U.S. patent application number 09/780604 was filed with the patent office on 2001-11-01 for optical compensation for dispersion-induced power fading in optical transmission of double-sideband signals.
Invention is credited to Adamczyk, Olaf H., Havstad, Steven A., Sahin, Asaf B., Willner, Alan E., Xie, Yong.
Application Number | 20010035996 09/780604 |
Document ID | / |
Family ID | 22662974 |
Filed Date | 2001-11-01 |
United States Patent
Application |
20010035996 |
Kind Code |
A1 |
Havstad, Steven A. ; et
al. |
November 1, 2001 |
Optical compensation for dispersion-induced power fading in optical
transmission of double-sideband signals
Abstract
Techniques and devices for compensating dispersion-induced power
fading in a double-sideband optical signal based on a tunable
optical dispersion element.
Inventors: |
Havstad, Steven A.;
(Fremont, CA) ; Sahin, Asaf B.; (Los Angeles,
CA) ; Adamczyk, Olaf H.; (Santa Monica, CA) ;
Xie, Yong; (Fremont, CA) ; Willner, Alan E.;
(Los Angles, CA) |
Correspondence
Address: |
SCOTT C. HARRIS
Fish & Richardson P.C.
Suite 500
4350 La Jolla Village Drive
San Diego
CA
92122
US
|
Family ID: |
22662974 |
Appl. No.: |
09/780604 |
Filed: |
February 8, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60181119 |
Feb 8, 2000 |
|
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|
Current U.S.
Class: |
398/147 |
Current CPC
Class: |
H04B 10/2519
20130101 |
Class at
Publication: |
359/161 ;
359/173 |
International
Class: |
H04B 010/00; H04B
010/12 |
Claims
What is claimed is:
1. A device, comprising: a first optical path having an input
terminal and an output terminal, said input terminal receiving a
first portion of an input optical signal at an optical carrier
frequency that is modulated to have a first modulation sideband and
a second modulation sideband; a second optical path having an input
terminal and an output terminal that are coupled to said input and
said output terminals of said first optical path, respectively,
wherein said second optical path receives a second portion of said
input optical signal; and an optical dispersion element configured
to produce different delays in optical signals at different
wavelengths and coupled to at least one of said first and said
second optical paths to produce a difference of about .pi. between
a sum of phases of said first and said second modulation sidebands
relative to a phase of the optical carrier at said carrier
frequency in said first portion, and a sum of phases of said first
and said second modulation sidebands relative to a phase of the
optical carrier at said carrier frequency in said second
portion.
2. The device as in claim 1, further comprising a polarization
element coupled to at least one of said first and said second
optical paths and operable to make a polarization of light at said
output terminal in said first optical path substantially orthogonal
to a polarization of light at said output terminal of said second
optical path.
3. The device as in claim 1, wherein said first and said second
optical paths have different path lengths to produce a relative
phase shift of about .pi./2.
4. The device as in claim 1, further comprising an optical delay
element coupled to one of said first and said second optical
paths.
5. The device as in claim 1, further comprising an optical
attenuator coupled to one of said first and said second optical
paths to substantially equalize a power of light at said output
terminal in said first optical path and a power of light at said
output terminal in said second optical path.
6. The device as in claim 1, where in s aid optical dispersion
element is operable to produce different dispersions at different
wavelengths and is operable to tune said dispersions in response to
a control signal.
7. The device as in claim 6, wherein said optical dispersion
element includes a tunable nonlinearly-chirped fiber Bragg
grating.
8. A device, comprising: an optical input port, receiving an input
optical signal at an optical carrier frequency that is modulated to
have a first modulation sideband and a second modulation sideband
at different modulation frequencies; a first optical path and a
second optical path coupled to said input port to receive a first
portion of said input optical signal as a first optical signal and
a second portion of said input optical signal as a second optical
signal, respectively, wherein said first and said second optical
paths have different path lengths to produce a relative phase shift
of about .pi./2; an optical output port coupled to said first and
said second optical paths to receive and combine said first and
said second optical signals to produce an output optical signal; an
optical dispersion element configured to produce different delays
in optical signals at different wavelengths and coupled to interact
with at least one of said first and said second optical signals to
produce a difference of about .pi. between a sum of phases of said
first and said second modulation sidebands relative to a phase of
the optical carrier at said carrier frequency in said first optical
signal, and a sum of phases of said first and said second
modulation sidebands relative to a phase of the optical carrier at
said carrier frequency in said second optical signal, at said
output optical port; and a polarization element coupled to at least
one of said first and said second optical paths and operable to
make a polarization of said first optical signal substantially
orthogonal to a polarization of said second optical signal at said
optical output port.
