having
the ability to propagate radiation within at least an attenuation
length.
53. A material according to claim 52, in which the separation
region has a pattern of index of refraction change that permits
propagation with an attenuation length greater than the separation
between the waveguides.
54. A material according to claim 47, in which the material
supports a non-linear interaction between two input wavelengths
that generates radiation of an output wavelength and the pattern of
index of refraction change suppresses propagation of the two input
wavelengths and the output wavelength; and At least one waveguide
is formed in the material for the propagation of the input and
output wavelengths.
55. A method of forming a two dimensional supergrating in a
modulation layer of grating material for converting input radiation
propagating from an input source through a propagation layer of
grating material to output radiation exiting from said grating on
at least one output path comprising the steps of: generating a two
dimensional analog refractive index profile in the modulation layer
that implements a transfer function relating electromagnetic fields
characteristic of the input radiation and output radiation;
digitizing the analog refractive index profile to generate an array
of pixels in the modulation layer having digitized refractive index
values by using a two-dimensional technique that conserves Fourier
information within one or more regions of the two-dimensional
spatial-frequency representation of said two-dimensional analog
refractive index profile; and imposing the array of pixels
representing the digitized refractive index profile on the
modulation layer.
56. A method according to claim 55, further comprising the steps of
selecting a two-dimensional sampling lattice of lattice pixels;
Setting a total device length and width; In which the step of
digitizing includes setting a value for the index of refraction in
each lattice pixel of the total sampling lattice.
57. A method according to claim 55, in which the step of digitizing
includes computing an intermediate sampled index profile wherein
the value at each sample point of the sampled index profile is
equal to the value for the index of refraction of the analog
refractive index profile at a corresponding point on the sampling
lattice.
58. A method according to claim 55, further comprising the steps
of: Converting the reflectance specifications of the transfer
function to the Fourier Domain; Specifying grating parameters in
the Fourier Domain; and Converting the grating parameters to the
spatial domain, thereby determining the analog-profile in the
spatial domain.
59. A method according to claim 55, further comprising specifying
phases of components of the analog refractive index profile such
that the maximum refractive index value of the analog refractive
index profile is minimized.
60. A method of forming an effective one dimensional supergrating
in a modulation layer of grating material for converting input
radiation propagating along an axis from an input source through a
propagation layer of grating material to output radiation exiting
from said grating on said axis comprising the steps of: generating
a two dimensional analog refractive index profile in the modulation
layer that implements a transfer function relating electromagnetic
fields characteristic of the input radiation and output radiation;
digitizing the analog refractive index profile to generate an array
of pixels in the modulation layer having digitized refractive index
values by using a two-dimensional technique that maintains Fourier
components within one or more regions of the two-dimensional
spatial-frequency representation of said two-dimensional analog
refractive index profile; and imposing the array of pixels
representing the digitized refractive index profile on a portion of
the modulation layer extending laterally from the axis by a lateral
distance.
61. A method of forming a three-dimensional supergrating in a
modulation volume of grating material for converting input
radiation propagating from an input source through the grating
material to output radiation exiting from said grating on at least
one output path comprising the steps of: generating a
three-dimensional analog refractive index profile in the modulation
volume that implements a transfer function relating electromagnetic
fields characteristic of the input radiation and output radiation;
digitizing the analog refractive index profile to generate an array
of pixels in the modulation layer having digitized refractive index
values by using a three-dimensional technique that conserves
Fourier information within one or more regions of the
three-dimensional spatial-frequency representation of said
two-dimensional analog refractive index profile; and imposing the
array of pixels representing the digitized refractive index profile
on the modulation layer.
62. A method of forming a one or two or three dimensional
supergrating in a modulation layer of grating material for
converting input radiation propagating from an input source through
a propagation layer of grating material to output radiation exiting
from said grating on at least one output path comprising the steps
of: Generating a one dimensional analog refractive index profile P
in the modulation layer that implements a transfer function
relating electromagnetic fields characteristic of the input
radiation and output radiation; generating a filter function H that
selects the spatial-frequency ranges in which spectral information
is conserved and assigns weights thereto; solving the optimization
problem represented by min X , V .times. C = min X , V .times. [ H
.function. ( P - X ) L + i .times. V i .times. ( X i - n low )
.times. ( X i - n high ) ] , ##EQU8## where X is a vector
containing the Binary Supergrating's refractive index values, V is
a vector of Lagrange multipliers, L determines the type of
optimization, and n.sub.low and n.sub.high are the Binary
Supergrating's low and high refractive index values, respectively;
thereby computing a Binary Supergrating refractive index profile,
X, in the modulation layer that converts the input radiation to the
output radiation; and imposing the array of pixels representing the
digitized refractive index profile on the modulation layer, whereby
the input radiation is converted to the outpt radiation.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates generally to detecting optical
signals and, more particularly, to detecting multiple optical
wavelengths with optical supergratings.
[0003] 2. Prior Art
[0004] Gratings are optical devices used to achieve
wavelength-dependent characteristics by means of optical
interference effects. These wavelength-dependent optical
characteristics can, for instance, serve to'reflect light of a
specific wavelength while transmitting or refracting light at all
other wavelengths. Such characteristics are useful in a wide range
of situations, including the extraction of individual
wavelength-channels in Wavelength Division Multiplexed (WDM)
optical communication systems, or providing wavelength-specific
feedback for tunable or multi-wavelength semiconductor lasers.
Gratings are usually implemented by modulating (varying) the
effective index of refraction of a waveguiding structure. These
changes in index of refraction cause incident light wavelengths to
be reflected or refracted: in the case of an abrupt interface
between two index values, light incident directly on the interface
is reflected according to the well known Fresnel reflection
law.
[0005] The term "multi-wavelength grating" generally refers to a
grating that is capable of exhibiting optical characteristics at a
number of wavelengths. For example, a multi-wavelength grating can
be a grating that reflects light at several select wavelengths
(which can correspond to specific optical communication channels),
yet is transparent to light at other wavelengths. In some
situations, however, there is a need to set the optical
characteristics for a continuous range of wavelengths, rather than
at specific wavelength values. For example, when trying to
compensate for the unevenness of optical gain profiles in laser
cavities and optical amplifiers by means of an optical grating.
However, achieving this requirement for a continuous range of
wavelengths is difficult to meet with traditional grating
technologies.
[0006] Similarly, a range of optical wavelengths may be used where
many communication channels are encoded into a single optical cable
by utilizing different wavelengths of light; more commonly known as
Wavelength Division Multiplexing (WDM) technology. Periodic
gratings are often used to separate or process these channels.
However, periodic grating technologies process one wavelength,
forcing devices intended to process multiple wavelengths to employ
multiple single-wavelength periodic gratings. This is not an
attractive solution because, on top of the additional losses that
each grating creates, even a single grating occupies a considerable
amount of space by today's standards of integration and
miniaturization. It is thus desired to have a single device capable
of processing several wavelengths in a space-efficient manner.
[0007] In the realm of semiconductor lasers, the output wavelength
of semiconductor lasers is largely determined by the presence of
"feedback elements" around, or inside the laser gain section, which
act to reflect light at the desired wavelength back into the laser.
For multi-wavelength operation, multi-wavelength feedback is
needed. Again, single-wavelength grating technology can only
address this demand with a cascade of simple gratings, leading to
the same (if not more notable) loss and space problems mentioned
above.
[0008] One such single-wavelength grating device, is a Bragg
Grating. The Bragg Grating consists of a periodic variation in
refractive index and acts as a reflector for a single wavelength of
light related to the periodicity (known as pitch, A) of the index
pattern; and is frequently used in both semiconductor systems and
fiber-optic systems. In practice, however, the Bragg Grating can
actually reflect at several wavelengths, corresponding to overtones
of its fundamental pitch. However, these higher-order wavelengths
tend to be at quite different spectral regions than the fundamental
wavelength, thus making the Bragg Grating less than useful as a
multi-wavelength reflector. Moreover, these higher-order
wavelengths cannot be tuned independently of one another.
[0009] Other multi-wavelength grating technologies include: analog
superimposed gratings, Sampled Gratings (SG), Super-Structure
Gratings (SSG) and Binary Supergratings (BSG).
[0010] Analog superimposed gratings are a generalization of the
Bragg Grating and are rooted in a principle of superposition: a
grating profile consisting of the sum of the index profiles of
single-wavelength gratings reflects at all of its constituent
wavelengths. Such a grating relies on an analog index variation,
that is, a refractive index that changes continuously along the
grating length (FIG. 30). However, it is difficult to inscribe
strong analog gratings using the well known photorefractive effect,
since the change of index under illumination varies non-linearly,
and generally saturates with stronger exposures. Likewise,
rendering surface-relief analog gratings (a typical embodiment for
semiconductors) is made impractical by the difficulty of
reproducibly etching analog features into a surface. The latter
difficulty brought about the introduction of binary gratings, i.e.,
gratings that rely only on two refractive index values
corresponding to the material being etched or not etched,
illuminated or not illuminated.
[0011] Two representations of multi-wavelength binary gratings are
sampled gratings (SG) and superstructure gratings (SSG). The SG is
constructed with alternating sections of grating and grating-free
regions of the waveguide. The alternating sections produce
diffraction spectra having multiple reflectance peaks contained
within a (typically) symmetric envelope. The SG is intrinsically
limited in the flexibility in the location and relative strength of
reflectance peaks, and, because of the large fraction of
grating-free space, is also spatially inefficient. The SG is
therefore particularly unsuitable where a short grating is required
or where waveguide losses are high.
[0012] With the super-structure grating (SSG), the grating period
is chirped by finely varying the grating pitch, which corresponds
to the length of one tooth-groove cycle. This can also be thought
of as a sequence of finely tuned phase shifts; common phase
profiles include linear and quadratic chirp. Such an implementation
in principle allows arbitrary peak positions and relative heights,
but only at the expense of extremely high resolution, corresponding
to a very small fraction of the size of the grating teeth
themselves.
[0013] Prior art regarding binary superimposed grating synthesis is
presented in Ivan A. Avrutsky, Dave S. Ellis, Alex Tager, Hanan
Anis, and Jimmy M. Xu, "Design of widely tunable semiconductor
lasers and the concept of Binary Superimposed Gratings (BSG's),"
IEEE J. Quantum Electron., vol. 34, pp. 729-740, 1998.
[0014] Other methods in the prior art address the synthesis of
"multi-peak" gratings i.e., gratings characterized by reflectance
at several "peaks", which can be controlled in their position and
strength. In these methods, a grating engineer begins with a set of
sinusoids, each sinusoid corresponding to a single reflectance peak
and weighted according to that peak's desired relative strength.
These peaks are added together (i.e. superimposed; hence the BSG is
known as a superimposed grating) to produce an "analog profile".
This profile is then digitally quantized by a simple threshold
method.
[0015] For example, if the analog profile value is positive (above
a pre-selected reference) then the corresponding BSG segment is a
high or binary 1 index value; if it is negative, the corresponding
BSG segment is a low or binary zero index value.
[0016] However, this approach is inadequate in at least two areas:
firstly, the threshold quantization process introduces
intermodulation, which largely limits the applicability of BSGs
synthesized in this manner to active applications (laser feedback
elements and the like). Secondly, this synthesis procedure is
limited to multi-peak gratings, and offers little or no control
over the individual peak shape. For example, it is entirely
incapable of generating flattop channels, as desired by some
communication applications, or of generating the near-arbitrary
reflectance spectra demanded by some gain-compensation and
dispersion-compensation methods.
[0017] Other methods for BSG synthesis include trial-and-error
methods that are most often computationally difficult and
inefficient.
[0018] Therefore, it is desirable to provide a method and apparatus
for overcoming the disadvantages noted above in designing and
synthesizing supergratings for detecting optical wavelengths.
