U.S. patent application number 11/445820 was filed with the patent office on 2007-12-06 for attenuating counter-propagating optical phase modulation.
Invention is credited to Peter Herczfeld, Yifei Li.
Application Number | 20070280579 11/445820 |
Document ID | / |
Family ID | 38775480 |
Filed Date | 2007-12-06 |
United States Patent
Application |
20070280579 |
Kind Code |
A1 |
Li; Yifei ; et al. |
December 6, 2007 |
ATTENUATING COUNTER-PROPAGATING OPTICAL PHASE MODULATION
Abstract
An attenuating counter-propagating (ACP) optical phase modulator
introduces zero propagation delay. An optical field is modulated by
an electromagnetic field. Within the ACP modulator, the optical
field is propagated in an opposite direction to the propagation
direction of the electromagnetic field. The electromagnetic field
is attenuated within the ACP modulator. In an example embodiment,
the length of the modulator is greater than the attenuation length
of the electromagnetic field.
Inventors: |
Li; Yifei; (Norwood, PA)
; Herczfeld; Peter; (Bala Cynwyd, PA) |
Correspondence
Address: |
WOODCOCK WASHBURN LLP
CIRA CENTRE, 12TH FLOOR
2929 ARCH STREET
PHILADELPHIA
PA
19104-2891
US
|
Family ID: |
38775480 |
Appl. No.: |
11/445820 |
Filed: |
June 2, 2006 |
Current U.S.
Class: |
385/3 |
Current CPC
Class: |
G02F 2203/19 20130101;
G02F 2201/15 20130101; G02F 1/0356 20130101; G02F 2203/50 20130101;
G02F 1/3558 20130101; G02F 2202/10 20130101; G02F 2202/20 20130101;
G02F 2/00 20130101 |
Class at
Publication: |
385/003 |
International
Class: |
G02F 1/035 20060101
G02F001/035 |
Claims
1. A modulator comprising: an optical channel configured to
propagate optical energy in a first direction; and an
electromagnetic channel positioned adjacent to the optical channel,
wherein: the electromagnetic channel is configured to propagate
electromagnetic energy in a second direction opposite the first
direction; the electromagnetic channel is configured to attenuate
the electromagnetic energy, for generating attenuated
electromagnetic energy; and the modulator is configured to modulate
the optical energy by the attenuated electromagnetic energy.
2. A modulator in accordance with claim 1, wherein a propagation
delay of the modulator is equal to zero.
3. A modulator in accordance with claim 1, wherein a length of the
modulator is greater than an attenuation length of the
electromagnetic energy.
4. A modulator in accordance with claim 3, wherein the length of
the modulator is at least three times greater than the attenuation
length.
5. A modulator in accordance with claim 1, further comprising a
first end and a second end opposite the first end, wherein the
optical energy is applicable to one of the first end and the second
end, and the electromagnetic energy is applicable to the other of
the first end and the second end.
6. A modulator in accordance with claim 1, wherein the optical
channel comprises an electro-optic material.
7. A modulator in accordance with claim 7, wherein the
electro-optic material comprises at least one of lithium niobate
crystal, potassium titanium oxide phosphate, lithium tantalate, and
a semiconductor.
8. A modulator in accordance with claim 1, wherein the
electromagnetic channel comprises a layered attenuating
material.
9. A modulator in accordance with claim 1, wherein the
electromagnetic channel comprises a composite attenuating
material.
10. A modulator in accordance with claim 1, wherein the optical
channel comprises a waveguide.
11. A modulator in accordance with claim 1, wherein the modulator
is a phase modulator.
12. A modulator in accordance with claim 1, wherein the modulator
comprises a low-pass filter response.
13. A modulator in accordance with claim 1, wherein the modulator
comprises a band-pass filter response.
14. A modulator in accordance with claim 13, wherein the optical
channel comprises alternately polarized domains.
15. A modulator in accordance with claim 14, wherein the optical
channel is periodically poled to achieve the band-pass filter
response.
16. A modulator in accordance with claim 1, wherein the
electromagnetic energy comprises microwave energy.
17. A method for modulating optical energy with electromagnetic
energy; the method comprising: propagating in a first direction,
the optical energy; propagating in a second direction opposite the
first direction, attenuated electromagnetic energy; and modulating
the optical energy with the attenuated electromagnetic energy.
18. A method in accordance with claim 17, wherein a propagation
delay of the modulated optical energy is equal to zero.
19. A method in accordance with claim 17, wherein the modulated
optical energy comprises one of a low-pass frequency response and a
band-pass frequency response.
20. A method in accordance with claim 19, further comprising
periodically poling of a medium through which the optical energy
propagates to achieve the band-pass frequency response.
