1 00-megabit-per-second resonant-cavity phasemodulator for coherent optical communications
Chien-Chung Chen, Deborah L. Robinson, and Hamid Hemmati
A resonant-cavity electro-optic phase modulator is designed, implemented, and experimentally verified tooperate at a data rate of 100 Mbits/s. The cavity is made up of a highly reflective backmirror and thepartially reflective end of an electro-optic crystal. A voltage signal applied to the electro-optic crystalperturbs the effective optical path length inside the cavity and hence its resonance frequency. Becausethe phase of the reflected optical signal from the cavity is highly dispersive when the cavity is tuned nearresonance, a cw incident signal will experience a large phase shift as the cavity is electro-optically tuned onand off resonance. This phase-dispersion effect can be used in the construction of an optical phasemodulator capable of modulating the signal at data rate in excess of 100 Mbits/s. The performance ofthe modulator was measured by first heterodyne detecting the signal to an intermediate frequency andthen measuring the spectral characteristics with a radio frequency spectrum analyzer.. The measuredphase shift is shown to be in good agreement with theoretical predictions.
1. Introduction
Coherent optical communication technology can pro-vide improved receiver sensitivity compared withdirect-detection systems in many applications. Byamplifying the weak incident signal with a stronglocal oscillator (LO) output, the system can overcomethermal noise limitations and achieve near quantum-limited sensitivity. In addition, coherent receptionoffers a better background noise rejection capabilitybecause the spectral filtering is performed at theintermediate frequency where the bandwidth can bemuch more selective. The bandwidth-selective na-ture of the coherent receiver can also lead to a moreefficient use of the optical spectrum and the potentialof multiple-access communications over a single-laserbandwidth.
For full benefits of the coherent system to berealized, it is desirable that the transmitted opticalsignal be phase encoded and coherently demodulated.A phase-encoded channel offers improved energyefficiency. That is, it can achieve higher receiversensitivity compared with frequency- or intensity-encoded channels. The efficiency of the channel can
The authors are with the Jet Propulsion Laboratory, CaliforniaInstitute of Technology, 4800 Oak Grove Drive, Pasadena, Califor-nia 91109.
Received 1 October 1992; revised manuscript received 8 Novem-ber 1993.
be improved further by the coherent demodulation ofthe optical signal. Coherent signal demodulationrequires that the signal and LO lasers be phase lockedwith respect to each other. We can accomplish thisby homodyne detecting the beat note between the twolasers and by feeding back the resulting phase error tothe tunable LO laser. Alternatively, we can accom-plish coherent signal demodulation by first hetero-dyne detecting the signal to an intermediate fre-quency (IF). The IF signal is then phase locked andcoherently demodulated with a stable IF reference.If the signal and LO lasers are properly phase locked,the output of the coherent demodulator will repre-sent the phase and amplitude information carried inthe incident optical signal and can be easily detected.
A critical component in a phase-encoded channel isthe phase modulator. Phase modulation for a semi-conductor laser can be accomplished by modulatingthe injection current density and hence the instanta-neous frequency of the laser. For cw lasers such asdiode-pumped solid-state lasers, an external modula-tor will be required. Bulk electro-optical phase modu-lation often requires a high modulation voltage that isnot practical to achieve in a flight system. Severalapproaches can be used to lower the driving voltagerequirement. These techniques include travelingwave modulators with long interaction lengths, andwaveguide modulators with narrow channels.1-2Resonant modulators in which the optical and radiofrequency (rf ) modulation signals are both resonatedas a way to improve the modulation efficiency have
also been proposed and implemented.- 5 To matchthe group velocity of optical and rf signals, however,the resonant modulators tend to have a narrowmodulation bandwidth, and they cannot be extendedto the broadband operation needed for data transmis-sion. An alternative is to use only a resonant opticalcavity that enhances the interaction length withoutrequiring a complex electrode configuration to matchthe optical and electronic group velocity.4 Becauseno electrical resonator is used, the method can inprinciple be operated near dc modulation frequency.The upper limit of the modulation bandwidth islimited by the response time of the cavity, which is afunction of the cavity finesse. A resonant-cavityphase modulator using this principle was investigatedby Kane and Wallace6 for coherent communication.Their study demonstrated that resonant-cavity phasemodulation, as expected from theory, can be accom-plished in practice. Previously, resonant cavitieswere explored for the amplitude (intensity) modula-tion of a cw laser source.7 8 The concept of a reso-nant cavity has also been extended to temperaturesensors and high-speed signal processing,9 and apassive resonant-ring-cavity laser gyroscope was inves-tigated as an alternative to the standard Sagnacinterferometer laser gyroscope.10
Here we present the development of an electro-optic resonant phase modulator that has been de-signed to operate at 100 Mbits/s. The rest of thispaper is organized as follows. The principle of opera-tion of the resonant phase modulator is described inSection 2. To achieve maximum phase modulation,we must lock the incident laser frequency to thecenter of resonance of the cavity. We stabilize theresonant cavity to the laser frequency by observingthe intensity fluctuation as a result of the datamodulation. We need a suitable amount of dataencoding to ensure a sufficient amount of symboltransitions within the data stream. The configura-tion employed to lock the cavity to the incident signalis described in Section 3. The actual cavity designedand its performance predictions are outlined in Sec-tion 4. Finally, the experiment and the resultingdata reduction are described in Section 5.