9. The device as in claim 8, further comprising an optical delay
element coupled to one of said first and said second optical
paths.
10. The device as in claim 8, further comprising an optical
attenuator coupled to one of said first and said second optical
paths to substantially equalize a power of light in said first
optical path and a power of light in said second optical path at
said output port.
11. The device as in claim 8, wherein said optical dispersion
element is operable to produce different dispersions at different
wavelengths and is operable to tune said dispersions in response to
a control signal.
12. The device as in claim 11, wherein said optical dispersion
element includes a tunable nonlinearly-chirped fiber Bragg
grating.
13. The device as in claim 12, further comprising a fiber stretcher
coupled to control said fiber Bragg grating.
14. The device as in claim 12, further comprising an optical
coupling element disposed to couple light from said first optical
path into said fiber Bragg grating and to couple reflected light
from said fiber Bragg grating back into said first optical path,
wherein said fiber Bragg grating has a first end coupled to receive
said first optical signal to change a delay between each modulation
sideband and the optical carrier.
15. The device as in claim 14, further comprising another optical
coupling element disposed to couple light from said second optical
path into a second end in said fiber Bragg grating opposing said
first end and to couple reflected light from said fiber Bragg
grating back into said second optical path.
16. A system, comprising: a fiber network; and at least one power
fading compensator disposed in an optical link in said fiber
network to compensate for a distance-dependent power fading in an
optical signal at an optical carrier frequency that is modulated to
have a first modulation sideband a second modulation sideband,
wherein said power fading compensator includes: a first optical
path having an input terminal and an output terminal, said input
terminal receiving a first portion of said optical signal; a second
optical path having an input terminal and an output terminal that
are coupled to said input and said output terminals of said first
optical path, respectively, wherein said second optical path
receives a second portion of said optical signal; and an optical
dispersion element configured to produce different delays in
optical signals at different wavelengths and coupled to at least
one of said first and said second optical paths to produce a
difference of about .pi. between a sum of phases of said first and
said second modulation sidebands relative to a phase of the optical
carrier at said carrier frequency in said first portion, and a sum
of phases of said first and said second modulation sidebands
relative to a phase of the optical carrier at said carrier
frequency in said second portion.
17. The system as in claim 16, wherein said optical dispersion
element includes a nonlinearly-chirped fiber Bragg grating.
18. A method, comprising: optically splitting an optical signal
into a first optical signal in a first optical path and a second
optical signal in a second optical path, wherein the optical signal
is at an optical carrier frequency and is modulated to have a first
modulation sideband a second modulation sideband; and controlling
dispersion in at least one of the first and the second optical
paths to produce a difference of about .pi. between a sum of phases
of the first and the second modulation sidebands relative to a
phase of the optical carrier at the carrier frequency in the first
optical signal, and a sum of phases of the first and the second
modulation sidebands relative to a phase of the optical carrier in
the second optical signal.
19. The method as in claim 18, further comprising: making a
polarization of the first optical signal to be substantially
orthogonal to a polarization of the second optical signal; setting
lengths of the first and second optical paths to produce a phase
difference of .pi./2; and combining the first and second optical
signals to produce an output signal.
Description
[0001] This application claims the benefit of U.S. Provisional
Application No. 60/181,119, filed Feb. 8, 2000.
TECHNICAL FIELD
[0002] This application relates to optical signal transmission and
detection over dispersive optical links such as optical fibers.
BACKGROUND
[0003] An optical wave at an optical carrier frequency f.sub.c may
be modulated at a subcarrier frequency f.sub.RF to produce two
modulation sideband signals at frequencies of (f.sub.c-f.sub.RF)
and (f.sub.c+f.sub.RF), respectively. The sideband signals may be
used to carry information for transmission over an optical link or
a network of optical links. The optical media in an optical link,
e.g., optical fibers, may exhibit chromatic dispersion where
spectral components at different frequencies in an optical signal
can travel at different group velocities. Therefore, in optical
systems where double-sideband signals are used, the two sideband
signals at different frequencies of (f.sub.c-f.sub.RF) and
(f.sub.c+f.sub.RF) in an optical signal may be delayed relative to
each other.