BRIEF DESCRIPTION OF THE DRAWINGS
[0019] The foregoing aspects and other features of the present
invention are explained in the following description, taken in
connection with the accompanying drawings, wherein:
[0020] FIG. 1 is a schematic of deep-grating BSG;
[0021] FIG. 2 is a k-space picture of rationale behind baseband
exclusion;
[0022] FIG. 3 is a prototypical diagram of a lateral BSG in a ridge
waveguide;
[0023] FIG. 4 is a schematic of a prototypical two dimensional (2D)
supergrating;
[0024] FIG. 5 is a schematic of a multi-level one-dimensional (1D)
supergrating implemented with a 2D BSG;
[0025] FIG. 6 is a schematic of a prototypical three dimensional
(3D) supergrating;
[0026] FIGS. 7a-7d show embodiments of programmable
supergratings;
[0027] FIG. 8 is a schematic of a co-directional
asymmetric-waveguide BSG coupler;
[0028] FIG. 9 is a schematic of a counter-directional
asymmetric-waveguide BSG coupler;
[0029] FIG. 10 is a schematic of a counter-directional
symmetric-waveguide BSG coupler;
[0030] FIG. 11 is a schematic of the grid-topology cross bar
switch;
[0031] FIG. 12 is a schematic of an embodiment of a 4-fiber switch,
utilizing 6 switching elements;
[0032] FIG. 13 illustrates a one-photon method of implementing a
BSG in optical fiber;
[0033] FIG. 14 illustrates a multi-photon method (two-photon shown)
of implementing a BSG in optical fiber;
[0034] FIG. 15 is a schematic of a demultiplexer employing a 1D
BSG;
[0035] FIG. 16 is a schematic of a demultiplexer employing a 2D
BSG;
[0036] FIG. 17 is a schematic of a static add/drop filter;
[0037] FIG. 18 is a schematic of a Vernier-tuning dynamic add/drop
filter;
[0038] FIG. 19 is a schematic of a programmable BSG add/drop
filter;
[0039] FIGS. 20a-20c are schematics of embodiments of BSG-based
wavelength stability monitors;
[0040] FIG. 21 is a schematic of a 2-D BSG network monitor;
[0041] FIG. 22 is a schematic of a BSG dynamic WDM equalizer;
[0042] FIG. 23 is a schematic of a gain-flattened optical
amplifier;
[0043] FIG. 24a-24b are schematics of lambda router
embodiments;
[0044] FIGS. 25a-25d are schematics of embodiments of BSG
dispersion-slope compensators;
[0045] FIGS. 26a-26b are schematics of tunable dispersion
compensators;
[0046] FIGS. 27a-27c are schematics of a variable-feedback
supergrating laser;
[0047] FIG. 28 is a schematic of beam combiners, in
coupled-waveguide and 2D BSG embodiments;
[0048] FIG. 29a is a schematic of a BSG-based isolator;
[0049] FIGS. 29b-29c are schematics of 4-port coupled-waveguide
circulators;
[0050] FIG. 30 is an analog index profile from a plot of refractive
index change delta-n (.DELTA.n) versus distance (x);
[0051] FIG. 31 shows a BSG index profile of .DELTA.n versus
distance x and the corresponding surface-relief implementation;
[0052] FIG. 32 is a block diagram showing a standard topology for
Delta-Sigma modulation;
[0053] FIG. 33 illustrates a synthesis technique for a BSG using
induced-symmetry;
[0054] FIG. 34 illustrates a synthesis technique for a BSG using
super-Nyquist synthesis; and
[0055] FIG. 35 is a flow chart showing method steps of one
embodiment of the present invention for synthesizing a BSG.
[0056] FIGS. 36a and 36b illustrate a simplified example of a
demultiplexer comared with discrete components.
[0057] FIGS. 37-45 illustrate embodiments that employ a pattern of
pixels that provides a photonic band gap structure
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
[0058] Although the present invention will be described with
reference to the embodiments shown in the drawings, it should be
understood that the present invention can be embodied in many
alternate forms of embodiments, and it is not intended that this
invention is limited only to the embodiments shown.
[0059] For the purposes of this invention, gratings are considered
to be optical devices used to achieve wavelength-dependent
characteristics by means of optical interference effects.
[0060] Starting with Binary Supergratings (BSG), it will be
appreciated that there are two main properties that differentiate
the BSG from other grating technologies. The first is that the BSG
relies on a discrete number of refractive index levels. This number
is historically 2 and hence the BSG is known as a binary grating.
For the sake of clarity and illustration this description will
focus on the binary embodiment of the present invention, however,
it will be appreciated that in alternate embodiments any suitable
number of discrete levels of refractive index may be used. For
convenience in the claims, the term supergrating will be used to
refer to gratings with two or more values of index of refraction,
unless specifically stated. The second defining property of the BSG
is that the grating resembles a sampled structure characterized by
a sample length. This refers to the fact that transitions between
the grating's index levels cannot occur at arbitrary positions but,
rather, occur at multiples of the sample length. The BSG is thus
similar in definition to a digital signal pattern--i.e., a discrete
sampled waveform. Thus, the BSG can be described by a series of
(often binary) digits, indicating the refractive index setting at
each sample point (see FIG. 31).
[0061] Referring now to FIG. 35, BSG design involves several key
choices. Step 351 selects the refractive index levels for the
device, as determined from material parameters and lithographic or
photoinscription constraints. Step 352 then determines the desired
sample length, considering the desired wavelength range for the
grating and the available lithographic resolution. Step 353 sets a
total device length for the grating, limited by the available
physical space and the technological limitations of the inscribing
process. It will be appreciated that the methods described herein
are for determining grating patterns for surface-relief gratings;
however, in alternate embodiments the methods may be readily
adapted to fiber grating patterns, or to programmable
implementations. The next step 354 converts the desired grating's
diffraction characteristics to the Fourier domain using a Fourier
approximation. These diffraction characteristics can be reflective,
transmissive, co- or counter-directional coupling, or scattering in
character, or any combination thereof; it will be appreciated that
"reflectance" and "reflection" can be replaced by
"cross-transmittance" and "cross-transmission" throughout this
document. Guided by the Fourier approximation, the designer can
initially design the grating by its Fourier spectrum. As will be
shown below, this step can also implement feedback to account for
various inaccuracies of the approximation in order to improve the
final result. Alternatively, any method for the design of an analog
refractive index profile to achieve the desired diffractive
characteristics is suitable, and many are known in the art.
[0062] The next step 355 performs a quantization of the analog
index profile. Delta-Sigma modulation is one such quantization
technique that can be used and can be efficiently implemented. It
will be appreciated that in alternate embodiments any suitable
quantization technique that conserves Fourier information within a
spectral band may be used. Methods of synthesis and resultant
gratings that use a threshold quantization technique such as that
shown in the cited reference by Avrutsky, et al., which does not
conserve Fourier information within a spectral band are disfavored,
but may be useful in some circumstances. In the case of two
dimensional or three dimensional radiation processing, where
radiation traveling in two or three dimensions is significant, and
a pixel array extending in two or three dimensions is significant,
any quantization method may be used to design an apparatus that
falls within the definition.
[0063] The next step 356 determines the BSG's actual diffractive
characteristics using an exact technique such as one known as the
transfer matrix method. This calculation determines residual errors
of the Fourier approximation, or other synthesis method used, and
quantifies an error that can be taken back into the Fourier domain
and added to the result of the step 353 if step 357 determines that
the error exceeds a predetermined threshold. This process can be
repeated as necessary, although one repetition is often sufficient.
It will be appreciated that any suitable technique for determining
error between the desired diffractive characteristics and actual
diffractive characteristics may be used.
[0064] Referring now to each of the above steps in more detail; in
step 353, the Fourier approximation is a mathematical relation that
relates a grating's diffraction characteristics (which can be
reflective, transmissive, or scattering in character, or any
combination thereof), to the structure of its index profile. In
other words, single-wavelength gratings have reflectance spectra
characterized precisely by their periodic structure, and simple
superimposed gratings have reflectance spectra characterized by
their wavelength or reflectance spectra components. Therefore, the
diffraction spectrum of a grating can be related to the Fourier
transform of its structure--the Fourier transform being the
standard method for evaluating the "frequency content" or
"wavelength content" of a waveform.
[0065] Thus, it will be appreciated that the invention
advantageously uses a Fourier approximation to provide a means (the
inverse Fourier transform) for generating an analog refractive
index profile from the desired reflectance specifications.
[0066] It will also be appreciated that the step of quantizing the
analog index profile (step 355) can be performed regardless of how
the analog profile was determined. In other words, the analog
profile need not have been obtained using Fourier-based
methods.
[0067] The following examples illustrate Fourier Approximation for
BSG synthesis:
Synthesis of Simple Peaks
[0068] In some situations, such as with laser feedback elements,
the BSG is desired to reflect light at a given set of wavelengths,
and to do so with the highest wavelength selectivity possible. That
is, the specification is for simple peaks with minimal channel
width. Such peaks can be derived from the superposition of
sinusoidal profiles: i .times. a i .times. cos .function. ( .omega.
i .times. x + .PHI. i ) ##EQU1## where a.sub.i, .omega..sub.i, and
.phi..sub.i are the amplitude, spatial frequency and phase of the
i.sup.th peak respectively, and x is the position along the
grating's length. Most situations dictate the amplitude
coefficients. However, many do not require anything specific of the
phase.
[0069] In general, component phases should be selected such that
they minimize the maximum height of the superposition (which
consequently flattens the overall envelope), given the component
amplitudes. The use of phase information to produce a flat envelope
can greatly increase the efficiency of the grating. This
illustrates a general principle of BSG design: in most cases, the
analog index profile (before quantization) should preferably have
an envelope that is as flat as possible. This is desirable because
a flat envelope represents an even distribution of grating
strength, and makes more efficient use of the available index
modulation.
[0070] The phase optimization step in accordance with this
invention facilitates large increases in a BSG's reflective
efficiency. It will be appreciated that increasing the number of
reflective peaks produces a sub-linear increase in the required
index modulation. That is, in order to double the number of peaks,
but maintain the same peak reflectance, the index step does not
need to be doubled.
Synthesis of Bandpass Channels
[0071] A grating is often required to separate or select wavelength
division multiplexed optical communication channels. These channels
are described by their wavelength (position) and their bandwidth
(width). Gratings are also typically accompanied by specifications
of the strength of the reflection and the spectral flatness of the
channel. Such bandpass filter design is commonly encountered in FIR
filter theory, and thus many approaches to its solution exist. The
technique presented here is based on the method of windowing.
[0072] The main principle in the synthesis of structured grating
spectra, such as the bandpass filter, is the use of analytically
determined solutions to an approximated design problem: certain
filter shapes, such as the flat-top filter, are known to correspond
to certain mathematical functions. For example, it is known that
the sinc function with the form: .delta..omega. .pi. .times. sin
.times. .times. c .function. ( .delta..omega. .times. .times. i ) =
sin .function. ( .delta..omega. .times. .times. i ) .pi. .times.
.times. i ##EQU2## where i is the BSG segment number, corresponds
to an ideal lowpass filter of width .delta..omega.. This filter can
be converted into a bandpass filter centered about the frequency
.omega..sub.c by multiplying it with an appropriate sinusoid,
resulting in the filter: .DELTA..omega. .pi. .times. cos .function.
( .omega. c .times. i ) .times. sin .times. .times. c .function. (
.delta..omega. 2 .times. i ) ##EQU3## where the peak is centered
about .omega..sub.c and has a width of .DELTA..omega..
[0073] Unfortunately, this filter, characterized by an abrupt
transition from the passband to the stopband, requires an infinite
length for its implementation. Simply cropping the filter to the
desired length produces undesirable oscillatory features known as
Gibbs phenomena. This is a common issue in FIR design, and one
approach to its solution is the method of windowing.
[0074] The method of windowing views cropping as a multiplication
by a window function that is zero in the cropped regions. Theory
views the cropping operation as multiplication by a "rectangular
window" which equals 1 within the region to be kept, and 0 outside
in the sections to be cropped. The theory argues that this
rectangular window is responsible for the Gibbs phenomena.
[0075] Window functions that can be used for cropping generally
make the bandpass filter non-ideal by producing a finite
"transition width" between the passband and the stophand, in
contrast to the ideal filter, which requires no width for the
transition. However, FIR filter theory suggests several acceptable
albeit non-ideal, window functions.