21. A method in accordance with claim 17, wherein a propagation
distance traveled by the electromagnetic energy to modulate the
optical energy is greater than an attenuation length of the
electromagnetic energy.
22. A method in accordance with claim 21, wherein the distance is
at least three times greater than the attenuation length.
Description
TECHNICAL FIELD
[0001] The technical field generally relates to modulators and
demodulators and more specifically relates to photonic phase locked
loop phase modulators and demodulators.
BACKGROUND
[0002] Fiber-optics links are known to possess the qualities of
high bandwidth, low attenuation, and good electromagnetic
interference (EMI) immunity. Because of these qualities, signals
can be modulated at high frequencies, such as microwave
frequencies, and transmitted over fiber-optic links. Optical
transmitters and optical receivers, modulate and demodulate,
respectively, the optical signals. Conventional optical modulators
and demodulators are known to be nonlinear over wide bandwidths due
to the nonlinearity attributed to propagation delays. Thus, the
very qualities that make fiber-optic links attractive are negated
by the nonlinear characteristics of optical modulators and
demodulators. That is, a phase modulated (PM) fiber optic link
employing a photonic phase locked loop phase demodulator has
intrinsic linear response. The photonic phase locked loop performs
phase demodulation by tracking the optical phase of a phase
modulated optical signal. Photonic phased locked loops thus demand
small loop latency.
SUMMARY
[0003] This Summary is provided to introduce a selection of
concepts in a simplified form. This Summary is not intended to be
used to limit the scope of the claimed subject matter.
[0004] An optical phase modulator possessing no propagation delay
includes an optical channel adjacent to an attenuating electrode.
Optical energy is modulated by the electromagnetic energy. The
modulator is in a counter propagating configuration. That is, the
optical energy propagates along the optical channel in a direction
opposite to the direction in which the electromagnetic energy
propagates along the attenuating electrode. The electromagnetic
energy is attenuated as it propagates along the attenuating
electrode. In an example embodiment, the length of the modulator is
greater than the attenuation length of the electromagnetic
energy.
BRIEF DESCRIPTION OF THE DRAWINGS
[0005] The foregoing summary, as well as the following detailed
description, is better understood when read in conjunction with the
appended drawings.
[0006] FIG. 1 is an illustration of an example electro-optic
attenuating counter-propagation (ACP) phase modulator.
[0007] FIG. 2 is a graph of modulation sensitivity versus
modulation frequency for various lengths of an example ACP phase
modulator.
[0008] FIG. 3 is a graph of modulation phase versus modulation
frequency for various lengths of an example ACP phase
modulator.
[0009] FIG. 4 is a graph of normalized group delay versus
normalized frequency for an example ACP phase modulator.
[0010] FIG. 5 is an illustration of an example ACP phase modulator
implemented as a band-pass ACP phase modulator.
[0011] FIG. 6 is a flow diagram of an example process for
modulating optical energy with attenuated, counter-propagating
electromagnetic energy.
[0012] FIG. 7 is a diagram of an example photonic phase locked loop
(PPLL) comprising an ACP phase modulator.
[0013] FIG. 8 is a graph depicting maximum allowable loop
propagation delay as a function of attenuation length and open loop
gain for a PPLL comprising an example ACP phase modulator.
[0014] FIG. 9 comprises a Bode magnitude diagram (FIG. 9A) and a
Nyquist diagram (FIG. 9B) of the open loop gain of a PPLL
comprising an ACP phase modulator.
[0015] FIG. 10 is a graph of normalized magnitude response of an
experimental ACP phase modulator versus frequency for the various
values of attenuation achieved via various concentrations of saline
solutions.
[0016] FIG. 11 is a graph of normalized group delay versus
normalized frequency for the experimental ACP phase modulator for
various values of attenuation achieved via various concentrations
of saline solutions.
DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS
[0017] Elimination of propagation delay in an electro-optic
modulator is accomplished by configuring the modulator as a
counter-propagating modulator, in which the optical energy
propagates in an opposite direction to propagation direction of the
electromagnetic energy. Further, the channel for carrying the
electromagnetic energy, referred to as the electrode, is configured
to attenuate the electromagnetic energy. The electro-optic
modulator is referred to as an attenuating counter-propagating
(ACP) phase demodulator. Moreover, the modulator is configured such
that the length of the attenuator is greater than the attenuation
length of the electromagnetic energy. In an example embodiment, the
length of the attenuator is at least three times greater than the
attenuation length of the electromagnetic energy.