2. Principle of Operation
The phase modulator under investigation is an exter-nal cavity phase modulator in which an optical cavityis biased near resonance with the incident laserbeam.1 ",12 Because the phase angle of the reflectedsignal from a tuned cavity is highly dispersive nearresonance, a small detuning of the cavity from reso-nance can result in a large output phase shift. Bymodulating the cavity near its resonance, therefore,one can modulate the output phase.
A particular realization of the resonant cavity is theGires-Turnois talon shown in Fig. 1. The talonconsists of a partially reflective input coupler withreflectivity R and a highly reflective backmirror.For a lossless beam-splitter material, the two counter-propagating incident optical signals Ej and Er are
PARTIALREFLECTIVECOATING
INCOMINGSIGNAL, Ej
OUTPUTSIGNAL, E0
Et
Er
HRCOATING
1010
Fig. 1. Gires-Turnois 6talon showing the four interfering wavesat the partially reflective surface: HR, high reflectance.
related to the output optical signals Et and E0 by thefollowing relationship:
(E -r* t*)(E) ' (1)
where t and r are the amplitude transmittance andreflectance of the input surface, respectively. Theintensity transmisivity and reflectivity of the beamsplitter are related to the amplitude transmittanceand reflectance by t 12 = T and I r 1 2 = R. Byconservation of energy, T + R = 1. In a Gires-Turnois 6talon, the signal transmitted into the cavityis reflected by the highly reflective backmirror. Around trip within the cavity will pick up an equivalentphase shift 4+ and an amplitude gain g such that
Er = g exp(i4)Et. (2)
The round-trip power gain G = Ig12 is less than orequal to one for a passive cavity (no gain). Equations(1) and (2) can be solved for the relationship betweeninput and output fields. The result is
[g exp(i-F) - r*]E0 1 -rg exp(i4)J(3
The output intensity I and phase shift CD can besolved from Eq. (3) as
1/h = 1 + GR - 2vG os +
cD = tan'1 [ G( - R)sin o_ s ,- FR( + G) + ,/G( + R)cos o
(4)
(5)
where Ii is the incident intensity.Shown in Fig. 2 is a plot of the reflected signal
phase versus the cavity detuning A. When + = 0, thecavity is in resonance with the incoming signal. Inthis case the reflected signal is in phase with theincoming signal. When the cavity is slightly offresonance, i.e., when + • 0, the reflected signalexperiences a phase shift that is highly dispersivenear the cavity resonance. The slope of the phase-
3 cavity detuning for a cavity with a 2% intracavity-- I £- _ absorption loss. An absorption dip is clearly visible
2 / g near 4+ = 0. This absorption loss is more prominentfor cavities with a higher input coupler reflectivity.This is because the number of round-trip passes
I experienced by the incident signal increases with Rwhen the cavity is on resonance. Consequently, the
o0 effect of intracavity loss is compounded and leads to ahigher loss. The absorption loss shown in Fig. 3 isgenerally undesirable because it reduces the amount
1 of output signal power. However, as shown in Sec-tion 3, we can also use it to provide the error signal for
2 locking the cavity on resonance with the incominglaser.