[0076] One such window function is the Kaiser window--a window
function conceived with the ideal lowpass (and thus bandpass)
filter in mind, and which allows the designer to customize the
transition characteristics through a parameter .beta.. The Kaiser
window is thus suitable for BSG synthesis and provides the added
flexibility of controlling the shape and sharpness of the
reflectance channels. However, this is only one of many FIR
techniques that can be used to achieve this result, and BSG
synthesis by Fourier methods is not restricted to this particular
method.
[0077] It will be appreciated that the analog profile corresponding
to a flattop channel makes most use of the center of the grating.
As with the multi-peak case, this situation is undesirable as it
makes inefficient use of grating resources away from the center. A
convenient solution to this problem is to stagger the waveforms
associated with individual channels-when superimposing them.
Together with a phase-optimization technique such as that used for
the multi-peak grating, this procedure can enable very efficient
use of the grating's resources.
[0078] In some embodiments the reflectance specifications do not
correspond to particular elementary shapes such as band pass
channels or peaks. Gain compensation profiles for optical
amplifiers and dispersion-compensation gratings fall into this
category. In these embodiments, gratings may be synthesized using
the discrete Fourier transform (DFT).
[0079] The discrete Fourier transforms and the related fast Fourier
transform (FFT) are versions of the Fourier transform that operate
on a finite number of sampled points. Being related to the regular
Fourier transform, the Fourier approximation and its implications
on BSG synthesis carry over to the DFT. A DFT operating on a set of
1 real-valued points returns a set of 1/2 independent frequency
components. Thus, a desired grating with 1 segments may be assigned
reflectance values at 1/2 wavelengths, but not between
wavelengths.
[0080] An example of BSG synthesis using the DFT is carried out as
follows:
[0081] The frequency-domain specifications are inserted into an
array of length l, the intended device length (in terms of number
of samples), in a manner suitable for the inverse-DFT operation.
This can be done by "sampling" the continuous version of the
Fourier-domain specifications at certain points, or, alternatively,
by "drawing" the specification directly in the form suitable for
the DFT. The inverse-DFT of the array is then determined. Various
known forms of "smoothing" can be applied to the resulting waveform
in order to reduce oscillatory features between the frequency
samples.
[0082] Once the analog index profile has been synthesized, it may
require several modifications. One such modification is filtering
by a discrete-sum filter. Another modification is that the waveform
should be scaled to a level appropriate to the upcoming Delta-Sigma
modulation stage. For example, this can be accomplished by
resealing the waveform to have an amplitude of 1.
Quantizing or Delta-Sigma Modulation (DSM)
[0083] The Fourier domain synthesis presented up to now produces an
analog grating profile. However, the BSG requires a discrete
profile utilizing only a small number (usually two) of index
values. It will be appreciated that in alternate embodiments any
suitable number of discrete values can be used, such as for
example, an Octal Super Grating (OSG). One technique for the
quantization (i.e., discrete rendering) of the grating profile is
Delta-Sigma modulation. However, any suitable quantization
techniques can be used.
[0084] A preferable requirement for the quantization of the analog
profile by Fourier methods is that it conserves spectral
information in the frequency band of importance. Delta-Sigma
modulation, for example, is designed to "filter out" quantization
noise from a given frequency band, leaving the spectral information
in that band mostly undisturbed. Other quantization methods can
also be applied, with improvements, such as an accounting for
grating effects that are not evident in the frequency domain. In
any case, the selected quantization method preferably conserves
small-amplitude spectral features in the band of importance, as
required by the Fourier approximation, which becomes exact in the
small-amplitude domain.
[0085] It will be appreciated that the method of BSG synthesis by
Fourier techniques and the following quantization presented here
are not restricted to Delta-Sigma quantization.
[0086] Referring to FIG. 32, there is shown a DSM feedback process
320 that improves quantization after a loop filter 322 by making
use of the measured quantization error 321. That is, DSM quantizes
its input using a threshold in unit 323, but keeps track of any
important information that is lost by the quantization in unit 323
and feeds this information back into its input in filter 322. It
will be appreciated that in alternate embodiments any suitable
digital quantizer can be used.
Error Feedback and Iteration
[0087] Once the Fourier grating reflectance spectra has been
quantized, the synthesis is almost complete. The grating's
performance can be evaluated using a standard test such as the
transfer matrix method to determine synthesis error. Synthesis
error refers to the difference between the desired reflectance
spectrum and the spectrum measured by the transfer matrix method.
In one embodiment, the error may be evaluated and used to offset
the design specifications by subtracting the error from the
grating's frequency-domain specifications. The new specifications
can then be used to repeat the synthesis process and generate an
improved grating. In an alternate embodiment, the error, which is
measured in the frequency domain, can be appropriately transformed
into the spatial domain and added to the analog grating profile
(the grating before quantization). This latter form is a general
and powerful technique that can be utilized independently of the
synthesis method used in the frequency domain. The error feedback
process can be repeated as desired, but a single iteration is often
sufficient. The convergence of the feedback process for
small-amplitude frequency regions is guaranteed by the Fourier
approximation described above.
[0088] It will be appreciated that the present invention
advantageously allows a designer to compare error feedback
correction with grating correction techniques in order to correct
for distortions in the diffraction-characteristics domain. For
example, certain peaks may have characteristic shapes to which they
distort in the reflectance domain, for which either the above
described error feedback may correct. The present invention allows
the designer to weigh the advantages of error feedback as compared
with application of grating resources.
Alternate Embodiments of BSG Synthesis
Induced-Symmetry Synthesis
[0089] Referring to FIG. 33, an elementary property of sampled
signals is that their Fourier spectrum displays a symmetry about
integer multiples of a characteristic frequency known as the
Nyquist frequency. In certain applications, such as filters with
large numbers of identical peaks, a similar symmetry exists in the
reflectance specification. The principle of Induced-Symmetry
Synthesis is that the symmetry of the reflectance specifications
can be reproduced by the symmetry about the Nyquist frequency, such
that the grating's resources need only be used to create one half
of the spectral features.
[0090] A good example for this method is the synthesis of a filter
with ten equally spaced reflectance peaks. Using the principle of
Induced-Symmetry Synthesis, the designer can choose a sampling
length that places the Nyquist frequency precisely in the middle of
the ten peaks, that is, on the line of symmetry of the
specifications. The designer can then proceed to synthesize a
grating for the five lower peaks. The upper five peaks appear
automatically due to the Frequency-domain symmetry.
Super-Nyquist Synthesis
[0091] Often the required resolution for grating-inscription
exceeds the available resolution. For example, when designing a BSG
for the 1550 nm wavelength range in Gallium-Arsenide (n=3.2), it is
convenient to place the Nyquist rate at 1550 nm (to make use of
Induced-Symmetry Synthesis, for example), which corresponds to a
sample length of about 120 nm. This feature size is too small for
optical photolithography, and requires the use of the more
expensive electron-beam lithography.
[0092] However, Nyquist states that the frequency content above the
Nyquist limit consists of repeated copies, known as images, of the
spectral information below the Nyquist limit. Thus, grating
features above the Nyquist rate (Super-Nyquist) may be generated by
synthesizing their grating image that are found below the Nyquist
limit.
[0093] In this manner, Super-Nyquist Synthesis is useful, for
example, for reducing the resolution required for the 1550 nm
Gallium-Arsenide grating discussed above. Choosing "third order"
synthesis, the designer can select the sample length such that the
1550 nm region corresponds to three times the Nyquist frequency, as
indicated in FIG. 34. The designer can then shift the Fourier
domain grating characteristics by integer multiples of the sampling
rate (twice the Nyquist frequency), such that they are in the
"baseband", below the Nyquist frequency. A grating synthesized for
these shifted characteristics displays grating characteristics
where intended, just below three times the Nyquist frequency, due
to the phenomenon of imaging. Furthermore, the sample length for
this new grating is 360 nm, which is more appropriate for optical
lithography. It will be appreciated that applying Super-Nyquist
Synthesis advantageously reduces the resolution requirements.
Super Grating Applications
Supergrating Scattering Reduction
[0094] Referring to FIG. 1 there is shown a schematic of a
deep-grating BSG 14 formed in upper cladding 13 that combines with
core 12 and lower cladding 11 to form the structure. A concern in
supergrating design is scattering losses due to radiative cladding
modes, arising from low spatial-frequency components in the
grating. This scattering arises from an incomplete enforcement of
phase-matching conditions in the direction normal to the grating,
and is more prevalent with shallow gratings.
[0095] Deeper etched features of the present invention reduce this
scattering by occupying a greater distance in the normal direction,
which from the well known Huygens principle and Fourier
considerations, leads to a more robust phase-matching requirement
in the normal dimension; thereby reducing (unwanted) scattering
efficiency. More quantitatively, grating features should ideally be
deep-toothed to a depth exceeding the material wavelength in the
cladding (.lamda..sub.mat=.lamda..sub.0/n.sub.clad), and the decay
constant of the modal tail should be less than 1/.lamda..sub.mat in
the grating region (alternatively, the BSG can be implemented in
the core region 12 at the mode's center, in which case the core 12
should be wider than .lamda..sub.mat; or in such a way that the
index perturbation spans the entire modal profile). This ensures
relatively even contributions from the normal extent of the
grating, thereby enhancing cancellation of the scattered
component.
[0096] The analysis follows by considering the product of the index
profile and modal profile 15: the wider and flatter this product
is, the narrower its Fourier transform, and hence the narrower the
k-space representation in the normal direction. This increased
restriction on the phase-matching condition decreases the range
(for example, in terms of output angle) over which a guided wave
can couple to radiative modes, and hence reduces the aggregate
scattering loss.
[0097] Referring also to FIG. 2 there is shown a k-space
illustration of the rationale behind baseband exclusion. Including
the k-space baseband (i.e. low spatial frequencies) as an
additional "region of interest" improves synthesis by drastically
reducing the unwanted higher-order coupling mediated by small-k
components.
[0098] In alternate embodiments, supergratings may be implemented
using any means of varying the effective (or modal) refractive
index, including a surface relief embodiment (see FIG. 31). One
alternative is to effect changes in modal index by varying the
lateral dimension(s) of a one-dimensional waveguide. This can be
accomplished in the case of a ridge waveguide 30 by varying its
width, as shown in FIG. 3 from a logic zero to a logic one value.
This embodiment possesses many advantages: the waveguide 30 and BSG
31 can be patterned and etched together, thereby simplifying
fabrication; the waveguide and grating are automatically
self-aligned, easing tolerances; and grating multi-level
supergratings can be produced as easily as two-level BSGs.
2D (Two-Dimensional) Supergratings
[0099] In one embodiment, the BSG takes the form of a
one-dimensional sequence of high-index and low-index lines, and can
emulate the near-arbitrary superposition of k-vectors (i.e. spatial
frequency components) of differing magnitude but like orientation.
The BSG can be extended to two dimensions, where it takes the form
of a matrix of high- and low-index pixels implemented in the plane
of a planar waveguide; this can be further extended to include any
number of discrete levels. The 2D BSG (and the more general 2D
supergrating) can emulate the near-arbitrary superposition of
k-vectors of differing magnitude and differing orientation (within
the plane of the grating). In practical terms, this means that the
2D BSG can route and focus light according to wavelength and
in-plane input and output angles, thereby permitting
functionalities such as beam-shaping, wavelength-selective lensing,
and spatial multiplexing and demultiplexing.
2D Supergratings Embodiments
[0100] Referring now to FIG. 4 there is shown a schematic of a
prototypical 2D "supergrating" 40, referred to as a BSG, standing
for binary supergrating. A 2D supergrating is an optical device
having a 2-dimensional array of index-modulated,
effective-index-modulated, gain-modulated and/or loss-modulated
pixels nominally employing a finite set of two or more levels of
the modulated parameter or parameters, and used in such a way that
light propagates in the plane of the array. The term "propagation
layer" will be used in referring to the layer through which the
light travels. The term "modulation layer" will be used to refer to
the layer carrying the physical change that causes the change in
the modal index of refraction of the structure. In some cases, the
two layers will be the same--e.g. when ion implantation is used. In
other cases, they will be different as when a cladding layer is
etched or when a controllable finger is applied to make contact
with the propagation layer. Those skilled in the art will readily
be able to understand when the terms are used. The pixels can be
arranged in any ordered or periodic structure, e.g. a lattice
arrangement, and can employ any arbitrary but repeating shape.