[0018] Because the ACP phase modulator exhibits no propagation
delay, it is ideally suited for applications in which propagation
delay is not desired, such as a photonic phase locked loop phase
demodulator, for example. The performance of photonic phase locked
loop phase demodulators is detrimentally affected by propagation
delay in the in-loop phase modulator. The ACP phase modulator,
implemented in a photonic phase locked loop phase demodulator,
provides zero propagation delay, and thus excellent photonic phase
locked loop phase demodulator performance.
[0019] FIG. 1 is an illustration of an example electro-optic ACP
phase modulator 12 comprising an optical channel 16 and an
electromagnetic channel 14. The electromagnetic channel 14,
referred to as the electrode, allows for propagation of
electromagnetic energy. The optical channel 16 allows for
propagation of optical energy 18. The optical channel can comprise
any appropriate material, such as lithium niobate crystal,
LiNbO.sub.3, potassium titanium oxide phosphate, KTiOPO.sub.4 (also
referred to as KTP), lithium tantalate, LiTaO.sub.3, and/or a
semiconductor, for example.
[0020] The electromagnetic energy can comprise any appropriate
electromagnetic energy. In an example embodiment, the
electromagnetic energy comprises microwave energy. Generally,
microwave energy refers to alternating current signals with
frequencies between 300 MHz (3.times.10.sup.8 Hz) and 300 GHz
(3.times.10.sup.11 Hz). As depicted, the ACP phase modulator 12 is
configured for counter propagation. That is, the optical energy
propagates in a direction 18 opposite to the propagation direction
20 of the electromagnetic energy. It is to be understood that the
depiction of propagations directions 18 and 20 is relative. For
example, each of the propagation directions 18 and 20 could be
reversed and still be counter propagating.
[0021] The electrode 14 provides attenuation of the electromagnetic
energy propagating therethrough. In an example embodiment, the
length, L, of the ACP phase modulator 12 is at least three times
greater than the attenuation length of the electromagnetic energy.
The length, L, is the propagation distance traveled by the
electromagnetic energy to modulate the optical energy. Attenuation
length is the propagation distance traveled by the electromagnetic
energy in which the amplitude of the electromagnetic energy is
attenuated by a factor of 1/e (e.g., approximately 63%). The
length, L, of the ACP phase modulator 12 can be greater than, less
than, or equal to the attenuation length of the electromagnetic
energy, however, as discussed in more detail below, lesser
propagation delay is observed when the attenuation length of the
electromagnetic energy is less than the length, L, of the ACP phase
modulator 12.
[0022] In operation, the optical energy is capable of being
modulated (modulateable) by the attenuated electromagnetic energy.
The electrode 14 is adjacent to the optical channel 16. As the
electromagnetic energy propagates along the electrode 14, the
electromagnetic energy is attenuated, and the phase of the optical
energy propagating along the optical channel 16 is modulated by the
attenuated electromagnetic energy. As described herein, the
electromagnetic energy is interchangeably referred to the microwave
modulation field. Also, the optical energy is interchangeably
referred to as the optical field. The microwave modulation field
and the optical field enter at opposite ends of the ACP phase
modulator 12. As depicted in FIG. 1, the microwave modulating field
enters at the end of the ACP phase modulator 12, indicated at z=L
and the optical field enters the end of the ACP phase modulator 12,
indicated at z=0. The microwave modulation field can be expressed
mathematically in the frequency domain by equation (1) below.
V.sub.m(.omega.,z)=V.sub.m(.omega.,z=L)e.sup.-.gamma.m(L-z), (1)
where .gamma..sub.m represents the complex propagation constant of
the electromagnetic field, defined as .gamma. m = .alpha. m + j
.times. .times. .omega. / .mu. m , ##EQU1## where .alpha..sub.m
represents the attenuation and .mu..sub.m represents the velocity
of the microwave modulation field. In general, .alpha..sub.m and
.mu..sub.m are functions of .omega., the modulation frequency. The
variable z represents the length of the ACP phase modulator 12.
[0023] As previously mentioned, the propagation delay of the ACP
phase modulator is zero. To determine the ACP phase modulator's 12
propagation delay, its transfer function is determined. Neglecting
the transverse profile of the optical field within the optical
channel 16, propagation of the optical energy can be described
mathematically by equation (2). .differential. .xi. .times. .times.
( t , z ) .differential. t + u .differential. .xi. .times. .times.
( t , z ) .differential. z = j .alpha. V m .function. ( t , z )
.xi. .times. .times. ( t , z ) , ( 2 ) ##EQU2## where .xi.(t,z)
represents the optical field envelope as a function of time, t, and
length, z, of the ACP phase modulator, V.sub.m(t) represents the
modulation voltage, .mu. represents the speed of light inside the
optical channel 16 of the ACP phase modulator 12, and .alpha.
represents attenuation related to the electro-optic effect as
described by equation (3) below.