2%ktracAvyLow Equation (5) shows that reflective signal phase-0.3 -0.2 -0.1 0.0 0.1 0.2 03 from a Gires-Turnois talon is highly dispersive
when the cavity is tuned across its resonance. We
PHASE DETUNING, rad can use this large phase-dispersion characteristic to' ~~~~encode the phase of the reflected optical signal from
Relative phase shift of the reflected signal from the tecai the et of the cai an be;wave for a Gires-Turnois talon with different values of the cavity f the detuning of the cavity, (+. can be
apler reflectivity modulated by an external signal. One can modulate*pler reflectivity. cavity detuning by changing the round-trip optical
path length through the use of piezoelectric or electro-sion curve near + = 0 depends on the Q value of optic effects. The use of the electro-optic effect isrity and hence on the width of the resonance. desirable at high modulation frequencies because the
rower the resonance, the more sensitive is the piezoelectric effect is limited in bandwidth by theAd signal phase to the cavity detuning. acoustic speed inside the crystal. In an electro-opticIdition to a highly dispersive phase shift, the (EO) tuned 6talon, an EO crystal is situated betweenAd signal also experiences intensity variation as the input coupler and the highly reflective backmirror.vity is tuned across resonance. Because the The index of refraction and hence the optical pathirror of the cavity has high reflectivity, most of length through the EO crystal can be modulated by
tergy is reflected back toward the incident the application of a voltage signal. The cavity isOn one hand, when the cavity is off reso- nominally biased near its reflective resonance with
the reflected intensity is close to the incident the incoming laser light. A voltage signal across thety. When the cavity is tuned near resonance, EO crystal will therefore result in a detuning angle +other hand, small absorption-scattering losses and hence a large phase shift at the output. Thethe cavity can multiply as the number of detuning angle 4 can be related to the applied voltage
through the cavity increases and can result in Vand the half-wave voltage V1, of the EO crystal byle drop in the output intensity. Shown in Fig.plot of the reflected signal intensity versus the = 27rV/V,. (6)
Note that a factor of 2 in Eq. (6) is introduced becausethe optical signal traverses twice through the crystalper round trip for a linear cavity. The half-wavevoltage for a crystal with a 3-m symmetry cut forphase modulation is given by"
dV = - X~3 (7)
.4- l lwhere X is the wavelength, n is the index of refraction,r33 is the EO coefficient, D is the thickness of thecrystal, and I is the length of the crystal.
3. Active Cavity Stabilization
>.0' 2%ntrmv Los From Fig. 2 we see that strong phase dispersion3 -0.2 -0.1 0.0 0.1 0.2 0.3 occurs only when the cavity is biased near its reflec-
tive resonance. A cavity biased away from reso-PHASE DETUNING, red nance will show little or no response to the modula-
Relative intensity drop of the reflected signal versus the tion voltage. Because acoustic vibrations and room-,tuning angle for cavities with different values of input temperature changes can alter the dimension of thereflectivity. cavity and hence its resonance frequency during
In a(reflectthe cabackmithe ensignal.nance,intension thewithinpassesa sizab3 is a I
I-
@3
zwI-
0
I.-
Fig. 3.phase dEcoupler
operation, the cavity must be maintained on reso-nance with the incoming laser signal.
We accomplish active cavity stabilization by sens-ing the change of cavity dimension and then feedingback the information to an active element to compen-sate for the changes. For a cavity that is not beingmodulated, either polarization discrimination orvariations of the Pound-Drever scheme'4 can beused. The polarization discrimination method moni-tors the change in the polarization state of thereflected signal, and the Pound-Driver method moni-tors the change in the phase of a reflected carrier.Neither of these schemes can be easily adapted tolocking a cavity that is being modulated at a high datarate. Furthermore, in a properly configured datamodulator, it is desirable that all optical power bemodulated. Thus there will be no cw carrier presentin the output optical signal for easy discrimination ofthe output phase.