[0004] One consequence of this delay between the sideband signals
in the double-sideband optical signal is the fading or decay of the
received subcarrier power, which varies as a function of the
subcarrier frequency, the transmission distance in the fiber, and
accumulated dispersion: 1 P cl , f .times. cos 2 ( 1 + 2 2 ) = cos
2 [ cLD ( f f c ) 2 ]
[0005] where .phi..sub.1, and .phi..sub.2 are respectively the
phases of the modulation sidebands at (f.sub.c-f.sub.RF) and
(f.sub.c+f.sub.RF) relative to the optical carrier at f.sub.c, c is
the speed of light, L is the transmission distance, D is the
dispersion parameter of the fiber in the link, and f is the
subcarrier modulation frequency f.sub.RF. FIG. 1 illustrates this
dispersion-induced power fading effect in a double-sideband optical
signal.
[0006] This signal fading is undesirable in many applications
because it can seriously deteriorate the detection of the optical
signals. In some optical networks where the actual optical paths
for transmitting signals may be reconfigurable, such power fading
may dynamically change with the transmission distance. Therefore,
it may be desirable to provide distance-independent power fading
compensation in some microwave- and millimeter-wave-based optical
systems that use double-sideband signals to transmit
information.
SUMMARY
[0007] The power fading compensation according to one embodiment
includes optically splitting a double-sideband optical signal into
a first optical signal in a first optical path and a second optical
signal in a second optical path and then controlling dispersion in
at least one of the first and the second optical paths to produce a
difference of about .pi. between a sum of phases of the first and
the second modulation sidebands relative to a phase of the optical
carrier at the carrier frequency in the first optical signal, and a
sum of phases of the first and the second modulation sidebands
relative to a phase of the optical carrier in the second optical
signal. A tunable optical dispersion element, such as a
nonlinearly-chirped fiber Bragg grating, may be used to produce the
desired dispersion.
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] FIG. 1 illustrates the distance-dependent power fading in a
double-sideband optical signal caused by the chromatic dispersion
in an optical transmission medium.
[0009] FIG. 2 illustrates one embodiment of an optical device that
provides distance-independent compensation for the
distance-dependent power fading in a double-sideband optical signal
transmitting through a dispersive optical link.
[0010] FIG. 3 shows one implementation of the optical device shown
in FIG. 2.
[0011] FIG. 4A shows one embodiment of a tunable optical dispersion
element in the device shown in FIG. 3 where a nonlinearly-chirped
fiber Bragg grating is used.
[0012] FIGS. 4B and 4C illustrate operations of the
nonlinearly-chirped fiber Bragg grating in compensating for the
distance-dependent power fading.
[0013] FIGS. 5, 6, and 7 show various measured signals obtained
from a device based on the design shown in FIG. 3.
[0014] FIG. 8 shows another implementation of the optical device
shown in FIG. 2.
DETAILED DESCRIPTION
[0015] FIG. 2 shows one embodiment of an optical device 200 that
provides distance-independent compensation for the
distance-dependent power fading in a double-sideband optical signal
transmitting through a dispersive optical link. The optical signal
at the optical carrier frequency f.sub.c has two modulation
sidebands at (f.sub.c-f.sub.RF) and (f.sub.c+f.sub.RF) that include
the information or data to be transmitted. The subcarrier frequency
f.sub.RF may be generally in the frequency range for the microwave
and millimeter-wave frequencies, e.g., from tens of kilohertz
(.about.10.sup.4 Hz) to hundreds of gigahertz (.about.10.sup.11
Hz). The device 200 uses a phase diversity configuration with two
separate optical paths 210 and 222 to perform the compensation for
the distance-dependent power fading.
[0016] The device 200 includes an optical input port 201 for
receiving the double-sideband optical signal from the dispersive
optical link and an optical output port 202 for combining the
optical signals from the two paths 210 and 220 to produce the
fading-compensated optical output. The input port 210 is designed
to split the input signal into the two separate optical paths 210
and 220. A tunable optical dispersion element 212 is placed in one
optical path, e.g., the optical path 210, to introduce different
time delays for the two different frequencies of (f.sub.c-f.sub.RF)
and (f.sub.c+f.sub.RF) so that the sum of the phases of the
modulation sidebands in the optical path 210 relative to the phase
of the optical carrier at the carrier frequency f.sub.c is shifted
by .pi. with respect to the sum of the phases of the modulation
sidebands relative to the optical carrier at the carrier frequency
f.sub.c in the other optical path 220. The optical dispersion
element 212 may be tunable in order to produce this desired
relative phase shift of .pi. for in optical signals with different
values for the modulation frequency f.sub.RF and the carrier
frequency f.sub.c.