.alpha.=.omega..sub.0rn.sub.0.sup.2/2d, (3) where .omega..sub.0
represents the optical frequency, .eta..sub.0 represents the
refractive index of the optical channel 16, r represents the
electro-optic coefficient of the optical channel, and d represents
the effective modulator thickness.
[0024] To solve equation (2), .xi.(t,z) is expressed in terms of
phase and amplitude as shown in equation (4).
.xi.(t,z)=A(t,z)e.sup.j.phi.(t,z), (4) where A(t,z) represent the
amplitude of the optical field envelope as a function of time, t,
and length, z, of the ACP phase modulator, e.sup.j.phi.(t,z)
represent the phase of the optical field envelope as a function of
time, t, and length, z, of the ACP phase modulator. Substituting
equation (4) into equation (2) shows that only the phase of the
optical signal is affected by the modulation, as can be seen in
equation (5) and equation (6). .differential. A .function. ( t , z
) .differential. t + u .differential. A .function. ( t , z )
.differential. z = 0 ( 5 ) .differential. .PHI. .times. .times. ( t
, z ) .differential. t + u .differential. .PHI. .times. .times. ( t
, z ) .differential. z = .alpha. V m .function. ( t , z ) , ( 6 )
##EQU3##
[0025] The Fourier transform of equation (6) is determined to
obtain the propagation equation for the optical phase in the
frequency domain. The result is represented mathematically by
equation (7). .differential. .PHI. .times. .times. ( .omega. , z )
.differential. z + j .times. .omega. u .PHI. .times. .times. (
.omega. , z ) = .alpha. u V m .function. ( .omega. , z ) ( 7 )
##EQU4##
[0026] The transfer function of the ACP phase modulator 12 is
obtained by substituting equation (1) into equation (7). The result
is represented mathematically by equation (8). H ACP .function. (
.omega. ) = .PHI. .function. ( .omega. , z = L ) V m .function. (
.omega. , z = L ) = .alpha. u 1 - e - ( .gamma. m + j .omega. / u )
.times. L .gamma. m + j .omega. / u ( 8 ) ##EQU5## In the simple
case wherein no attenuation is introduced by the electrode 14
(represented mathematically as .alpha..sub.m=0), equation (8)
reduces to equation (9). H ACP .function. ( .omega. ) = .alpha.
.times. .times. L u e - j .omega. .times. .times. .tau. d sin
.function. ( .omega. .times. .times. .tau. d ) .omega. .times.
.times. .tau. d , ( 9 ) ##EQU6## where .tau..sub.d represents the
average traveling time of the optical field and the modulation
field (.tau..sub.d=(L/u+L/u.sub.m)/2). The exponential phasor
e.sup.-j.omega..tau..sup.d represents a pure propagation delay
equal to the average traveling time of the optical and the
modulation fields. This phasor causes feedback instability in a
photonic phase locked loop because as co increases it induces
unbounded phase lag that diminishes the photonic phase locked loop
phase margin. The sensitivity of the ACP phase modulator 12 is
.about..alpha.L/u. Minimizing propagation delay amounts to reducing
L, which significantly diminishes sensitivity.
[0027] When attenuation is present and the length of the ACP phase
modulator, L, approaches infinity, equation (8) reduces to equation
(10), which resembles the response of a lumped-element low pass
filter. H ACP .function. ( .omega. ) = .alpha. L a u 1 1 + j
.omega. / .omega. ACP , ( 10 ) ##EQU7## where
L.sub.a=1/.alpha..sub.m and represents the attenuation length of
the modulation field, and
.omega..sub.ACP=1/(L.sub.a/u.sub.m+L.sub.a/u), and represents the
bandwidth of the ACP phase modulator.
[0028] This modulator response contains no phasor representing
propagation delay. Thus, it is ideally suited for the applications
demanding a tight propagation delay, such as a photonic phase
locked loop. As the attenuation length, L.sub.a, in equation (10)
approaches infinity, the magnitude of the ACP phase modulator
reaches maximum. In this limit, equation (10) reduces to equation
(11) below, which resemble the response of an ideal frequency
modulator. H ACP .function. ( .omega. ) = .alpha. / ( 1 + u / u m )
j.omega. ( 11 ) ##EQU8##
[0029] FIG. 2 is a graph of modulation sensitivity versus
modulation frequency for various lengths, L, of an example ACP
phase modulator. The modulation sensitivity is represented in
radians/volt (rad/volt) and the frequency if represented in Hertz
(Hz). The graph of FIG. 2 was calculated using a fixed value of
attenuation, .alpha..sub.m, equal to 50 NP/m (neepers per meter).