Instead, we achieve cavity stabilization for the100-Mbits/s modulator by monitoring the drop inoutput intensity caused by intracavity absorptionnear the cavity resonance. Because the intensity dipis symmetric with respect to the cavity detuning,however, a dither signal must be applied for us todifferentiate the direction of the detuning. Whenthe cavity is biased on resonance, the symmetricdisplacement at both sides of the absorption dipresults in an output intensity modulation that is attwice the frequency of the modulation signal. Whenthe cavity is biased away from resonance, however,the modulation results in asymmetric displacementaround the absorption dip. In this case the outputintensity exhibits a frequency component at themodulation frequency. Depending on the directionof the cavity detuning, this intensity fluctuationsignal can be either in phase or 180° out of phase withthe modulation voltage. By correlating the outputintensity with the driving signal, therefore, we canderive an error voltage for maintaining the cavity onresonance. The dithering signal is typically a peri-odic modulation signal. However, it is straightfor-ward to show that the correlation characteristics andhence the error signal remain similar for nonperiodicinput signals (i.e., random data modulations). As aresult, we can use the random data stream for thecommunication channel to provide the necessarydither to the cavity and hence maintain the cavity onresonance with the incoming laser signal. However,if the spectrum of vibration contains high-frequencycomponents, the required tracking loop bandwidthmay be high. In this case care must be taken so thatthe cavity stabilization loop is prevented from track-ing out the data modulation. We can accomplishthis by employing source coding to remove low-frequency components in the data stream.
Figure 4 shows a block diagram of the active cavitystabilization loop. The data stream is first dividedinto two paths. One path of the data stream is fedinto a driver amplifier, the output of which we use todrive the EO crystal. The intensity of the signal is
HVEO AnTP
Crystal r
Fig. 4. Block diagram of the cavity stabilization loop using theinput data stream as the dither signal to the modulator. Alsoshown is the optical setup that includes a tandem Faraday isolatorfor separating the input-output signals and a photodiode posi-tioned behind the cavity for monitoring the intracavity intensity:HV, high voltage; LPF, low-pass filter.
then monitored through the use of a fast photodiodeas the cavity is being modulated. Instead of monitor-ing the output intensity directly, the high intracavityoptical power permits a sensitive photodetector tomeasure the small amount of leakage power throughthe highly reflective backmirror. A focusing lensand a photodetector positioned at the back of thehigh-reflectivity mirror sense the variation of intracav-ity intensity as the cavity is being modulated. Thiseliminates the need to split off part of the reflectedsignal for stabilization purposes. The second datastream is delayed through an rf delay line and iscorrelated with the output of the photodetector.The length of the delay line is adjusted so that thepropagation delay through the modulator-optical de-tector is equal to the delay through the rf delay line.We implement the correlation process by using asimple rf mixer, followed by a low-pass filter. Shownin Fig. 5 is a typical output of the rf mixer as thecavity is swept across its resonance. Notice thestrongly dispersive characteristics near the center ofthe dispersion curve that will permit the cavity to be
50mV
trigd
L2
.. 5yt I-1. 776me 200us/div EE 224us
Fig. 5. Output of the rf mixer showing the discriminator curvethat one can use to lock the cavity to resonance.
locked to the center of the curve. We then filter theoutput of the mixer by using a low-pass integrator toderive a control signal for closing the stabilizationloop.
Actual control of the cavity can be done through theuse of an active backmirror mounted on a piezoelec-tric transducer translation stage. Alternatively, ifthe mechanical displacement to be tracked is small,one can track the displacement directly by controllingthe bias on the EO crystal and hence its optical pathlength. In this case the output error signal from thelow-pass integrator is simply fed into a high-voltageamplifier so that the EO crystal is biased.
4. Performance Predictions and Cavity Design
Given an input phase detuning A, we can evaluate thesteady-state phase shift and intensity at the modula-tor output by using Eqs. (5) and (6). Plotted in Fig. 6is the phase shift of the reflected signal from thecavity versus the applied voltage for different valuesof mirror reflectivity R. The applied voltage hasbeen normalized to the half-wave voltage VI,, and ithas been assumed that the cavity is on resonancewhen V = 0. The plot is generated by the assump-tion of no intracavity loss (G = 1). It is seen fromFig. 6 that the output phase shift per unit voltageinput increases as the reflectivity of the input cou-pling mirror and hence the cavity finesse increases.For cavities with a high-reflectance input couplingmirror, only a small voltage has to be applied for alarge output phase shift to be produced.