Shaded pixels indicate a high index value and blank pixels indicate
a low index value. Examples are arrays of rectangular pixels on a
rectangular array, point scatterers in a triangular mesh, or
hexagonal pixels in a hexagonal mesh.
[0101] The manufactured form of this device can exhibit non-binary
or even a continuum of modulation levels due to the technical
difficulties associated with producing a perfect physical
structure, but the pixels are nonetheless inscribed with a finite
set of inscription methods or parameters corresponding to the ideal
set of levels that makes the device a 2D BSG. Such a device can
allow angle- and wavelength-specific optical processing, in
addition to emulating traditional optical components such as
mirrors and lenses.
[0102] The pixels of a 2D BSG are the quantized representation of
an analog profile that has been quantized by a method that
preserves Fourier information (neither adding or subtracting
features significantly) in one or more regions of interest in the
two-dimensional spatial frequency representation of the grating,
that correspond to regions of interest in terms of angle and
wavelength-specific diffraction characteristics.
Synthesis of 2D Supergratings
[0103] One method of synthesizing two-dimensional supergratings may
be as follows:
[0104] A) Determine a set of mathematical conditions that describe
the electromagnetic fields at the inputs and outputs of the BSG in
all modes of operations and wavelengths.
[0105] B) Compute an analog profile by solving a system of
equations corresponding, say, to the Born approximation with
boundary conditions corresponding to the input-output
conditions.
[0106] C) Digitize the analog profile using a two-dimensional
technique designed to maintain Fourier components within one or
more regions of interest. One suitable method is Floyd-Steinberg
dithering, where the quantization error made at each pixel is
spread to the yet-to-be-quantized pixels using a finite impulse
response function containing spectral information in the region(s)
of interest.
[0107] The process of grating synthesis may be illustrated with
reference to a simplified example. FIG. 36A shows a simple
demultiplexer 36-10 for separating radiation coming in from below
on waveguide 36-2 and having two wavelengths La and Lb into two
outgoing paths 36-4 and 36-6, each having a single wavelength. FIG.
36B shows a simple demultiplexer using discrete components that
performs the same function. The example of FIG. 36B uses a prism 3
to separate the incoming wavelengths along two paths 24' and 26'
(both beams being bent in the same direction). The separated
radiation beams are bent back into the correct path to enter the
outgoing waveguides 4 and 6 by prisms 34 and 36. The beams are then
focused into the waveguides 4 and 6 by lenses 34' and 36'.
[0108] FIG. 36A shows the same functions being carried out by an
embodiment formed in a planar waveguide by solid-state techniques.
An X-Y (directions indicated by axis 36-15) array of pixels,
denoted by lines along the left edge and bottom of box 36-10 form a
BSG that perform the functions of separating the beams (in this
case bending one wavelength to the left and the other to the right)
at angles that vary with distance (angles A1 and A2 and B1 and B2)
to provide separation. The angles are reversed in the region
denoted by brackets 36-34 and 36-36, where the pixels perform the
angular change and also focus the radiation. At the lower portion
of box 36-10, the wavefronts are indicated by straight lines and at
the upper portion, denoted by curved lines representing the result
of focusing into the outgoing waveguides 36-4 and 36-6.
[0109] It will be appreciated that the example of FIG. 36A is
simplified in that the pixels in the upper portion only process a
single wavelength, since the radiation has been separated in space.
In many actual embodiments of a demultiplexer, the outgoing paths
will be close or superimposed and the pixels will be processing
more than one wavelength. It is an advantageous feature of the
invention that the synthesis of a refractive index profile to carry
out the required functions is performed mathematically, rather than
by illuminating a layer of material by a first interference
pattern, then a second pattern, etc., as in the past.
[0110] Referring to FIG. 5, a 2D BSG can be used in applications
and devices that use 1D supergratings 50 or other types of gratings
in order to provide potential advantages. These advantages stem
from the fact that the two-dimensional grating has well-defined
coupling wave vectors in both dimensions of the grating plane, and
hence offers direct control over coupling with radiative modes and,
therefore, the potential for reduced scattering. The 1D grating 50,
in contrast, often has coupling wave vectors that are poorly
defined in the direction perpendicular to the waveguide, due to its
narrow width.
[0111] The "effective one-dimensional grating" corresponding to a
given two-dimensional grating can be thought of as the D index
profile derived by integrating the 2D grating along lateral lines
perpendicular to the 1-dimensional guiding. This effective 1D
grating has index levels that span a wide range of values between
the two binary levels, and with sufficiently high lateral sampling
can be almost analog in character (the number of levels will be 21
for 1 binary lateral samples). As analog gratings do not suffer
from quantization problems, this can be used as a method for a
multi-level grating design that still enjoys the robustness and
eased fabrication benefits of a binary-like physical structure.
[0112] The method can be summarized as including the following
steps: [0113] Compute an analog profile as with the prior method.
[0114] Convert each pixel into a line of binary (or multi-level)
pixels, placed in the lateral direction perpendicular to the 1D
grating axis in such a way that the average taken along that line
closely fits the desired analog value. This set of pixels is
preferably constrained to maintain certain symmetry properties in
order to reduce coupling to higher modes (with the tradeoff of
limiting the number of available lateral averages). This line can
be computed using a DSM-like process (fed with the desired averaged
value or with a desired lateral profile); with a random-search
optimization method (for small numbers of pixels); or by other
methods.
[0115] The 2D supergrating can be implemented in a 1-dimensional
configuration by first sufficiently widening the 1D waveguide to
contain the 2D supergrating. The waveguide can extend beyond the
area and there contract to a smaller (possibly single-mode) size.
Additionally, two waveguides can expand into such a 2D grating area
(and similarly contract on the other side) to create waveguide
couplers. 2D supergratings also offer reduced scattering when
implemented in conjunction with supergrating waveguide
couplers.
3D (Three-Dimensional) Supergratings
[0116] The BSG can be further extended to three dimensions, where
it takes the form of a three-dimensional array of high- and
low-index pixels. As before, this definition can be expanded to
include any number of discrete levels. The 3D BSG (and the more
general 3D supergrating) can emulate the near-arbitrary
superposition of k-vectors (i.e. spatial frequency components) of
any magnitude and orientation within one or more regions of
interest defined in 3D spatial-frequency space. In practical terms,
this means that the 3D BSG can route and focus light according to
wavelength, input angles (i.e. polar and azimuthal), and output
angles, thereby permitting functionalities such as those described
for two-dimensional gratings, but in the three dimensions of
wavelength, polar angle, and azimuthal angle.
[0117] Referring to FIG. 6 there is shown a schematic of a
prototypical 3D supergrating 60 in an optical device including a
3-dimensional array of index, effective-index-, gain- and/or
loss-modulated pixels; nominally employing a finite set of two or
more levels of the modulated parameter or parameters. The pixels
can be arranged in any ordered or periodic structure and can employ
an arbitrary but repeating shape. The manufactured form of this
device can exhibit non-binary or even a continuum of modulation
levels either by design or due to the technical difficulties
associated with producing a perfect specimen, but the pixels are
nonetheless inscribed using a finite set of inscription methods or
parameters that correspond to the ideal set of levels that makes
the device a 3D BSG. Such a device can allow angularly and
chromatically specific optical processing, in addition to emulating
traditional optical components such as mirrors and lenses.
Synthesis of 3D Supergratings
[0118] Methods for synthesizing 3D supergratings include approaches
very similar to those described above for 2D supergratings, except
that the equations describe 3-dimensional spaces and the
quantization method uses a 3-dimensional impulse response function
to distribute the quantization error.
[0119] A 2- or 3-dimensional supergrating can be designed to create
a structure featuring a complete or incomplete photonic band-gap
(PBG). This can be done by designing a grating with any of the BSG
design methods that possesses spectral features within or near the
desired band-gap with sufficient strength and density to create the
gap. Synthesis can involve the entire applicable area, or apply on
a smaller scale to create a pattern that can be tiled to cover a
larger area. The design may also use higher-order synthesis methods
to allow for reduced resolution requirements.
[0120] A complete photonic band-gap material is one that exhibits a
range of frequencies that cannot propagate through the medium,
regardless of the propagation direction. The applications of such a
medium are numerous and abound in the literature. Some examples
are: optical filters and resonators, inhibitors or enhancers of
optical radiation, materials for (super-) prisms, environments for
novel laser and detector structure's, and substrates for optical
guiding and wiring.
[0121] The BSG-based photonic band-gap offers key advantages over
prior-art PBG materials, including: lower index-contrast
requirements, and relaxed resolution requirements (both leading to
higher compatibility with optical devices and eased
manufacturing).
Synthesis of Supergratings by Optimization
[0122] A general method of designing supergratings of the one-,
two-, or three-dimensional variety is presented here in addition to
the methods described above: [0123] Generate an analog profile with
a procedure such as that of the first synthesis method (let the
function be called P). [0124] Generate a filter H that determines
the wavelength range(s) of importance (in which spectral features
are conserved) and their weights. H essentially assigns a weight
for each frequency, where a high weight leads to better
preservation of spectral information than a low weight. The filter
H can be written in the form of a matrix operator to allow for a
matrix solution of the following step, but may also employ
impulse-response or pole-zero forms. [0125] Solve the optimization
problem: min X , V .times. C = min X , V .times. [ H .function. ( P
- X ) L + i .times. V i .function. ( X i - n low ) .times. ( X i -
n high ) ] ##EQU4## [0126] where X is a vector containing the
values of the BSG, V is a vector of Lagrange multipliers, and L
determines the type of norm for the optimization (L=2 corresponds
to least-squares optimization, for example). The Lagrange
multipliers force the BSG values to one of the allowed index values
(n.sub.low or n.sub.high), leading to a binary form. The function
can be modified to allow for multi-valued supergratings in
accordance with the teachings of the present invention. [0127] The
optimization can be carried out using any optimization method,
although Newton-type methods are particularly useful and are
presently preferred because of the matrix nature of the
equation.
[0128] The approach can be applied to the synthesis of 2D and 3D
gratings by taking the analog profile generated by the
corresponding synthesis method and performing a similar
optimization procedure, with the matrix equation modified to
properly account for the dimensionality. This can be done by
stacking the rows of the 2-dimensional grating into one row of the
X variable, likewise with the P variable, and synthesizing a
corresponding H matrix.
[0129] An H matrix can be generated as a Toeplitz matrix of a given
impulse response function, or with other methods including:
[0130] Let h.sub.f be a vector representing the importance weight
of the spatial frequency f. Then H is given by:
H=F.sup.-1diag(h.sub.f)F, where the n-dimensional F is the Fourier
matrix given by: F jk = 1 n .times. e 2 .times. .pi.I .times.
.times. j .times. .times. k / n .times. .times. ( i = - 1 ) .
##EQU5##
[0131] Multiplication by the matrix F is equivalent to taking a
Fourier transform of a vector, an operation which can be sped up by
using the Fast Fourier Transform (FFT) method. This fact can be
used with H filters of this sort to speed up the calculation of the
cost function and its derivative to order n log(n).
[0132] Another alternative is to perform the optimization in the
Fourier domain by considering both the P and X variables as their
Fourier representations (generated by multiplying by F), while
suitably converting the equality constraints: min X , V .times. C ~
= min X , V .times. [ h f T .function. ( P ~ - X ~ ) 2 + X ~ T
.times. F .times. .times. diag .function. ( V ) .times. F - 1
.times. X ~ - V ] ##EQU6## P ~ = FP , X ~ = FX ##EQU6.2##
[0133] This representation can have the advantage of allowing for
sparse representations for the {tilde over (P)} and/or h.sub.f
vectors, which can help reduce the computation time.