[0017] This optical device 200 further includes a polarization
control mechanism to control the polarization of light in at least
one optical path so that the optical signals in the two optical
paths 210 and 220 have orthogonal polarizations relative to each
other at the output port 202 where the two optical paths 210 and
220 are coupled together. A polarization rotator or controller, for
example, may be placed in one of the two optical paths to achieve
this condition. As a result, optical signals in the two paths 210
and 220 can be combined at the output port 202 without substantial
cross-talk effects that would otherwise be present due to optical
coherence. Hence, an optical receiver that receives the combined
optical signal from the output port 202 produces a detector output
that is a sum of the individual powers of the two optical signals
from the two optical paths.
[0018] The photocurrents representing the two optical signals can
be written as: 2 I g .times. c g cos ( 1 + 2 + 2 ) cos ( 2 f t + g
) I o .times. c o cos ( 1 + 2 2 ) cos ( 2 f t + o )
[0019] where c.sub.g and c.sub.0 are constants representing the
optical powers from the two paths 210 and 220 incident on the
optical receiver at the output port 202, and .theta..sub.g and
.theta..sub.0 represent the relative subcarrier phases in the two
paths 210 and 220. Hence, if c.sub.g=c.sub.0 and
(.theta..sub.g-.theta..sub.0)=.pi./2, the total received power at
the receiver will be a constant without the effects of the
dispersion-induced power fading: 3 P cl , f = cos 2 ( 1 + 2 2 ) +
sin 2 ( 1 + 2 2 ) = constant
[0020] The condition of c.sub.g=c.sub.0 may be achieved by
adjusting the optical intensity in one optical path relative to
another by using an optical attenuator. The condition of
(.theta..sub.g-.theta..sub.0)=.pi./2 may be achieved by controlling
the relative optical path length difference of the two optical
paths 210 and 220.
[0021] Notably, the operation of the device 200 is independent of
the state of accumulated dispersion in the received double-sideband
optical signal. Therefore, the device 200 may be deployed at any
desired location in an optical link within an optical network to
compensate for the distance-dependent power fading.
[0022] FIG. 3 shows one exemplary optical device based on the
design shown in FIG. 2 for installation in a fiber link 350 that
carries a double-sideband optical signal 352. This device includes
an input fiber optical coupler 300 as its input port to receive the
optical signal 352. The input coupler 300 is coupled to receiving
terminals of two separate fiber optical paths 310 and 320 and is
operable to split the input optical signal 352 into two optical
signals 301 and 302 in the fiber optical paths 310 and 320,
respectively. The optical path 310 includes a tunable optical
dispersion element 314 and a control unit 316 that controls the
operation of the element 314. The element 314 is operable to
produce different dispersions on spectral components at different
wavelengths in the optical signal 301 to produce a
dispersion-modified signal 301A in which the sum of the phases of
the modulation sidebands relative to the phase of the optical
carrier at the carrier frequency f.sub.c is shifted by .pi. with
respect to the sum of the phases of the modulation sidebands in the
optical signal 302 relative to the optical carrier at the carrier
frequency f.sub.c in the optical path 320.
[0023] An output optical fiber coupler 330 is used to couple the
output terminals of the fiber optical paths 310 and 320 to combine
the signals 301A and 302 into an output optical signal 303. An
optical polarization-rotating element 318 is implemented in either
one of the optical paths 310 and 320 to make the polarizations of
the signals 301A and 320 orthogonal to each other at the output
coupler 330. For example, a fiber polarization controller or a
90-degree polarization rotator may be used as the element 314 and
placed in the optical path 310 between the optical dispersion
element 314 and the output coupler 330. The polarization of the
signal 301A is rotated by 90 degrees to produce a
polarization-rotated signal 301B. The signals 301B and 320 is then
combined at the coupler 330 to produce the output signal 303. An
optical receiver 340 may be coupled to receive the signal 303.