Figure 6 shows that a high-finesse cavity requiresless voltage input to produce a desired phase shift atthe output. At the same time, it has been shown inFig. 3 that the output intensity of a high-finessecavity is very sensitive to the intracavity loss. Thisis because for a high-finesse cavity the optical signaltraverses through the cavity many times. Conse-quently, any loss within the cavity can result in asignificant loss at the output. Figure 7 shows a plotof the output intensity versus the intracavity loss
4.00
I-
0
U)lU
<: Z
Xot
3.00
2.00
1.00
00 0.025 0.05 0.075
Fig. 6. Output phase shift versus applied modulation voltage forcavities with different values of input coupler reflectivity.
1.0
Z 80%LuZ3 0.6 5ECU-
:3 0.4-
0 02
incdn lih.I9i5entatfr% = 5,a2
1 2 3 4 5
INTRACAVITY LOSS, %
Fig. 7. Plot of output intensity versus intracavity loss for aresonant-cavity modulator with different values of input couplerreflectivity.
when the cavity is biased on resonance with theincident light. It is seen that for R = 95%, a 2%intracavity loss will result in a return power loss ofgreater than 80% when the cavity is biased onresonance. In contrast, a 2% loss for a cavity withR = 85% will only result in an output drop of slightlyless than 40%: Because ofthe sensitivity to intracav-ity loss, tight control of the intracavity loss will berequired for the overall throughput efficiency of themodulator to be improved. This is particularly im-portant for cavities with higher values of inputcoupler reflectivity.
Another problem in using a high-finesse cavity isthe slower switching speed that results from thelonger photon lifetime. The transient response forthe cavity is in general a complicated function of thecavity parameters, and it cannot be predicted directlythrough the use of Eq. (5). Parameters that canaffect the cavity transient response include the inputcoupler reflectivity, the cavity length, and the intracav-ity loss. An inspection of Fig. 2 reveals that the totaloutput amplitude E0 is a sum of the reflected incidentsignal and the leakage from the intracavity field,which is built up from the transmitted incident andthe successive reflections of the incident signals.Consequently, one can develop a discrete-time com-puter model of the phase modulator to simulate theresponse. The output phasor amplitude after succes-sive round trips in the modulator can be modeled as
Et(tN) = tE + rgE(tN-j)exp[i4(tN-1)]
EO(tN) = -rE + tgE(tN.j)exp[i4(tN-l)], (8)
where Et(tN) and E0 (tN) are the amplitudes of thecirculating and the output fields after the Nth roundtrip, respectively. At time tN, the two input signalsto the front surface of the 6talon are the cw incidentEj and the signal reflected from the backmirror Er.The forward-transmitted signal into the cavity will
eventually bounce off the backmirror and return tothe partially reflective surface after a time AT, whichis equal to the round-trip time of the cavity. Thereflected signal can be modeled as a delayed andphase-shifted copy of the transmitted signal Er(tN) =gEt(tN_1)exp[i4(tN_1)]. The amplitude transmittancet, the reflectance r, and the cavity amplitude gain gare modeled as real numbers because any phaseangles resulting from these parameters can be com-bined into the round-trip phase shift + and a staticphase shift at the output. It is straightforward toshow that, after a sufficient number of iterations, theoutput phase shift converges to a value predicted byEq. (5).
Given the reflectivity of the input coupler R, theround-trip power gain G, and the phase modulation+(t), we can simulate the output of the modulator byusing Eq. (8). Plotted in Fig. 8 is the calculatedoutput phase shift versus time for the resonant-cavity phase modulator. The phase detuning pro-cess +(t) is modeled as a step input signal:
r-o t < 0(t) = (9)(N t t0
The amplitude of the detuning signal P0 is adjusted sothat a steady-state phase shift of r/2 is produced.As we see from Fig. 8, the amount of switching timerequired to switch the output phsae increases withincreasing cavity finesse and the front coupler reflec-tivity.
From the analysis above we see that there aredesign trade-offs between the required switchingvoltage, the switching time, and the cavity finesse.On one hand, a cavity with a higher finesse wouldrequire a lower switching voltage. On the otherhand, cavity finesse cannot be increased indefinitelybecause the required switching time also increases
ff2
02
"Ca.