Tuning Mechanisms for Supergratings
[0134] The spectral characteristics of a supergrating can be
shifted by any mechanism that produces a change in effective modal
index. This can be accomplished if an electro-optic,
electro-strictive, magneto-optic, electrochromic, and/or
photosensitive medium is present as part of the device thereby
allowing one or more of the design parameters to be modified using
electronic control. Alternatively, modification of one or more of
the design parameters can be effected using a change of the
temperature, application of mechanical stress, and/or illumination
of either the whole device or a section thereof.
[0135] Tuning mechanisms can include, but are not restricted to,
the following: thermal, electro-optic, magneto-optic,
opto-restrictive, mechanical strain (external, piezo,
electrostatic, magnetostatic, accoustic), current injection,
optical illumination, liquid crystal, reconfigurable molecules,
chemical interaction, and mechanical translation.
[0136] For some devices, the benefit corresponds to a shift or
change in strength of spectral characteristics; for others,
functionalities beyond this emerge. In any case, it is implicit
throughout this patent application, and in all device descriptions
that follow, that the functionality of devices employing static
supergratings can be further enhanced by replacing these with
tunable supergratings.
[0137] Programmable Supergratings
[0138] Referring to FIGS. 7a-7d, there are shown exemplary
embodiments of programmable supergratings. A programmable
supergrating is a device that includes, in part, an array of
electrically addressable electrodes together with a suitable
medium, whereby the electrodes are used to establish a grating
pattern in the medium. The grating pattern can be programmable,
dynamic, or fixed. The grating pattern can nominally utilize a
finite number of modulated levels (e.g. two levels for a BSG, more
for a supergrating), or utilize a continuum of modulated
levels.
[0139] Another embodiment (FIG. 7a) includes an array of MEMS
(micro-electro-mechanical system) 7a2 fingers placed above one or
more waveguides 7a3; where each finger corresponds to a "bit" of
the BSG, and can be individually deflected downwards to touch the
waveguide 7a2 surface. Alternately, the "off" state can correspond
to contact between finger and waveguide, with "on" deflection
upwards and away from the waveguide. In any case, the state with
waveguide contact will generally yield a higher effective index,
and that with no contact will yield a lower index. The preferred
embodiment has an off-waveguide separation sufficiently large that
slight errors in this value negligibly change the lower effective
index value, thereby facilitating true binary operation.
[0140] Yet another embodiment, shown in FIG. 7b includes a
plurality of electrodes disposed over encapsulated liquid crystals
7b2 (LCs) that affect propagation. In the nematic phase, LCs
exhibit a birefringence that can be tuned with voltage, thereby
yielding a means of tuning effective index. This voltage-dependence
typically has some threshold voltage Vt (corresponding to full
alignment of nematic LCs) above which little or no further index
change occurs. A method employing control voltages of V=0 and
V>V.sub.t should therefore facilitate true binary operation,
even in the face of confounding effects such as field fringing.
Co- and Counter-Directional Asymmetric-Waveguide BSG Couplers
[0141] We begin by describing two fundamental elements of many of
the more complex devices that follow: namely, co-directional and
counter-directional asymmetric-waveguide BSG couplers. These
elements (which can indeed be devices in themselves) couple light
from one waveguide to another parallel waveguide, with a desired
spectral response: i.e. light at a given wavelength can be coupled
fully, fractionally, or not at all, and with a desired phase.
[0142] The general embodiment, FIG. 7c, includes two parallel
asymmetric waveguides, which will have differing effective modal
indices (n.sub.eff).sub.1 and (n.sub.eff).sub.2, and hence
different propagation vectors
k.sub.1(.lamda..sub.0)=2.pi.(n.sub.eff).sub.1/.lamda..sub.0 and
k.sub.2(.lamda..sub.0)=2.pi.(n.sub.eff).sub.2/.lamda..sub.0, where
.lamda..sub.0 is free-space wavelength.
[0143] The effective indices will in general be dependent on
wavelength .lamda..sub.0. Signals from electronics drivers 7c3 are
applied to electrodes denoted by 7c2 that change the modal
distribution to induce coupling.
[0144] Light will couple co-directionally from one waveguide to
another neighboring waveguide if their respective modal profiles
overlap; this is known as intrinsic coupling, and will generally
occur for all input wavelengths. Intrinsic coupling is a parasitic
effect in the context of BSG-enhanced coupling, and the optimal
design seeks to ensure that the latter dwarfs the former. This
condition becomes easier to satisfy as waveguide asymmetry (i.e.
the difference between (neff).sub.1 and (neff).sub.2)
increases.
Co-directional Asymmetric-Waveguide BSG Coupler
[0145] Referring to FIG. 8, there is shown a schematic of
co-directional asymmetric-waveguide BSG coupler 80. Co-directional
coupling from one waveguide 81 to another neighboring waveguide 82
(i.e. with overlapping modal profiles) will be enhanced at a
particular wavelength .lamda..sub.0 if the waveguides' effective
indices are perturbed with spatial frequency
K.sub.g(.lamda..sub.0)=k.sub.1(.lamda..sub.0)-k.sub.2(.lamda..sub.0).
This can be accomplished using any BSG embodiment, including
possibilities such as, but not limited to, placing a BSG 83 between
the two waveguides, as described above; or implementing BSGs
laterally in one or both waveguide, also described above. Arbitrary
spectral coupling characteristics are achieved by having the BSG 83
emulate the appropriate spectrum of K.sub.g(.lamda..sub.0).
Counter-Directional Asymmetric-Waveguide BSG Coupler
[0146] Referring to FIG. 9 there is shown a schematic of
counter-directional asymmetric-waveguide BSG coupler 90 coupling
waveguides 91 and 92. For the above embodiment, counter-directional
coupling will occur for a given input wavelength .lamda..sub.0 if
the index perturbation instead includes a spatial frequency of
K.sub.g(.lamda..sub.0)=k.sub.1(.lamda..sub.0)+k.sub.2(.lamda..sub.0).
The BSG 93 should be kept free of spatial frequencies of
2k.sub.1(.lamda..sub.0) and 2k.sub.2(.lamda..sub.0) over the entire
spectral band of interest, as these will produce back-reflection
within the respective waveguides, thereby decreasing coupling
efficiency and yielding undesired back-reflection. Satisfying this
condition requires that waveguide asymmetry be sufficient to avoid
any overlaps between grating spatial frequencies (K.sub.g's)
yielding inter-waveguide coupling and those yielding
intra-waveguide coupling, over all wavelength range(s) of interest;
mathematically, this can be expressed as:
k.sub.l(.lamda..sub.1)+k.sub.2(.lamda..sub.1).noteq.2k.sub.1(.lamda..sub.-
2) and
k.sub.1(.lamda..sub.1)+k.sub.2(.lamda..sub.1).noteq.2k.sub.2(.lamda-
..sub.2) where k.sub.1 and k.sub.2 are defined earlier with
wavelength-dependent effective index, and .lamda..sub.1 and
.lamda..sub.2 are any combination of wavelengths lying within the
range(s) of interest.
[0147] It will be appreciated that if either of the waveguides is
multimode, other overlaps should also be avoided, namely between
the range of grating frequencies pertaining to desired and
undesired coupling (whether co- or counter-directional).
Counter-Directional Symmetric-Waveguide BSG Coupler
[0148] Referring to FIG. 10 there is shown a schematic of
counter-directional symmetric-waveguide BSG coupler. The symmetric
BSG counter-directional coupler performs the same functions as the
asymmetric counter-directional coupler (programmable, dynamic or
static) but allows the two waveguides to be weakly asymmetric or
even symmetric in their effective index. Thus, the limits expressed
in the previous expression can be exceeded, albeit that this would
normally lead to intra-waveguide reflection. The method outlined
below allows for efficient coupling between neighboring symmetric
waveguides, while suppressing intra-waveguide reflection.
[0149] The device includes two waveguides (symmetric or otherwise)
with a BSG 612 placed between them. The BSG can be static, tunable,
or programmable as necessary. Two more BSGs 611 and 622, identical
to the middle BSG but with opposite contrast (1's become O's and
vice-versa), are placed on either side of the two waveguides such
that they mirror the center BSG about the corresponding
waveguide.
[0150] The principle of operation is as follows: let m.sub.1 be the
modal profile of guide 1 and m.sub.2 be the modal profile of guide
2. With loose notation, the coupling coefficients relating the two
waveguides can be written to first order in grating strength as:
c.sub.12.varies..intg.m.sub.1*m.sub.2G.sub.12+.intg.m.sub.1*m.sub.2(G.sub-
.11+G.sub.22).apprxeq..intg.m.sub.1*m.sub.2G.sub.12, where G.sub.12
is the center grating and G.sub.11 & G.sub.22 are the gratings
on the far side of waveguides 1 and 2 respectively. The second term
is negligible because the two side gratings are very far from the
opposite waveguide (more precisely, the opposite waveguide's modal
profile is negligible in this region).
[0151] However, the coupling coefficient from the first waveguide
to itself (corresponding to intra-waveguide reflection) follows:
c.sub.11.varies..intg.|m.sub.1|.sup.2G.sub.11+.intg.|m.sub.1|.sup.2G.sub.-
12=0 (because G.sub.11=-G.sub.22 and symmetry)
[0152] The result is identical for the second waveguide. The only
assumption necessary for the cancellation is that the modal
profiles of both waveguides be substantively symmetric (about their
waveguide, not necessarily identical to each other; it will be
appreciated that waveguide coupling will generally introduce at
least some element of asymmetry) and that the gratings be properly
symmetrized about the guide. The cancellation is independent of
many material parameters such as the waveguides' effective indices,
even if they vary independently.
BSG Couplers Using Lateral Waveguide Variations
[0153] This particular embodiment of implementing a BSG is given
special mention here due to its particular advantages, as well as
some anticipated further subtleties which will be discussed later,
such as: optimal width variation for asymmetric-waveguide coupling,
with particular regard to the relative BSG strength in each
waveguide; and how to design the reverse-contrast grating of the
symmetric-waveguide coupler so as to minimize intra-waveguide
reflection.
[0154] The advantages of this embodiment are similar to those
described above, distinguished by the fact that there are now two
(or more) waveguides, where the waveguide alignment is critical. It
will be appreciated, that the waveguides and BSGs can be
advantageously patterned and etched together, thereby simplifying
fabrication; further, the waveguides and grating are automatically
self-aligned, easing tolerances.
BSG Crossbar Switch
[0155] Referring to FIG. 11, there is shown a schematic of a
grid-topology cross bar switch. The crossbar switch is a device
that routes wavelength channels from a number of input waveguides
to a number of output channels (usually matching the number of
input waveguides). The crossbar switch generally needs to be able
to route any wavelength from any input waveguide to any output
waveguide. These switches are typically denoted by a N.times.N
notation, where N represents the product of the number of
input/output waveguides and the number of wavelength channels; for
example, a switch with 4 input waveguides, 4 output waveguides, and
16 wavelength channels per waveguide is called a 64.times.64
switch.
[0156] Traditional crossbar switches use a grid topology where each
of the n input waveguides is first de-multiplexed into its c
wavelength channels, resulting in nxc input "rows" that are crossed
over with nxc output "columns". These columns are then multiplexed
into groups fed into the n output waveguides. Routing occurs by
means of an optical switch placed at each intersection of row- and
column. This design is especially common with
micro-electro-mechanical systems (MEMS), where the switches are
implemented using movable mirrors. Clearly, this topology requires
(n.times.c).sup.2 switching elements. Another topology can use
2.times.2 switches, that is, switching elements with two inputs
(I.sub.1 and I.sub.2) and two outputs (O.sub.1 and O.sub.2); that
either connects I.sub.1 to O.sub.1 and I.sub.2 to O.sub.2, or
I.sub.1 to O.sub.2 and I.sub.2 to O.sub.1. The problem lies in
choosing the arrangement and number of switches so that the input
optical signals can be rearranged to all possible permutations at
the output. To determine the number of switches required we can
note that there are (n.times.c)! possible permutations of the
inputs; since every 2.times.2 switch provides one bit of control we
can say that: O(log.sub.2(nc)!)=O((nc)log.sub.2(nc))
[0157] It will be appreciated that a programmable BSG (e.g., a
tunable co-directional or counter-directional coupler as described
above) can be used to form the 2.times.2 switch. Thus, each BSG
switching element can provide the 2.times.2 functionality
independently for each input wavelength. Advantageously, this
eliminates the need to first demultiplex the input waveguides, and
reduces the number of required switches: no. of switching
elements=O(n log.sub.2 n) where n is the number of input waveguides
only, leaving no dependence on the number of wavelength channels c.