The sensitivity was calculated for values of modulator length, L,
equal to L=0.5/.alpha..sub.m, L=1/.alpha..sub.m, L=2/.alpha..sub.m,
L=3/.alpha..sub.m, L=infinity. As can be seen in FIG. 2, the
sensitivity exhibits a persistent oscillation at a period of
f.sub.r=1/2.tau..sub.d, which is referred to as the modulator
resonance frequency. As the length, L, increases, the oscillation
diminishes, and when L>3/.alpha..sub.m, the modulator response
is nearly identical to the monotonically decaying shape of an ideal
ACP modulator with infinite L.
[0030] FIG. 3 is a graph of modulation phase versus modulation
frequency for various lengths, L, of an example ACP phase
modulator. The modulation phase is represented in angle
(H.sub.ACP(.omega.)) and the frequency if represented in Hertz
(Hz). Similar to FIG. 2, the graph of FIG. 3 was calculated using a
fixed value of attenuation, .alpha..sub.m, equal to 50 NP/m. The
phase was calculated for values of modulator length, L, equal to
L=0.5/.alpha..sub.m, L=1/.alpha..sub.m, L=2/.alpha..sub.m,
L=3/.alpha..sub.m, L=infinity. The graph of FIG. 3 also exhibits
the persistent oscillation at the modulator resonance frequency,
f.sub.r=1/2.tau..sub.d. As the length, L, increases, the
oscillation diminishes, and when L>3/.alpha..sub.m, the
modulator response is nearly identical to the monotonically
decaying shape of an ideal ACP modulator with infinite L. Thus, as
can be seen from FIG. 2 and FIG. 3, the modulator response is
nearly identical to the monotonically decaying shape of an ideal
ACP modulator with infinite L, when L is greater than 3 times the
attenuation length (attenuation length=1/.alpha..sub.m).
[0031] FIG. 4 is a graph of normalized group delay versus
normalized frequency for an example ACP phase modulator. Normalized
coordinates are introduced for generality. Frequency is normalized
by the modulator resonance frequency, f.sub.r. Thus the normalized
frequency is f/f.sub.r. The group delay is normalized by the
average traveling time of the optical field and the modulation
field, .tau..sub.d. The normalized group delay is
.tau./2.tau..sub.d. The length, L, of the modulator is
standardized. The normalized group delay of the ACP modulator is a
function of frequency, and has minimum values at the multiples of
the resonance frequencies: f.sub.n=nf.sub.r (n is an integer).
These local minimum values of the normalized group delay intensify
for lesser attenuation, and tend to extend to negative values of
normalized group delay. Away from the resonance frequency values,
as .alpha..sub.m vanishes, the normalized group delay of the ACP
modulator approaches approximately 0.5. When increasing
.alpha..sub.m, the group delay diminishes at frequencies much
higher than f.sub.r. This indicates vanishing of propagation delay
because the propagation delay of a low pass filter approaches the
group delay in frequencies well above the filter cutoff. The case
in which .alpha..sub.m=0.1/L is also depicted in the graph of FIG.
4. When .alpha..sub.m=0.1/L, the modulation field as seen by the
optical field slightly increases (instead of being attenuated).
This can occur, for example, when the counter-propagating fields
are not perfectly aligned. As seen in FIG. 4, when
.alpha..sub.m=0.1/L, the group delay is enhanced near the modulator
resonances.
[0032] FIG. 5 is an illustration of an example ACP phase modulator
implemented as a band-pass ACP phase modulator. The ACP phase
modulator described up to this point has a low-pass frequency
response. In an example embodiment, the ACP phase modulator also
can be implemented as a band-pass phase modulator having a band
pass frequency response. The ACP phase modulator can obtain a
band-pass response by introducing periodical poling to the
electro-optic medium as depicted by the alternating arrows 22, and
thereby is able to operate at high microwave or millimeter wave
frequencies. Periodic poling is accomplished by forming the
electro-optic medium with layers of electro-optic material (e.g.,
crystal), wherein each layer has an alternate optical axis
orientation. The optical energy propagates through the optical
medium and the optical medium is periodically poled.
[0033] Introducing periodic pulling to the electro-optic medium
allows the ACP phase modulator to yield a band-pass response. With
the introducing periodic pulling, equation (7) has the form of
equation (12) below.: .differential. .PHI. .times. .times. (
.omega. , z ) .differential. z + j .times. .omega. u .PHI. .times.
.times. ( .omega. , z ) = .alpha. .function. ( z ) u V m .function.
