78 OPTICS LETTERS / Vol. 19, No. 2 / January 15, 1994

Frequency acquisition with photorefractive two-wave mixing

Christopher T. Field and Frederic Davidson

Department of Electrical and Computer Engineering, The Johns Hopkins University, Baltimore, Maryland 21218

Received July 6, 1993

We describe how two-wave mixing of light scattered at the entrance face of a photorefractive crystal can be usedto measure the frequency difference between two independent lasers. This method can be used to accomplishinitial frequency acquisition in coherent optical homodyne receivers.

Conventional coherent optical receivers containoptical beam splitters that coherently combine thesignal and the local-oscillator optical fields beforephotodetection. When the difference between thetwo optical field center frequencies falls within thephotodetector electronic bandwidth, a detectabledifference-frequency signal appears in the photode-tector output signal. A phase-lock loop can thenbe used to perform phase or frequency trackingof the local-oscillator laser with the much weakerreceived signal optical field. Coherent homodyneoptical receivers that contain photorefractive opticalbeam combiners, instead of fixed beam splitters, haverecently been demonstrated." Photorefractive two-wave mixing, however, first requires the initialfrequency difference between the two independentlasers to be brought within a few inverse gratingformation times before a transient refractive-indexgrating will begin to form. Once this occurs, acarrier phase-tracking loop can be used to maintainphase coherence between the signal and the localoscillator optical fields.' The grating formation timedepends on the optical power incident upon thephotorefractive material and, for many materials,ranges from milliseconds to several seconds. There-fore the initial laser difference frequency must bebetween a few kilohertz and a few millihertz for aphotorefractive grating to form. Since the lasersmay be tuned over many gigahertz, initial frequencyacquisition can be difficult.

Fixed scattering centers introduced at the entranceface of a photorefractive medium can be used toprovide frequency-difference information. The scat-tered local-oscillator laser light, which is phase coher-ent with unscattered local-oscillator light, will experi-ence amplification by two-wave mixing, whereas themuch weaker signal beam will not experience signifi-cant amplified scattering. Some amplified scatteredpump light will be mode matched to the signal beamand will generate a photodetector output currentwith a strong frequency component at the differencefrequency. The difference-frequency signal can thenbe used to maintain phase coherence between thetwo optical fields with an appropriate phase-trackingloop. This technique is similar to spoiling the local-oscillator field in a conventional coherent receiver inorder to scatter enough local-oscillator light into thesignal beam field mode that a detectable difference-

frequency signal appears in the photodetector output.No amplification of scattered local-oscillator light oc-curs in the conventional receiver, however.

The difference-frequency signal has maximumsignal-to-noise ratio when the photodetector viewsonly the field mode of the signal beam. Conse-quently, both methods require the field of viewof the receiver to be initially restricted to thesignal field mode. This is usually accomplishedwith a system of focusing lenses and irises. Oncecarrier phase synchronization has been attained,the scattering centers in the photorefractive receivermay be removed. This is because a steady-staterefractive-index grating between the phase coherentsignal and pump light has been established and thetwo-wave mixing properties couple pump light intojust the signal beam direction. A single microscopeobjective used to focus signal and coherently coupledlocal-oscillator light onto the active area of thephotodetector will generally allow for a 1-2-degtolerance in the angle of arrival of the signal beam.The irises used to restrict the field of view can beremoved, as the grating will automatically adjustto slow (compared with the grating formation time)changes in the angle of arrival of the signal beamthat do not exceed this tolerance. This does nothappen in a conventional coherent receiver, whichmust maintain a single-mode field of view.

The scattered local-oscillator light is amplified bythe two-wave mixing process as follows. A weaksignal beam, e8 (P, t), and a strong local-oscillator orpump beam, ep(P, t), are incident upon a photorefrac-tive crystal as shown in Fig. 1. The two beams aregiven by

D8 (r, t) = A8 (i)exp[j(wot - ks i P)] + c.c.,gp(P, t) = Ap(P)exp[j(wpt - k, * i)] + c.c.,

(1)

(2)

where (p)(p#, t) is the signal (pump) electric fieldassumed polarized in the y direction, As(p)(r) is thecomplex-valued field envelope, cos(p) is the opticalfrequency, and k,(p) is the propagation direction in thephotorefractive material. Assume that co, - wcp issufficiently large that no space-charge field can formand no photorefractive two-wave mixing between thetwo beams occurs. Also assume that 1A< I « IAp I.