(See FIG. 12, showing a schematic of one embodiment for a 4-fiber
switch, utilizing 6 switching elements 120.
[0158] Another embodiment can use layered 2.times.2 BSG switching
elements, where each layer has the same number of switching
elements equaling n/2, where n represents the number of input
waveguides, each carrying c wavelength channels. In this
embodiment, the switches can be connected with each other in the
following way: [0159] Let waveguide w connect to waveguide
w+2.sup.l-1, where l is the layer number (starting from l). [0160]
When 2.sup.l=n use the above formula by setting l=1 again (wrap
back).
[0161] This is only one particular wiring method and many more can
be conceived, especially by drawing from prior art in binary
switching tree design.
[0162] The number of switching elements employed by a design of
this sort is given by: no . .times. of .times. .times. switching
.times. .times. elements = n 2 .times. ceil .function. [ ceil
.function. [ log 2 .function. ( n ! ) ] n .times. / .times. 2 ] ,
##EQU7## where the cell function generates the smallest integer
number that is greater than its argument.
[0163] It will be appreciated that the savings generated by this
design method can be enormous and are illustrated in table 1.
TABLE-US-00001 TABLE 1 switching elements wavelength single- multi-
Input channels wavelength wavelength waveguides per input grid
layered layered (n) (c) design design design 4 16 256 96 6 6 32
1152 384 12 8 64 4096 1024 16
[0164] While the number of switching elements in the supergrating
case are given by the formula above, the number of switches in the
grid design case are specified by cn.sup.2, while the number of
single-wavelength switches in the layered design is given by c
times the number of switching elements in the BSG design.
[0165] In addition, embodiments using Programmable BSGs avoid the
need for multiplexers and demultiplexers, further enhancing the
savings. The single-wavelength design can also be implemented with
co-directional and counter-directional couplers employing Bragg
gratings instead of BSGs.
Direct Writing of BSGs in Optical Fiber
[0166] The following sections describe methods of implementing BSGs
in an optical fiber whose index and/or effective modal index can be
altered via exposure to intense and/or high-energy laser light.
One-Photon Process
[0167] Referring to FIG. 13 there is shown a One-photon method of
implementing a BSG in optical fiber. In this embodiment, a grating
employing binary or multi-level features (index or effective index
change, ablation, loss modulation, etc.) is impressed upon a photo
sensitive optical fiber 13-1 by means of a switchable, focused
laser beam 13-10, that directly imprints the grating information on
the fiber as it is moved with respect to the laser's focus as
indicated by the arrow, at either constant or variable speed. In an
alternate embodiment, the fiber is stationary and the laser's focus
is manipulated to scan the fiber.
Multi-Photon Process
[0168] Referring to FIG. 14 there is shown a Multi-photon device
(two-photon shown here) 140 implementing a BSG in optical fiber. A
method similar to the above, with the exception that two or more
laser beams 144, 145 are employed for the process, and the
information (i.e. shift in index) is preferentially imprinted where
a subset of these beams intersect 143 and/or constructively
interfere. It will be appreciated that this embodiment offers
advantages whether the underlying photosensitivity mechanism be
intensity-dependent or energy-dependent. In the former case, the
constructive interference of N (equal amplitude) beams yields
N.sup.2 times the intensity of a single beam; in the latter, the
setup can be arranged so that aggregate photonic energy sufficient
to effect the transition in questions exists only where the beams
intersect.
[0169] This embodiment allows for increased control over the region
within the fiber upon which the information is impressed (for
example, index can be altered only at the core 141 if the beams are
made to intersect here), and can also simplify manufacturing in
that the outer cladding need not necessarily be stripped, as can be
required for the single-photon process.
[0170] The following describes alternate embodiments of the present
invention that employ some combination of supergratings and the
modular elements of the previous section. It will be appreciated
that any BSG mentioned here can be replaced by the more general
multi-level supergrating embodiment, which can in turn be replaced
by tunable and/or programmable embodiments in accordance with the
teachings of the present invention.
Wavelength Demultiplexer
[0171] A demultiplexer separates a multi-wavelength (i.e.
multi-channel) input into its constituent channels. This
demultiplexer functionality can be achieved using BSGs in a variety
of embodiments, described in more detail below.
[0172] Multi-level supergratings in accordance with the teachings
of the present invention are also suitable for demultiplexers and
filters with uneven channel spacing (or any other channel-spacing
scheme). It will be recognized that an advantage of such a
demultiplexer embodiment of the present invention advantageously
reduces problems such as SRS (stimulated Raman scattering), which
are compounded when channels are equally spaced in terms of
photonic frequency (energy).
Demultiplexer Employing 1D Supergratings
[0173] Referring to FIG. 15 there is shown a schematic of a
demultiplexer employing 1D BSG. This device includes, in part, a
set of waveguides coupled using counter-directional and/or
co-directional BSG couplers 15-1-15-3, as described above, with the
effect that multi-wavelength light entering the device through a
specified input port is divided into its wavelength components, and
which leave the device through their assigned output ports.
[0174] Particular embodiments include: a cascade of co-directional
and counter-directional BSGs, which successively divide the
channels in two sub-bands until individual channels are extracted;
and a sequence of tilted single-channel gratings which direct
individual channels to their respective output waveguide.
Demultiplexer Employing 2D Supergratings
[0175] This embodiment, shown in FIG. 16, includes a 2D BSG with
the effect that multi-wavelength light entering the device through
a specified input port is divided into its wavelength components,
which leave the device through their assigned output
waveguides.
Add/Drop Filters
[0176] In this embodiment, an optical add/drop filter, as shown in
FIG. 17, is an optical device 170 including an "in" port 171, which
accepts an input of multiple wavelength-channels; a "drop" port
172, through which one or more channels separated from the "in"
stream are routed; and a "through" port 174, from which the
remaining channels emerge. An additional "add" port may also be
present, which accepts inputs at wavelength-channels being dropped
from the "in" stream, and routes them to the "through" output.
Static Add/Drop Filter
[0177] Referring to FIG. 18, there is shown an optical device
embodiment of the present invention, including one or more 2D BSGs
and/or a set of waveguides coupled using counter-directional,
and/or co-directional BSG couplers. In this embodiment, one or more
wavelength components of light entering the device through a
specified input ("in") port 181 is separated and leaves the device
through a specified output ("drop") port 184. The remainder of the
input light leaves the device through a different output
("through") port 182. In addition, the device can include an
additional input ("add") 183 port with the property that
particular, or all wavelength components, entering the device
through that port, also leave through the "through" port 182
thereby being added to the light routed there from the "in"
port.
[0178] Still referring to FIG. 18. BSG 1 couples a subset of input
.lamda.'s from waveguide A to waveguide B. BSG-2 couples a subset
of the first subset from B to C. This process continues until only
the desired wavelength(s) remain in DROP waveguide. It will be
appreciated that BSG-1 and BSG-2 can be tuned to select desired
.lamda. over a range which exceeds an intrinsic tuning range
.DELTA..lamda./.lamda..apprxeq..DELTA.n/n. It will be further
appreciated that in alternate embodiments that a counter
directional coupling may be employed. In this embodiment the Add
port 183 can be made .lamda. selective through a similar Vernier
approach.
Dynamic Add/Drop Filter
[0179] Referring to FIG. 19, there is shown an optical device
embodiment 190 including one or more 2D BSG and/or a set of
waveguides, where the waveguides are coupled-using tunable or fixed
counter-directional and/or co-directional BSG couplers with the
same effective functionality as the static BSG add/drop filter, but
with the addition that the wavelength(s) directed from the "in"
port to the "drop" port and/or the wavelength(s) directed from the
"add" port to the "through" port are controllable by means of
external control signals.
[0180] One particular embodiment makes use of the Vernier tuning
principle, with a design motivated by the fact that the spectral
shifts accessible through index tuning are often much less than the
total desired tuning range. Multi-channel input enters along one
waveguide, with light coupled to an adjacent waveguide by a
multi-peak tunable BSG (with peak spacing generally less than the
available tuning range). A subsequent tunable BSG (generally
multi-peak with a different spacing which also less than the
available tuning range) couples a subset of this first set of
channels to a third waveguide. This decimation process can continue
as desired, with the BSGs independently tuned relative to one
another to drop desired channel(s). The channel selection range can
thus greatly exceed the available index-tuned spectral shift. The
same set of BSGs can be used to add the dropped channels from a
second input, as shown in FIG. 18.
[0181] Another embodiment uses a programmable BSG, enabling a
structure such as that shown in FIG. 19 that can dynamically add
and drop any subset of input channels.
Wavelength Stability Monitor
[0182] To function properly, optical networks require that channel
wavelengths remain within some range of their nominal value.
Drifting can be caused by a number of factors, including variations
in environmental conditions, device aging, and mechanical
disruptions.
[0183] Wavelength drift can be monitored using a 1D supergrating in
accordance with the teachings of the present invention, as shown in
FIG. 20a. While light incident at a given input angle on a tilted
1D 20a3 grating will nominally diffract at only a particular output
angle, detuning from a central peak-reflectance wavelength will in
fact yield a detuning in angle, along with a decrease in
diffraction efficiency.
[0184] This behavior may be used to detect shifts in wavelength,
or, assuming the wavelength to be true, shifts in device
characteristics which can then be compensated through a variety of
mechanisms (e.g. temperature tuning). In one embodiment, a
photodetector array 20a4 symmetrically aligned along the
diffraction path 20a2 of the desired central wavelength may be used
to detect wavelength shift; in this configuration, the signal from
each will match if local wavelength matches the desired value.
(Note that diffraction efficiency will normally be intentionally
low, so that most power passes through un-deviated.) Deviations in
local wavelength are then manifested by a change in the relative
values of the photodetectors 20a4, which can be monitored by
passing their outputs through a logarithmic subtraction processor
20a5 (other more sensitive functions may be employed). These
deviations can then be corrected for using temperature or any other
influencing parameter.
[0185] Similarly, an alternate embodiment can be implemented with a
2D BSG 20b4 as shown in FIG. 20b, which can focus diffracted light
to the detectors 20b3 and/or detect drifts in wavelength on several
channels simultaneously; or with a sequence of quasi-1D (i.e.
point-source) features 20c3 etched along a waveguide 20c2 as shown
in FIG. 20c (detection and processing being done in units 20c3 and
20c4), which will lead to symmetric diffraction in both lateral
directions. A mirror may optionally be etched at one side, for
optimal collection of scattered light.
[0186] Tap-Off Network Monitor
[0187] To dynamically re-configure channel assignments ("wavelength
provisioning"), a network requires feedback on channel usage; such
reconfigurability is particularly needed for metropolitan optical
networks (MONs).
[0188] Network monitoring can be accomplished using 1-D or 2-D
supergratings in accordance with the teachings of the present
invention (FIG. 21 shows a 2D network monitor embodiment) to tap
off a portion (typically small by design) of input light and
separate it into individual channels. The separated channels are
then focused on a detector array 212, where their power is measured
and the information converted into a single electrical signal. This
signal can be processed by processor 214 and transmitted to a
monitoring station (not shown) in a metro network along an
electrical network, and provide diagnostic data facilitating
wavelength provisioning; or aid in identifying problems in the
network (e.g. showing where a channel is losing power); compiling
load statistics; and measuring fault tolerance.