( .omega. , z ) , ( 12 ) ##EQU9## where the .alpha..sub.z parameter
has a form of a periodic function, and can be expanded to the
Fourier series shown in equation (13). .alpha. .function. ( z ) = n
= - .infin. .infin. .times. .times. .alpha. n e - I .times. .times.
2 .times. .pi. n ( L - z ) / .LAMBDA. , ( 13 ) ##EQU10## where
.alpha..sub.n is the Fourier coefficient and .LAMBDA. is the
pulling period.
[0034] Upon substituting equation (13) and equation (1) into
equation (12), the transfer function of the ACP modulator with
periodic pulling can be determined. This transfer function is
represented by equation (14). H ACP_Pulling .function. ( .omega. )
= .times. n = - .infin. .infin. .times. .times. .alpha. n .alpha. u
1 - e - [ .gamma. m + j ( .omega. - n 2 .times. .pi. u / .LAMBDA. )
/ u ] .times. L .gamma. m + j ( .omega. - n 2 .times. .pi. u /
.LAMBDA. ) / u ( 14 ) ##EQU11##
[0035] Comparing equation (14) with equation (8), it is evident
that with period pulling, the ACP modulator response (equation (8))
is translated to the frequencies determined by the pulling period:
n2.pi..mu./.LAMBDA.. In order to obtain a band-pass response with
pass-band near the frequency u/.LAMBDA., .alpha..sub.1 to chosen at
the dominant term by controlling .alpha..sub.z. Also, similar to
the low-pass ACP modulator, a lump-element band-pass response is
obtained by letting the ACP modulator length, L, approach
infinity.
[0036] FIG. 6 is a flow diagram of an example process for
modulating optical energy with attenuated, counter-propagating
electromagnetic energy as described above. Optical energy is
propagated in a first direction at step 24. Electromagnetic energy
is counter-propagated at step 26. That is, the propagation
direction of the optical energy is opposite the propagation
direction of the electromagnetic energy. The electromagnetic energy
is attenuated at step 28, and the optical energy is modulated by
the attenuated electromagnetic energy at step 30. Modulating energy
in accordance with the process described in FIG. 6 can result in
zero propagation delay when the length of the modulator is longer
than the attenuation length. In an example embodiment, the length
of the modulator is at least three times greater than the
attenuation length. Attenuation can be accomplished by any
appropriate means. For example, the electromagnetic channel can
comprise a composite attenuating material, the electromagnetic
channel can comprise layered materials that provide attenuation
(such as by placing a saline solution on the non-attenuating
electrode as described below), and/or separate attenuating
materials can be positioned in proximity to one another to provide
attenuation.
[0037] As mentioned above, the ACP phase modulator is ideally
suited to applications benefiting from a modulator having no
propagation delay. One such application is a photonic phase locked
loop because a photonic phase locked loop relies on tight tracking
of the optical phase to perform linear phase demodulation. It is to
be understood that application of the ACP phase modulator is not
limited to applications benefiting from a modulator having no
propagation delay. It is further to be understood that the
description herein of the ACP phase modulator as applied to a
photonic phase locked loop is merely one example and that the
application of the ACP phase modulator is not limited thereto.
[0038] FIG. 7 is a diagram of an example photonic phase locked loop
(PPLL) 32 comprising an ACP phase modulator 36. The description of
the PPLL 32 herein is with reference to the ACP phase modulator 36
having a low-pass response (see equation (8)). It is to be
understood that an ACP phase modulator having band-pass response
also is applicable to a PPLL. The PPLL 32 comprises a photodetector
(PD) 34, a local oscillator (LO) 38, and the ACP phase modulator
36. The phase of the incoming optical signal is denoted as
.theta..sub.in and the phase of the optical signal from the local
oscillator 38 at the output of the ACP phase modulator 36 is
denoted as .theta..sub.LO. The voltage at the output of the PD 34
is a function of frequency, .omega., and is denoted as
V.sub.pd(.omega.). The component of optical power at the output of
the PD 34 corresponding to the phase of .theta..sub.in is denoted
as P.sub.in. The component of optical power at the output of the PD
34 corresponding to the phase of .theta..sub.LO, is denoted as
P.sub.LO. The photodetector responsivity of the PD 34 is denoted as
R.sub.pd. The terminal resistance of the PD 34 is denoted as
R.sub.term. The bandwidth of the PD 34 is denoted as .omega..sub.p,
which is determined in part by the RC time constant of the PD 34.
In the configuration depicted in FIG. 7, the PD 34 further
functions as a loop filter.