[0024] The optical paths 310 and 320 are designed to have different
optical path lengths so that the phase associated with the path
length difference at the output coupler 330 is .pi./2 to satisfy
the condition of (.theta..sub.g-.theta..sub.0)=.pi./2. A variable
optical delay element 322, such as a fiber loop with a fiber
stretcher, may be placed in one optical path, e.g., 320, to adjust
the phase difference (.theta..sub.g-.theta..sub.0) under different
operating conditions to maintain the condition of
(.theta..sub.g-.theta..sub.0)=.pi./2. In addition, the powers the
optical signals 301B and 302 in the output signal 303 should be
substantially equal. Hence, an optical attenuator 324, preferably
adjustable, may be placed in at least one of the optical paths 310
and 310 to satisfy this condition.
[0025] One example of the tunable dispersion element 314 is a
nonlinearly-chirped fiber Bragg grating (FBG). See, U.S. Pat. No.
5,982,963 to Feng et al. Referring to FIG. 4A, the
nonlinearly-chirped Bragg grating 410 is a grating that can be
formed along an optical waveguide, e.g., an optical fiber, and has
a grating parameter n.sub.neff(z).LAMBDA.(z) that changes
nonlinearly with the position z along the fiber optic axis, where
n.sub.neff(z) is the effective index of refraction and .LAMBDA.(z)
is the period of the grating. The grating 410 has a long-wavelength
end 411 and a short-wavelength end 412 where the grating parameter
n.sub.neff(z).LAMBDA.(z) monotonically decreases from the end 411
to the end 412. In operation, this nonlinearly-chirped grating 410
may be used to receive an optical signal and to reflect light
satisfying a Bragg condition of
.lambda.(z)=2n.sub.neff(z).LAMBDA.(z) and transmits light that
fails the Bragg condition. Hence, different spectral components are
reflected back at different positions in the grating to produce
different group delays. A Bragg reflection band centered at a
center wavelength .lambda..sub.0 can be generated and the
bandwidth, .DELTA..lambda..sub.FBG, of the grating is determined by
the chirping range of the grating parameter
n.sub.neff(z).LAMBDA.(z). Either end of grating may be used
depending on the type of dispersion is needed.
[0026] Notably, as shown in FIG. 4B, the relative group delays for
different spectral components at different wavelengths are
different and tunable in the nonlinearly-chirped fiber grating,
that is, the grating dispersion is tunable by adjusting the grating
parameter n.sub.neff(z).LAMBDA.(z). This is caused by the
nonlinearity in the chirp of the grating parameter
n.sub.neff(z).LAMBDA.(z). A grating control unit 420, which is part
of the control unit 316 in FIG. 3, may be coupled to the grating
410 to change the grating parameter n.sub.neff(z).LAMBDA.(z) so as
to shift the center wavelength .lambda..sub.0 of the Bragg
reflection band and tune the dispersion. This grating control unit
420 may be a fiber stretcher to control the total length of the
fiber grating to adjust .LAMBDA.(z). Referring back to FIG. 3, an
optical circulator 312 may be used to couple the tunable fiber
grating 314 to the optical path 310 so that the signal 301 is
directed to a receiving end of the grating 314 (either 411 or 412)
and the reflected signal 301A is coupled into the optical path 310
towards the output coupler 330.
[0027] FIG. 4C illustrates the operation of the fiber grating 410
for compensating the power fading in the device in FIG. 3. In this
example, the short-wavelength end 412 is used to receive the signal
301 and to produce the signal 301A in the optical path 310. Since
the modulation sideband signals are at different frequencies
(f.sub.c+f.sub.RF) and (f.sub.c-f.sub.RF), they are reflected at
different positions in the fiber grating 410 as illustrated in FIG.