Multi-Wavelength Equalizer and Gain-Flattening Filters
[0189] For optimal functioning, optical networks generally require
that wavelength channels be balanced in power. Balancing typically
occurs either within, or following the amplification stage, and is
correspondingly named "gain-flattening" or "equalizing"
respectively. A power-balancing device can additionally serve to
suppress undesired signals such as the pump wavelength in optical
amplifiers.
Dynamic Multi-Wavelength Equalizer
[0190] In this equalizer embodiment, dynamic equalization can be
achieved by routing input wavelengths through a tap-off network
monitor (FIG. 22A) that separates channels and monitors their
respective power levels % (see FIG. 22B, showing a curve of power
versus wavelength). The signals are then transmitted to an
electronic processor, whose output tunes (or programs) a sequence
of BSGs in accordance with teachings of the present invention,
which equalize the power across channels, e.g. by removing power in
various wavelength bands. FIG. 22C shows an example of power
removed as a function of wavelength. Suitable, methods for clipping
wavelength power include using BSGs to couple input channels to an
output waveguide with lower efficiency or using. BSGs to impose
higher scattering losses. FIG. 22D shows the result of subtracting
appropriate amounts of power in a set of wavelength bands, thereby
producing substantially equal power in each band.
[0191] One embodiment employs a cascade of BSGs that includes
"basis functions" which can be independently tuned to effect the
loss spectrum required for equalization; suitable basis functions
include step-like spectra that can be shifted relative to one
another.
Gain-Flattened Optical Amplifiers
[0192] FIG. 23 illustrates an alternate channel-balancing
embodiment. In this embodiment a BSG 23-1 (FIG. 23A) is
incorporated directly within the amplifier that serves to shape the
gain spectrum as desired. The gain spectrum (shown unperturbed in
FIG. 23B) can be flattened, or tailored to any other profile,
perhaps in anticipation of wavelength-dependent losses following
amplification. FIG. 23C shows a loss coefficient spectrum matched
to the gain spectrum of FIG. 23B. FIG. 23D shows the combined gain
coefficient spectrum, combining the gain of the medium and the
losses imposed on it. It will be appreciated that this embodiment
offers much greater efficiency than typical post-amplifier
equalization, which follows from recognizing that flattening the
gain coefficient (the gain per unit length within the amplifier)
wastes far less power than flattening post-amplification gain.
[0193] Gain flattening, in accordance with the teachings of the
present invention, can be applied to any optical amplifier
including Raman amplifiers, erbium-doped fiber amplifiers (EDFAs),
and semiconductor optical amplifiers (SOAs); as well as to
multi-wavelength sources such as tunable lasers.
[0194] It will be appreciated that, gain flattening not only
improves efficiency, but also can dramatically extend amplifier
bandwidth, particularly where the intrinsic gain spectrum is
strongly peaked. This is especially true with semiconductor optical
amplifiers (SOAs), whose bandwidth is so narrow as to provide gain
for only a very few (often one) channels.
Lambda Router
[0195] Lambda routers--also known as called wavelength routers, or
optical cross-connects are devices positioned at network junction
points which route wavelength(s) from a specific fiber optic input
to another specific fiber optic output. Lambda routers are
generally N.times.N devices (i.e. with N input fibers and N output
fibers), with each input fiber typically conveying a single
wavelength channel.
[0196] In a Lambda routing embodiment of the present invention,
Lambda routing can be accomplished by coupling demultiplexed input
from a BSG-based device into an array of waveguides as shown in
FIGS. 24a and 24b (i.e. one channel per waveguide). It will be
appreciated that FIGS. 24a-24b represent lambda routers when there
is one input/output fiber and cross-bar switches when there are
multiple input and output fibers. A second array of waveguides
exists beneath the first set, with each pair of top-waveguides and
bottom-waveguides separated by a BSG with a flattop spectrum
centered at the channel wavelength (i.e. co-directional or
counter-directional coupling). Cross/bar operation (i.e. channel
light on one waveguide will couple to the other, and vice versa; or
will remain on the same waveguide) is achieved by locally tuning
the BSGs in or out of alignment with the channel wavelength. It
will be appreciated that add/drop functionality is a built-in
aspect of this embodiment.
[0197] In FIG. 24b, a grid topology router accepts multiplexed
input on the left, having more than on incident wavelength on a
channel in a lower waveguide. At each intersection, a pass-band BSG
couples wavelengths in a particular channel to the waveguides in an
upper waveguide, running vertically in the drawing. The result is
that .lamda..sub.i,j (wavelength lambda entering on the i.sup.th
guide and having a wavelength for the j.sup.th channel) is combined
with the radiation of the same channel coming from other
inputs.
[0198] FIG. 24A, having the same topology as shown in FIG. 12, is a
more efficient arrangement for achieving the same result.
Dispersion-Slope Compensator
[0199] Optical networks generally contend with a property known as
dispersion, especially where long transmission distances and high
bit-rates are involved. Dispersion arises from the
wavelength-dependence of effective index, which in turn produces a
wavelength-dependent group delay spectrum for a given type and
length of optical fiber. The spectrum of an optical pulse is
necessarily finite (i.e. non-zero) in width, dispersion therefore
spreads out a pulse as it travels along a fiber, because its
various wavelength components will travel at slightly different
speeds.
[0200] Dispersion compensation can be achieved by "chirping" a
Bragg grating: modulating a grating's pitch along its length z, as
shown in FIG. 25. FIG. 25A shows an embodiment in which the chirped
grating is associated with a circulator. Radiation is directed into
the grating, processed and returned to the circulator. FIG. 25B
shows a transmissive fiber design. FIG. 25C shows a
counter-directional BSG in which the grating the couples two fibers
also performs the chirping. FIG. 25D shows a co-directional design.
These designs produce a wavelength-dependent phase spectrum which
can be tailored to provide the desired group delay spectrum:
.tau..sub.g=-d.phi./d.omega.. The delay for a given free-space
wavelength .lamda..sub.0 then follows from the round-trip distance
to where local pitch has .lamda..sub.0 as its Bragg wavelength:
.tau..sub.g(.lamda..sub.0)=2n.sub.effz(.lamda..sub.0), where
z(.lamda..sub.0) is the spatial coordinate at which
.LAMBDA.(z)=.lamda..sub.0/2n.sub.eff.
[0201] One dispersion embodiment of the present invention begins by
determining the ideal (analog) input chirp function, as derived
from the group delay spectrum .tau..sub.g(.lamda..sub.0)
(grating-imposed delay should of course be the opposite of that at
the input). The ideal analog profile is then fed into a
quantization filter producing a binary profile that emulates the
desired phase characteristics. The quantization filter can be
further optimized for minimal phase noise.
[0202] Alternate dispersion embodiments stem more directly from the
desired group delay spectrum.
[0203] It will be appreciated that a variety of these types of
embodiments are possible. One embodiment includes a 3-port
circulator (light input at port i exits at port i+1, with port 3
"wrapping around" to port 1) that directs light input to port 1 to
a waveguide via port 2. A reflective BSG, in accordance with the
teachings of the present invention, in the waveguide effects the
desired compensating group delay spectrum, thereby directing the
dispersion-compensated light back to port 2 of the circulator,
following which it emerges at output port 3.
[0204] An alternate embodiment shown in FIGS. 26a and 26b that
avoids the need for (and cost of) a circulator employs
co-directional and/or counter-directional BSG couplers, which
couple light from an input waveguide to subsequent waveguide(s) so
as to impose the desired group delay spectrum. Depending on factors
such as the compensation bandwidth, the temporal span of the group
delay spectrum, and whether compensation is full-band or
channelized, the intra-device propagation length can exceed the
maximum desired device size. In this case, dispersion compensation
can be effected over successive waveguide couplings, with coupled
waveguides arranged in a winding cascade.
[0205] It will be appreciated that embodiments of BSG-based
dispersion compensators offer many advantages such as emulating
complicated chirp functions in a simpler fashion than present
methods (present methods either tackle successive terms in a Taylor
expansion of the dispersion characteristic, or achieve a "best-fit"
to the ideal delay spectrum using relatively few input parameters).
Embodiments using BSG devices in accordance with teachings of the
present invention can also provide dispersion compensation
individually tailored to multiple simultaneous channels, offering
an improvement over solutions, which impose the same correction
across all channels. Also, in contrast to some chirped-grating
approaches, the embodiments using BSG devices in accordance with
teachings of the present invention can be designed to yield a flat
in channel reflectance spectrum.
Tunable Dispersion Compensator
[0206] Tunable dispersion compensation can be achieved through an
arrangement bearing some similarity to a combination of the cascade
of co-directional and counter-directional BSGs described above, and
the earlier disclosed Vernier-tuning method, along with the dynamic
multi-wavelength equalizer, also described above. Referring to FIG.
26a, the cascade of BSGs includes group delay "basis functions"
which can be independently tuned relative to one another to effect
the desired group delay spectrum.
[0207] One embodiment, illustrated in FIG. 26B, employs two tunable
counter-directional BSG couplers, each implementing quadratic
dispersion functions D.sub.1 and D.sub.2, with the functional
forms: D.sub.1=a.sub.1(.lamda.-.lamda..sub.1).sup.2+C.sub.1 and
D.sub.2=a.sub.2(.lamda.-.lamda..sub.2).sup.2+C.sub.2, where the
center wavelengths .lamda..sub.1 and .lamda..sub.2 can be shifted
independently through a tuning mechanism such as those outlined
above. If the BSGs are cascaded and designed with a.sub.2=-a.sub.1,
the resulting dispersion is:
D.sub.net=D.sub.1+D.sub.2=[2a.sub.1(.lamda..sub.2-.lamda..sub.1)].lamda.-
+[(.lamda..sub.1.sup.2-.lamda..sub.2.sup.2)+(C.sub.1-C.sub.2)]
which can be re-written in terms of
.DELTA..lamda.=.lamda..sub.2-.lamda..sub.1:
D.sub.net=[2a.sub.1(.DELTA..lamda.)].lamda.+[(2.lamda..sub.1+.DELTA..lamd-
a.)(2.lamda..sub.1-.DELTA..lamda.)+(C.sub.1-C.sub.2)]
[0208] Thus, dispersion slope 2a.sub.1(.DELTA..lamda.) can be
adjusted as desired by appropriately selecting .DELTA..lamda., and
the intercept is set by appropriately setting .lamda..sub.1. This
approach can be applied to arbitrarily high orders of dispersion by
employing next-higher-order dispersion basis functions.
[0209] Variable-Feedback Supergrating Laser (Tunable and/or
Multi-Wavelength)
[0210] Referring to FIGS. 27a-27c, there is shown embodiments of
variable feedback supergrating lasers. In these embodiments, the
programmable BSG is combined with an optical gain medium to produce
a tunable laser with single-wavelength or multi-wavelength
operation. In FIG. 27A, two programmable BSGs can create resonance
at one or more wavelengths. In FIG. 27B, a programmable BSG grating
within the gain medium can control the output spectrum and also its
power distribution. In FIG. 27C, the programmable BSGs can change
the wavelength and also the angle, so that the wavelength and also
the phase of the output radiation can be controlled.
[0211] It will be appreciated that any configuration employing
gratings as feedback elements, including but not limited to DBR,
DFB, alpha-laser, and ring oscillator configurations, can be
retrofitted by replacing some or all of the corresponding
diffractive element(s) in the traditional design with programmable
BSGs, in accordance with the teaching of the present invention.
[0212] For a single-wavelength laser embodiment, the BSG-based
device can control the position of the laser line, its line width,
and/or its strength. In addition, it can be combined with
monitoring of the above parameters (directly or indirectly, such as
through temperature, current, or voltage) to form a feedback
system, to control one or more of these same parameters.
[0213] The BSG's design (or "program") can be altered in an
otherwise similar configuration to produce a multi-wavelength
laser, offering independent control for each of several laser
wavelengths or selection of a single wavelength. Lasing channels
can be tuned, added, and dropped independently, and their relative
output power can be balanced as desired. As described above, a
monitor can be added to form a feedback loop to control any of
these parameters.