[0039] The open loop gain the PPLL 32 is used to determine the
linearity and stability of the PPLL phase demodulator. The open
loop gain, denoted as G(.omega.) is determined in accordance with
the output voltage, V.sub.pd(.omega.), of the PD 34 and the
transfer function, H.sub.ACP(.omega.), of the ACP phase modulator
36, as represented in equation (8). The output voltage,
V.sub.pd(.omega.), is represented by equation (15) below. V pd
.function. ( .omega. ) = R pd .times. P in P LO R term 1 + j
.omega. / .omega. p .times. ( .theta. LO - .theta. in ) ( 15 )
##EQU12##
[0040] Accordingly, the open loop gain, G(.omega.) is represented
by equation (16) below. G .function. ( .omega. ) = .times. [ R pd P
in .times. P LO R term exp .times. ( - j.omega. .times. .times.
.tau. .times. l ) 1 1 + j .omega. / .omega. p ] H ACP .function. (
.omega. ) , ( 16 ) ##EQU13## where .tau..sub.1 represents the
propagation delay contributed by the loop components, PD 34 and
interconnects, exclusive of the ACP phase modulator 36.
[0041] Although the propagation delay of the ACP phase modulator
diminishes, its phase response is affected by the attenuation of
the electromagnetic signal, which is accounted for in determining
the stability of the PPLL. For the sake of simplicity an example
ACP phase modulator having infinite length is analyzed. It is to be
understood that the results from the analysis of the example ACP
phase modulator having infinite length are also applicable to an
ACP phase modulator having length, L, that is at least three times
longer than the attenuation length.
[0042] FIG. 8 is a graph depicting maximum allowable loop
propagation delay, .tau..sub.1, in pico-seconds (ps), as a function
of attenuation length in millimeters (mm) and open loop gain for a
PPLL comprising an example ACP phase modulator. The maximum stable
propagation delay, .tau..sub.1, was calculated as a function of
attenuation length and the minimum open loop gain for an example
information bandwidth of 500 MHz and the PD bandwidth,
.omega..sub.p, equal to 1 GHz. As shown in the graph of FIG. 8, the
loop latencies are achievable for very high loop gain. This is due,
in part, to the example ACP phase modulator having infinite length
and therefore not contributing to the propagation delay. This is
also the case for an ACP phase modulator having a length that is at
least three times longer than the attenuation length.
[0043] An example PPLL having specific parameters and comprising an
ACP phase modulator, was analyzed. The parameters are listed in
Table 1, below. The PPLL had a 30 dB open loop gain over a 500 MHz
bandwidth. As seen in Table 1, the effective modulator thickness d
is 13 micrometers (.mu.m), which is approximately 12 .mu.m . A
modulator thickness of 12 .mu.m is achievable in lithium niobate
crystal (LiNbO3) waveguide devices. The modulator length and the
attenuation length are determined in accordance with the open loop
gain requirement. TABLE-US-00001 TABLE 1 Parameters Used For An
Example PPLL Implementation Parameter Value Transmission optical
power 300 mW LO optical power 300 mW Modulator material E/O
Coefficient, r 31 pm/m (LiNbO.sub.3) Modulator effective thickness,
d 13 .mu.m PD sensitivity 0.8 Amp/W Loop propagation delay
excluding the 5 ps in-loop phase modulator Information bandwidth
500 MHz Minimum open loop gain 30 dB
[0044] FIG. 9 comprises a Bode magnitude diagram (FIG. 9A) and a
Nyquist diagram (FIG. 9B) of the open loop gain of a PPLL
comprising an ACP phase modulator having a length of 30 mm, wherein
the attenuation length is 100 mm, for a PPLL configuration having
the parameters listed in Table 1. As shown in Bode diagram in FIG.
9A, the PPLL having the parameters listed in Table 1, comprising an
ACP phase modulator having a length of 30 mm, and an attenuation
length of 100 mm is capable of obtaining 30 dB gain over a 500 MHz
bandwidth. Further, the Nyquist diagram in FIG. 9B shows that the
configuration is stable because no portion of the diagram
encompasses the (-1,0) point in the complex plane.
[0045] An experimental configuration of an ACP phase modulator was
analyzed. The experimental configuration included a custom modified
Mach-Zehnder (MZ) lithium niobate crystal (LiNbO.sub.3) waveguide
modulator. The MZ modulator was biased in quadrature, thus
generating a photocurrent, I(t).about.sin(.phi.(t)), where .phi.(t)
represents the modulator output phase. Under small signal
approximation, the photocurrent is approximately equal to the
modulator output phase; I(t).about..phi.(t). Thus, by measuring the
transmission scattering parameter between the modulation port of
the device and the PD output, the transfer function of the phase
modulator can be determined.