0
-Xd2 - . I I I
0 20 40 60 80 100
TIME, VTround trip
Fig. 8. Phase shift versus time for a resonant-cavity phasemodulator for cavities with different values of input couplerreflectivity. The horizontal axis is plotted in units of round-triptime within the cavity.
with the cavity finesse. Furthermore, a high-finessecavity is also sensitive to intracavity loss and requirescareful control of the loss in order for a reasonablethroughput to be maintained. The choice of the EOcrystal is also a factor in the design of the modulator.The half-wave voltage of the crystal depends on itsEO coefficient and its aspect ratio [/d in Eq. (7)].In order to minimize the required switching voltage,we find it desirable to use crystals with a high EOcoefficient and a high aspect ratio. In practice, crys-tals with a high aspect ratio are difficult to align in theoptical system. Furthermore, they are difficult tohandle. As a result, we find it desirable to keep theaspect ratio of the EO crystal to within 20:1.
For a reasonable performance at 100 Mbits/s to beachieved, the pulse rise time should be shorter than 5ns. Furthermore, because the complexity of con-structing a high-voltage driver increases rapidly withvoltage requirements, one should limit the maximumamount of voltage applied to the modulator to lessthan 20 V. Several point designs for the modulatorthat use different values of input coupler reflectivitywere evaluated. Table 1 shows the results of thesedesigns. It is seen that for a similar cavity dimen-sion, the switching time of the R = 95% cavity is twicethat of the R = 90% cavity, and it is more than threetimes that of the 85% cavity. The required switch-ing voltage, in contrast, is lowest for the R = 95%cavity. The R = 85% cavity will require more than afactor of 3 increase in the voltage requirement. Fora cavity consisting of a 1-cm-long LiNbO3 crystal anda 2-mm air gap between the EO crystal and thebackmirror, the switching time is approximately 7 nsfor a R = 95% cavity.
5. Experimental Demonstrations
A simple experimental demonstration of the resonant-cavity modulator was implemented based on theabove design considerations. A block diagram of theexperimental setup is shown in Fig. 4. The resonantcavity consists of a 1-cm-long LiNbQ3 crystal and ahigh-reflectance (HR) backmirror. One side of theLiNbO3 crystal is coated with a 85% reflectivitycoating and is used as the input coupler to theresonant cavity. The second side of the EO crystal isantireflection coated as a way to reduce intracavityloss. Contact electrodes were deposited on two sides
Table 1. Summary of Several Point Designs for the 1OO-Mbits/sModulator with 1% Intracavity Loss
SwitchingTime
Switching for 10-mm Phase RequiredInput Time LiNbO3 Detuning Voltage for a
Coupler (Round- Crystal for ±'ir/2 1 cm x 1 mmReflectivity Trip with 2-mm Phase LiNbO3
of the LiNbO3 crystal for modulation voltage applica-tion. The total interaction length through the crys-tal is measured to be 7.5 mm, as the electrodes do notcover the entire 10-mm surface of the crystal. TheHR backmirror has a 20-cm radius of curvature.The long radius of curvature is chosen so that thesensitivity to mode-matching optics is reduced. A2-mm air gap between the EO crystal and the backmir-ror results in an effective cavity length of 12 mm anda round-trip time of 0.16 ns. A 10-cm focal lengthlens is used to mode-match the output signal from aLightwave Model 120-OlA laser into the modulationcavity. Because the input and output beams arecollinear, we used a two-stage Faraday isolator toseparate the two beams and to prevent undesirableoptical feedback into the laser.
We amplify the data stream from a pattern genera-tor to the desired voltage level by using a MotorolaCR2424 hybrid amplifier. This amplifier provides a20-dB signal gain, and it has a 3-dB bandwidth inexcess of 200 MHz. We also use the data stream tocorrelate with the measured intracavity intensity andto derive a locking signal. The length of the delayline is adjusted so that the discrimination curveshown in Fig. 5 is maximized. We perform initialalignment of the cavity by first aligning the EOcrystal and the backmirror so that the reflectedsignals from the mirror and the crystal front facet arecolinear. We then perform further alignment byobserving the output optical signal and by sweepingthe bias voltage across the EO crystal until a typicalFabry-Perot transmission peak is observed on theoscilloscope. Finally, we optimize the Fabry-Perottransmission peak by adjusting the mode-matchingoptics.