Beam Combiner (Reverse of Beam-Splitter)
[0214] A beam combiner as embodiment, as shown in FIG. 28, accepts
input from one or more sources and streams them into a common
output. In FIG. 28A, successive BSG couplers add power at one or
more wavelengths to the power flowing from left to right in the
horizontal waveguide. In FIG. 28B, a two-dimensional BSG accepts
three inputs and directs the radiation out along the waveguide.
Applications include combining the power from multiple lasers
(termed "power combiner" in this context), as is done for example
with Raman amplifiers to achieve sufficient pump power. It would be
especially attractive in this case to integrate such a device
directly with the semiconductor laser array; the BSG is very well
suited for this purpose.
[0215] A variety of embodiments are possible, including some
combination of one or more BSG couplers and 2D supergratings to
combine multiple beams (possibly of the same wavelength) into one.
In the case of the 2D supergrating, this essentially corresponds to
the reverse of splitting an input into multiple output beams.
Multi-Wavelength/Broadband Isolator/Circulator
[0216] Optical isolators are devices that block the passage of one
or more wavelengths along a waveguide, in one or both directions.
They are used to suppress back-reflection, cross talk, and/or
unwanted wavelength bands (e.g. pump wavelengths).
[0217] A circulator is an N-port device which routes light input at
port i to port (i+1), with input to port N "wrapped around" to port
1, and is often used in conjunction with optical devices with an
output emerging from the input port (e.g. certain embodiments of
optical delay lines, dispersion compensators, and lambda
routers).
[0218] FIGS. 29a and 29b-c show schematics of a BSG-based isolator
embodiment and 4-port coupled-waveguide circulator, respectively.
Both isolators and circulators employ some means of subverting
time-reversal symmetry: i.e. light approaching the device from one
direction is treated differently from light approaching from the
opposite direction. This is typically achieved using magneto-optic
and/or optically active materials (such as a Faraday rotator), in
conjunction with birefringent and/or polarizing elements.
[0219] FIG. 29A, for example, shows an isolator in which radiation
coming in from the left passes through a polarizer, then through a
Faraday rotator that rotates the polarization by 45 degrees, which
passes through the second polarizer. Radiation entering from the
left is polarized, rotated by the rotator and then blocked by the
second polarizer.
[0220] FIG. 29B shows an example of a circulator, in which
radiation entering from the right on port 1 is rotated by the
rotator (e.g. 45 degrees), reflected back from port 3, rotated
again and passes through the splitter to port 2.
[0221] FIG. 29C shows an example of a rotator that may be used with
the foregoing or other apparatus. Radiation enters from the left on
the upper waveguide, is coupled to the lower waveguide by a BSG
coupler in the presences of a, Faraday material and therefore also
is rotated in polarization.
[0222] Supergratings, in accordance with the teachings of the
present invention can be combined with magneto-optic materials
and/or polarizing elements to produce isolators and circulators
offering wavelength-selective operation on pre-selected channels,
or over broad band(s) of wavelengths.
BSG Photonic Band Gap Materials
[0223] An important advance in optical theory in the past few
decades is the concept of the photonic band gap (PBG). This
realization that a two- or three-dimensional periodic modulation of
a material's refractive index can create optical wavelength ranges
at which no light can propagate, regardless of direction, has
proved to be fruitful in application. Applications include
micro-dot lasers, sharp waveguide turns, high-Q optical filters,
and wavelength-selective optical couplers.
[0224] Nevertheless, the PBG is essentially a two- or
three-dimensional extension of the Bragg grating. The BSG concept,
as an extension of the Bragg grating into wavelength space, may be
combined with the PBG to create a whole new set of optical
materials.
[0225] A highly advantageous feature of BSG-PBG materials may well
be their departure from the high refractive index contrasts
required by conventional PBG materials. Embodied as a periodic
lattice of refractive index features, conventional PBGs exhibit
different periodicity in different directions. Each direction is
therefore characterized by a different effective Bragg grating,
each in turn associated with a particular band gap--a range of
wavelengths prohibited from propagating in that direction as a
consequence of the grating. The width of this wavelength gap is
directly proportional to the effective grating's strength, which in
turn corresponds to the PBG's refractive index contrast. However,
to forbid propagation for a particular wavelength for all
directions, thereby forming the "complete" bandgap which defines
the PBG, all the individual wavelength gaps must overlap at the
wavelength in question, thus, as those skilled in the art are
aware, imposing a minimum refractive index contrast for the
PBG.
[0226] FIG. 37 shows in FIG. 37A a hexagonal arrangement of dots
representing regions of different refractive index. FIG. 37B shows
a corresponding hexagon in wave number space. Those skilled in the
art are aware that ordinary materials exhibiting the PBG effect
have a regular geometric arrangement that produces an outline in
wave number space. In FIG. 37B, for example, the hexagonal array of
dots in FIG. 37A is reflected in a hexagon in k-space. In order to
suppress radiation propagation (of a certain wavelength represented
by the dotted circle) in all directions, therefore, the thickness
of the hexagon in k-space must be such that the circle representing
the relevant wavelength can be inscribed within the band-gap
hexagon. This requirement imposes a requirement of unneeded band
gap suppression. For example, the regions at the outer corners of
the hexagon in FIG. 37B is not needed, since the dotted line is at
the inner corners. Similarly, the regions in the centers of sides
are not needed because the dotted line is at the outer edge in that
area.
[0227] Unlike conventional PBGs, the BSG is not restricted to a
periodic lattice and its implied directional variation in
periodicity. Instead, a two- or three-dimensional BSG can be
designed to exhibit a near-arbitrary band of effective periodicity
in any direction. This corresponds directly to the one-dimensional
BSG's control over its diffractive spectrum This design freedom
obviates the reliance on the grating's refractive index contrast to
thicken the individual band gaps until they overlap. Instead, the
pattern of index change may be set geometrically to reinforce the
refractive index patterns of the band gaps that cause overlap in
the first place. Any extra strength afforded by the available index
contrast can then be applied to subject more wavelengths to the
PBG's effect. FIG. 38 shows in FIG. 38A a non-periodic arrangement
of pixels that provide for the suppression of transmission in a
particular wavelength range in any direction in a more economical
use of resources. The angular dependence of the pixel pattern is
set such that the dotted line (the same dotted line as in FIG. 37)
is bounded by a smaller, uniform margin. If desired, the margin in
FIG. 38 could be increased to cover a greater wavelength range.
[0228] Thus, for a given technique of index modulation (e.g. ion
implantation) a BSG-PBG material can exclude a greater wavelength
range than conventional PBG materials.
[0229] In addition, the new materials adcording to the invention
may, in the same area, exclude radiation in a first wavelength
range and manipulate radiation in one or more other wavelength
ranges--e.g. exclude pump radiation while deflecting, focusing,
etc. radiation in a generated wavelength band.
[0230] The dramatic reduction in the necessary refractive index
contrast offered by the BSG-PBGs synthesis may indeed overcome a
major practical challenge in PBG fabrication. However, this
reduction comes at a cdst: a lower-contrast grating also implies a
longer required interaction length through which the grating
affects light. This is also true for the PBG, however, and while
the effect may be an important consideration for certain
applications, it may be mitigated, overcome or even prove
beneficial for many others.
[0231] The BSG can do more than simply improve upon the
practicality of PBG implementation. For example, the BSG enables
materials exhibiting several photonic band gaps, stemming directly
from the capacity to emulate several superimposed gratings which
inspired our first explorations. Such materials may be useful in a
number of applications, primarily those employing several optical
wavelengths, such as systems with separate pump and signal
wavelengths, as well as wavelength converters. More generally, the
BSG allows for complete control over the optical band structure,
including the width and position of band gaps as well as the
optical density of states and the dispersion relation.
[0232] FIG. 39 shows a cross section of a high efficiency solar
cell or other photodetector using a PBG material according to the
invention. Substrate 39-10 is a conventional material that exhibits
the photoelectric effect, e.g. silicon. Layer 39-20 is a material
that ordinarily permits the propagation of light of the relevant
wavelength. According to the invention, a BSG-PBG pattern has been
impressed on the material 39-20, so that propagation in the
transverse direction indicated by arrow 39-17 is suppressed.
Radiation that would otherwise propagate transversely is then
scattered by the BSG-PBG pattern and winds up preferentially
scattering with a vertical component (e.g. according to arrow
39-15). A greater fraction of the incident radiation is thus
absorbed by the photoelectric material 39-10.
[0233] FIG. 40 shows an array of PBG material 40-1 arranged in a
customary pattern. Two dots of the pattern, 40-2, have been
removed, establishing a pair of micro-dot lasers (conventional pump
radiation being omitted for clarity). As many microdot lasers as
desired may be arranged in any desired geometrical layout.
[0234] FIG. 41 shows a top view of a BSG-PBG material 41-5 that
excludes radiation in a relevant wavelength range. The BSg pattern
does not extend to waveguide 41-10, which therefore permits the
passage of radiation in that wavelength range. A curve having a
radius of curvature R, less than the conventional limit, referred
to as a reference value, has been formed in the waveguide. Those
skilled in the art are aware that a conventional material would
have an excessive amount of scattering when passing through a curve
with a radius of curvature less than the reference value. The
BSG-PBG material permits the formation of the waveguide with
reduced losses.
[0235] FIG. 42 illustrates a pair of waveguides 42-10 and 42-12
formed in a BSG-PBG material 42-5. As an optional feature, the area
42-25 between the two waveguides has been provided with a BSG-PBG
material 42-25 that has a longer attenuation length at the
wavelength being transmitted by waveguides 42-10 and 42-12. Thus,
coupling between the waveguides is facilitated. The different
material is not necessary, and the same material could be used,
with an appropriate spacing between waveguides (or the BSG-PBG
material could be omitted between the waveguides).
[0236] As an additional option, the general provision of PBG could
be dispensed with and a PBG could be placed between the waveguides
42-10 and 42-12. The material between the two waveguides could be
fabricated to permit coupling between the waveguides, e.g. by
structuring the PBG pattern such that propagation parallel to the
waveguides is not allowed, but propagation (i.e. coupling) between
the waveguides is allowed.
[0237] The foregoing is an example of a directional PBG material
meaning a material having a pixel pattern that suppresses
propagation within a wavelength band in selected directions.
[0238] FIG. 43 illustrates a top view of a unit employing a
non-linear effect. Rectangle 43-05 represents an area of a material
that exhibits a non-linear effect and also has been impressed with
a PBG pattern that suppresses propagation at wavelengths
.lamda..sub.1, .lamda..sub.2 and .lamda..sub.3. In the example
illustrated, .lamda..sub.1 and .lamda..sub.2 are pump wavelengths,
propagating along waveguides 43-10 and 43-15, respectively and
.lamda..sub.3 is the output wavelength of the relevant non-linear
interaction, propagating along output waveguide 43-20. The initial
section of waveguide 43-20 is an optional waveguide in this device
that may be used, e.g. to supply input radiation at .lamda..sub.3,
to which the result of the non-linear interaction will be
added.
[0239] Radiation at .lamda..sub.1 and .lamda..sub.2 combine in the
overlap area to generate radiation at .lamda..sub.3, as is known in
the art. The PBG pattern outside the waveguides confines the
radiation.
[0240] Within section 43-12 of waveguide 43-20, a pixel pattern
43-26 focuses the output radiation to a point as shown. Section
43-25 of the waveguide 43-20 reflects radiation at the output
wavelength, so that it is directed as required (upward in the
drawing) and is not wasted. If desired, or if required by limited
resources, the PBG pattern on the left, denoted by 43-07, could be
set to confine radiation of .lamda..sub.1 and the pattern on the
right, denoted by 43-06, could be set to confine radiation of
.lamda..sub.2, with the radiation .lamda..sub.3 being confined only
by the pattern in the area 43-12. Thus, the (limited) capabilities
of the PBG pattern could be reserved for use only where
required.
[0241] It should be understood that the foregoing description is
only illustrative of the invention. Various alternatives and
modifications can be devised by those skilled in the art without
departing from the invention. Accordingly, the present invention is
intended to embrace all such alternatives, modifications and
variances, which fall within the scope of the appended claims.
* * * * *