[0046] In the experimental configuration, the ACP phase modulator
electrode was a 3.7 cm long coplanar waveguide (CPW) fabricated on
a lithium niobate crystal, LiNbO.sub.3, substrate. A saline
solution was applied over the CPW waveguide to introduce
attenuation to the modulation field. The attenuation was adjusted
by varying the salinity level of the saline solution. Two saline
solution concentrations were utilized: a 2% saline solution and a
4% saline solution. The attenuation of the electrode was calculated
and shown to be frequency dependent. On average, the 2% yielded 50
Np/m attenuation, which corresponds to an attenuation length of 20
mm. The 4% saline solution, on average, yielded 85 Np/m
attenuation, which corresponds to an attenuation length of 12
mm.
[0047] The experimental configuration was calibrated to eliminate
various effects arising from the coaxial cables, optical fibers,
driver amplifiers, the photodetector, and the like. The transfer
function of the experimental ACP phase modulator was measured. FIG.
10 is a graph of normalized magnitude response of the experimental
ACP phase modulator versus frequency for the various saline
solutions. As shown in FIG. 10, when no saline solution was
applied, the measured response was a approximately and ideal sinc
(sin(x)/x) function. The valleys of the sinc function occur close
to the resonance frequencies (.about.multiples of 2 GHz). The
resonance frequencies were determined from the average propagation
time of the modulation field and the optical field.
[0048] After applying the saline solutions, the velocity of the
microwave field decreased due to the high dielectric constant
(.epsilon..sub.r=80) of saline, which is the same for both the 2%
and the 4% solutions. This is reflected in the graph of FIG. 10 by
the change in the resonance frequencies when the 2% and 4% saline
solutions are applied. It is observed that the peaks and the
valleys of the magnitude response start diminishing with increasing
attenuation. With 4% salinity, the peaks and valleys are barely
discernible. This behavior agrees well with the theoretical
prediction for the curves of L=2/.alpha..sub.m, and
L=3/.alpha..sub.m. The magnitude response was also analyzed versus
frequency normalized by the modulator resonance frequency, and
results were consistent.
[0049] The group delay of the experimental ACP phase modulator also
was measured. FIG. 11 is a graph of the normalized group delay
versus normalized frequency for the experimental ACP phase
modulator for the various saline solutions. For an accurate
comparison with the theoretical results, the measured group delay
is normalized by the modulator round trip time .tau..sub.d. As
shown in FIG. 11, in the absence of saline solution, the measured
group delay is enhanced near the resonance frequencies. This is
attributed to a slight misalignment between the optical waveguide
and the electrode of the experimental configuration. The
misalignment strengthens the interaction between the modulation
field and the optical fields as the former propagates along the
electrode, which is equivalent to increasing (amplifying) the
modulation field. This leads to enhancement of the group delay near
the resonance frequencies.
[0050] When the saline solutions are applied to introduce the
desired attenuation, the enhancement in group delay near the
resonances is reversed, and the group delay diminishes. With the 2%
salinity level, the normalized group delay develops a fluctuation
around 0 with amplitude of approximately 0.01. This correlates well
with the theoretical calculations, which indicated that the
normalized group delay fluctuates between -0.013 and 0.013. With 4%
salinity level, this fluctuation is barely discernible and the
normalized group delay decays to 0 as frequency increases, which
suggests elimination of the propagation delay.
[0051] The various techniques described herein can be implemented
in connection with hardware or software or, where appropriate, with
a combination of both. Thus, the methods and apparatuses described
herein, or certain aspects or portions thereof, can take the form
of program code (i.e., instructions) embodied in tangible media,
such as floppy diskettes, CD-ROMs, hard drives, or any other
machine-readable storage medium, wherein, when the program code is
loaded into and executed by a machine, such as a computer, the
machine becomes an apparatus for practicing the invention. The
program code can be implemented in a high level procedural or
object oriented programming language to communicate with a
computer. The program(s) can be implemented in assembly or machine
language, if desired. In any case, the language can be a compiled
or interpreted language, and combined with hardware
implementations.
[0052] The program code can be transmitted over a transmission
medium, such as over electrical wiring or cabling, through fiber
optics, or via any other form of transmission, wherein, when the
program code is received and loaded into and executed by a machine,
such as an EPROM, a gate array, a programmable logic device (PLD),
a client computer, a video recorder, or the like, the receiving
machine becomes an apparatus for practicing the invention.
Additionally, any storage techniques can invariably be a
combination of hardware and software.
[0053] While illustrative embodiments have various figures, it is
to be understood that other similar embodiments can be used or
modifications and additions can be made to the described embodiment
for performing attenuating counter-propagating phase modulation
without deviating therefrom. Therefore, attenuating
counter-propagating phase modulation should not be limited to any
single embodiment, but rather should be construed in breadth and
scope in accordance with the appended claims.
* * * * *