The output of the modulator is heterodyne detectedby first mixing with the output of a (LO) laser of nearidentical wavelength. The interference between thetwo lasers results in an IF signal that can be regardedas a frequency-translated version of the modulatedoptical signal. The IF signal, after ignoring the shotnoise at the output of the photodetector, is given by
where R is the detector responsivity, Ps and PLO arethe signal and LO powers, and Whet is the heterodynemixing efficiency that depends on the spatial align-ment between the signal and LO beams. The fre-quencies of the signal and LO lasers are offset by anamount 00IF so that the interference signal can beeasily discriminated against dc background. Thephase angle of the IF signal is composed of themodulated output OS(t) and the relative phase driftbetween the signal and LO laser, tD. The relativephase drift SDe can be tracked out by phase-locking thesignal and LO lasers. For a completely suppressedcarrier system such as binary-phase shift-keying chan-nel, one needs a suppressed carrier tracking loop suchas the Costas loop to track the signal and LO phases.
After phase-locking the signal and LO lasers, i.e.,after removing the phase drift term 4be from Eq. (10),we find that the IF signal will contain only theamplitude and phase modulation introduced by themodulator, and it can be examined directly by using aRF spectrum analyzer. Shown in Figs. 9(a) and 9(b)are the resulting IF spectra observed on the spectrumanalyzer after the IF signal is phase locked to a localRF signal at 00IF = 300 MHz. The modulator isdriven by a sinusoidal signal that produces equallyspaced sidebands at increments of modulation fre-quency from the carrier. Ideally, with a pure sinusoi-dal phase modulation, the signal can be decomposedinto
sin(ot + 'D sin omt) = E JQ(D)sin(o) + nwm)tn=O
+ X Jn()sin(w - nfm)t,n=1
(11)
where X and wnm are the IF carrier and modulationfrequencies, respectively; Jn((Q) is the nth order Bes-sel function; and 'D is the modulation index of thephase modulated signal. Equation (11) shows thatfor an ideal phase modulator, the amount of powerthat falls within the nth sideband is proportional toJn2(cF). Therefore, we can calculate the phase modu-lation index by measuring the sideband powers byusing the spectrum analyzer and then fitting themeasured data to the expected sideband-power ra-tios.,5
The method outlined above has been used in thecalculation of the modulation index. Note that theresidual amplitude modulation can result in a smallimbalance of sideband powers, as is evident in thefigures. For this reason, the two measured nthorder sideband powers are averaged before they arefitted to Eq. (11). Shown in Fig. 10 is the resultingphase modulation index as calculated by fitting themeasured sideband powers to the Bessel coefficientsat several sinusoidal driving frequencies. Also plot-ted in Fig. 10 is the expected phase modulation indexcalculated by using Eqs. (5) and (6). At a low drivingfrequency (10 MHz), the data points calculated byfitting the measured sideband powers are in reason-able agreement with the theoretical predictions.When the frequency of modulation increases, how-ever, the higher-order sidebands will be distorted bythe finite modulation bandwidth of the modulator.This bandwidth limitation is a result of the finiteround-trip propagation time within the cavity, and itwill result in suppressions of higher-order sidebands.Another complication when one uses Eqs. (11) di-rectly to compute the modulation index is the residualamplitude modulation introduced by the intracavityabsorption. As we can see from Fig. 3, the outputintensity of the cavity will experience an absorptiondip as one applies voltage to switch the cavity fromone side of the resonance to the other. This inten-sity modulation will further distort the measuredspectrum from the ideal spectrum given by Eq. (11).As a result, the calculated modulation index willexhibit deviations from the theoretical curve at highermodulation frequencies.
An alternative way for us to verify the performanceof the modulator is to correlate the measured IFspectrum with that which is predicted by using thecomputer simulation. This is accomplished by mod-eling the phase detuning process, +(t) in Eq. (7) as atime-varying sinusoid with amplitude +O, and thenrecording the simulated output waveform over sev-eral modulation periods. A Fourier transform of the
2
LU2-I___.