4A to produce different delays .DELTA..tau..sub.1 and
.DELTA..tau..sub.2 relative to the optical carrier at the optical
carrier frequency f.sub.c. Such grating-induced delays are added to
the relative delays .DELTA..tau.'.sub.1 and .DELTA..tau.'.sub.2
caused by the chromatic dispersion in the fiber link so that the
total relative delays of the modulation sideband signals with
respect to the optical carrier in the optical signal 301B at the
output coupler 330 are (.DELTA..tau..sub.1+.DELTA..tau.'.sub.1) and
(.DELTA..tau.'.sub.2+.DELTA.- .tau..sub.2), respectively. The sum
of the relative delays in the optical signal 301B is
(.DELTA..tau..sub.1+.DELTA..tau.'.sub.1)+(.DELTA..tau..sub-
.2+.DELTA..tau.'.sub.2)=(.DELTA..tau.'.sub.1+.DELTA..tau.'.sub.2)+(.DELTA.-
.tau..sub.1+.DELTA..tau..sub.2), where the delay of
(.DELTA..tau..sub.1+.DELTA..tau..sub.2) is produced by the grating
410. On the other hand, the modulation sideband signals at sideband
frequencies (f.sub.c+f.sub.RF) and (f.sub.c-f.sub.RF) in the signal
302 in the optical path 320 also have the relative delays
.DELTA..tau.'.sub.1 and .DELTA..tau.'.sub.2 respect to the optical
carrier caused by the chromatic dispersion in the fiber link.
Hence, the total relative delays of the modulation sideband signals
with respect to the optical carrier in the optical signal 302 at
the output coupler 330 are
(.DELTA..tau..sub.1+.DELTA..tau.'.sub.1). The overall length of the
fiber grating 410 is controlled so that the phase delay
corresponding to the total relative delay in time,
(.DELTA..tau..sub.1+.DELTA..tau..sub.2), is .pi.. If there is any
additional relative delay between the sidebands and the carrier in
the optical signals 301B and 302 at the output coupler 330 due to
dispersion in the paths 310 and 320 that is not caused by the fiber
grating 410, the grating-induced phase delay corresponding to the
total relative delay (.DELTA..tau..sub.1+.DELTA..tau..sub.2) may be
different from .pi.. However the operating conditions may be, the
fiber grating 410 is tuned to produce a total relative delay
(.DELTA..tau..sub.1+.DELTA..tau..sub.2) so that, at the output
coupler 330, the sum of the phases of the modulation sidebands
relative to the phase of the optical carrier at the carrier
frequency f.sub.c is shifted by .pi. with respect to the sum of the
phases of the modulation sidebands in the optical signal 302
relative to the optical carrier at the carrier frequency f.sub.c in
the optical path 320.
[0028] FIG. 5 compares magnitudes of the power fading in a
double-sideband optical signal after transmission over a dispersive
fiber of 150 km in length with and without the above power fading
compensation. The subcarrier frequency is 8 GHz. The above
compensation scheme essentially eliminates the power fading and
achieves a power uniformity within 1 dB over the 150-km fiber. FIG.
6 shows the results when the subcarrier frequency is 12 GHz.
[0029] FIG. 7 further shows measured bit error rates after
transmission over dispersive fibers of 27.7 km and 52.4 km in
length for a double-sideband signal modulated at a subcarrier
frequency of 8 GHz. The carrier is modulated to carry 155-Mb/s
pseudorandom data. For the subcarrier frequency at 8 GHz, 0 km
corresponds to maximum power fading in the grating path of our
module, while 52.4 km corresponds to maximum power fading in the
nongrating path. Thus BER performance is independent of whether the
received electrical subcarrier power originated from the grating
path or the nongrating path. The 3-dB optical power penalty (6-dB
electrical power penalty) relative to a back-to-back BER
measurement comes from optical power splitting in the device shown
in FIG. 3.
[0030] The above embodiments controls and tunes the chromatic
dispersion in one of the optical paths to achieve a phase shift of
.pi. between the sum of the phases of the modulation sidebands
relative to the phase of the optical carrier in one optical path
and the sum of the phases of the modulation sidebands in the
optical signal relative to the optical carrier in the other optical
path. This may also be achieved by controlling and tuning the
chromatic dispersion in both optical paths. Two separate tunable
optical dispersion elements may be respectively coupled to the two
optical paths. Alternatively, a single optical dispersion element
may be used to control the dispersion in both optical paths.
[0031] FIG. 8 shows an implementation of the device shown in FIG. 3
where the two terminals 411 and 412 of the tunable fiber grating
410 are coupled to both optical paths 410 and 420, respectively. A
second optical circulator 810 is used to couple the terminal 412 of
the fiber grating 410 to the second optical path 320. Since the
dispersions produced by the two terminals 411 and 422 are opposite,
the fiber grating 410 can be stretched to produce only one half the
.pi.-phase shift at each terminal in order to achieve a total of
phase shift of .pi..
[0032] Although only a few embodiments are disclosed, various
modifications and enhancements may be made without departing from
the following claims.
* * * * *