00 LU 0.~~~~~~
Calculated Output0 Phase Shift
M. 0 10MHz Data Fit
10MHz Data Fit00.4
0 1 2 3 4
DRIVE AMPLITUDE, V
Fig. 10. Output phase shift calculated by using Eq. (11) versusthe sinusoidal drive amplitude.
0.04
S 0Z
Z~~~~~
LU 0.02 Eq.(7)@3IC 0 10MHz Data
0 30MHz Data
10OMHz Data
0.00.0 1 2 3 4
DRIVE AMPLITUDE, V
Fig. 11. Phase detuning inferred from the measured sidebandpowers and computer simulation. Also shown is the round-tripphase shift calculated by using Eqs. (6) and (7).
waveform then produces the expected spectrum thatcan be correlated to the measured sideband powers.Because the finite bandwidth limitation caused byround-trip propagation time and the residual ampli-tude modulation caused by intracavity absorption areincluded in the model, the output of the Fouriertransform should closely approximate the measuredIF spectrum with the same phase detuning amplitude.A number of simulations were conducted with vary-ing phase detuning amplitude, and the resultingsideband-power distributions were recorded. Theactual phase detuning amplitude experienced by themodulator can then be inferred by choosing the +0 forwhich the simulated sideband-power distribution bestapproximated that from the measured IF spectrum.Figure 11 shows the inferred phase detuning ampli-tude versus the modulation voltage for the resonantcavity driven at different modulation frequencies.Also shown in Fig. 11 is the expected phase detuningamplitude given by Eq. (7). As we can see, the phasedetuning inferred from the experimental data is ingood agreement with predictions.
Ep REF
POS PK [
1 M 7 I
~_Oj e - - --.=-_ g = = n s i =~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I I = = .i
CENTER 300 MHRES SW M. VOW 3 MN.
SPAN 500 MHzSWP 20. 0 ...
Fig. 12. IF signal spectrum for a modulator driven by a 23-bitpseudorandom sequence at 100 Mbits/s. The amplitude of thesignal is 6.6 V peak to peak: center frequency, 300 MHz; span,
Thus far it has been shown that for sinusoidalmodulation, the amount of phase shift at the outputof the resonant-cavity modulator is in good agree-ment with theoretical prediction. It is of interest toverify that, given a random binary sequence, themodulator will indeed produce a suppressed carrieroutput. Shown in Fig. 12 is the measured IF spec-trum when the modulator is driven by a 23-bitpseudorandom data sequence. The modulation volt-age with maximum carrier suppression is measuredto be 6.6 V peak to peak. This voltage requirement isin good agreement with that predicted through theuse of Eqs. (5) and (6).
6. Conclusion
A resonant-cavity modulator was designed to operateat data rates in excess of 100 Mbits/s. By carefullychoosing the cavity finesse and its dimensions, wefound it possible to control the pulse switching timeto 5 ns and to limit the required switching voltage towithin 10 V. Experimentally, we maintained theresonant cavity on resonance with respect to theinput laser signal by monitoring the fluctuation ofoutput intensity as the cavity was switched. Weaccomplished this cavity locking scheme by using onlythe random data sequence, without the need foradditional dithering of the cavity. One must takecare, however, to prevent the tracking loop fromtracking out the data modulation. This can be accom-plished through the use of simple coding schemessuch as run-length-limited codes.
Compared with waveguide modulators, the reso-nant cavity has a similar modulating voltage require-ment. For example, the design demonstrated in thelaboratory required a switching voltage of 6.6 V at a1.06-pm operating wavelength. Because of its bulkgeometry, the resonant-cavity modulator has thepotential of accommodating higher throughput power.Furthermore, mode matching into a bulk device iseasier and typically can be achieved with higherefficiency. In contrast, unlike waveguide modula-tors, which are essentially traveling wave devices, theresonant-cavity modulator requires that the cavity bemaintained on resonance with respect to the incom-ing laser signal. This results in a more complicatedsystem because additional control loop electronicsmust be incorporated into the modulator design forthe cavity to be maintained on resonance. Further-more, one must take care to control the intracavityloss in order to maintain a high throughput.
This work was carried out by the Jet PropulsionLaboratory, California Institute of Technology, un-der contract with NASA. The authors acknowledgehelpful discussions with R. W. Wallace, T. J. Kane,and E. A. P. Cheng of Lightwave Electronics Corpora-tion.
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