In our experiments the entrance face of thephotorefractive material contained fixed scattering

0146-9592/94/020078-03$6.00/0 © 1994 Optical Society of America

January 15, 1994 / Vol. 19, No. 2 / OPTICS LETTERS

Fig. 1. Optical setup for difference-frequency measure-ment.

centers that weakly scattered some of the incidentpump and the signal light. The scattering wassufficiently weak that the photorefractive couplingbetween the individually scattered beams couldbe neglected. Since the scattered beams do notinteract, they may be considered separately. Letkpd and ksd be representative propagation vectorsof scattered pump and signal beams, respectively.These scattered light beams can form stationaryinterference patterns with the corresponding originalbeam and undergo photorefractive amplification bytwo-wave mixing. By assumption, gratings cannotform between the signal and either the original orthe scattered pump because the optical frequencydifference between them is too large. Therefore insteady state the optical field envelopes are coupled as

,Alp rp,pdA ApdApd (3a)az 2I,

aApd FppdApdApA', (3b)

aA'8 _ -r FSdAAsAdA~d (3c)az 2I,,

aA~d = 1F,SdA~dAAs, (3d)az 2I,,

where A!,(,) is the envelope of the unscattered signal(pump) beam, I is the total optical intensity insidethe crystal, and absorption has been neglected. Thephotorefractive two-wave mixing intensity exponen-tial gain constants of the scattered signal and pumpare rsd and Fppd, respectively. Their values dependon the propagation directions of the beams. Underthe undepleted-pump approximation, Al and Al areessentially constant with distance, and the scatteredsignal and pump envelopes change with distance as

A8d(z) = A~d(0)exp[(1F8,d)dI,'/2I], (4a)

Apd(z) = Apd(0)exp[(Fppd)dI,/2I.], (4b)

where d is the interaction length, IS' = IA'J2, andIp = IAVI2. By assumption, the pump beam intensityis much larger than the signal and the scattering isweak, so IO IP, Ip/Io 1, and IS/IO is negligible.Therefore the scattered signal and pump have enve-lope functions given by

A~d(z) A.d(0), (5a)Apd(z) = Apd(0)exp[(Fppd)d/2]. (5b)

The scattered signal intensity is nearly constantthroughout the material, while the scattered pumpexperiences the normal two-wave mixing intensitygain.

The intensity on the photodetector surface at thepoint r is given by

Id(r) = 1A8(0)exp[j((ot - ks * r)]+ AP(O)exp(dTP,pd/2)exp[j(wct'- kpd _ p)]12,

(6a)

= IS(O) + Ipd(0)exp(dFppd) + 2 CIs(0)Ipd(O)

X exp(dFp pd/2)cos[(w, - wP)t + r * (k8 - kpd)]-

(6b)

If the difference r * (ks - kpd) averaged over thephotodetector area and field of view is small enough,the beat signal can be detected. The photodiodeoutput current is proportional to an average over thephotodiode area and may be expressed as

id t)= qG 7/ U. + Ipd + 277mpd Cos(wo - P)t],

(7)

where q is the electron charge, G is the photodetectorgain, 77 is the photodetector quantum efficiency, hpis the photon energy, I, and Ipd are the averagedintensities of the two optical beams, and 77m is theheterodyne mixing efficiency. The latter is expectedto be small because pump beams scattered from dif-ferent scattering centers have arbitrary phase rela-tionships with respect to one another. The signal-to-noise ratio (SNR) of the difference-frequency signalis given by

SNR = 127m2 7)181pd/hv[F77 (Is + Ipd) + TN]2B

(8)

where F is the photodiode excess noise factor, B is theelectronic bandwidth, and TN is the thermal noise,expressed as

TN==- 2KBTRLq2 G2 /hv (9)

with KB Boltzmann's constant, T the receivernoise temperature, and RL the photodetector loadresistance. Even though the heterodyne mixingefficiency is small, the beat signal can be identified,provided that IS/2B is large enough. When thedenominator of Eq. (8) is dominated by the thermalnoise term, the SNR is linear in the signal beamoptical power.

Two diode-laser-pumped Nd:YAG nonplanar ringoscillator lasers operating at 1.06 ,tLm (LightwaveElectronics Models 120 and 122) provided the signaland the pump optical beams, respectively. Theoptical output power of each laser was 50 to 60 mW.The natural divergence of the pump laser fullyilluminated a 1 cm X 1 cm X 1 cm InP:Fe crystal.The signal beam passed through roughly a meterof single-mode optical fiber and was attenuated to

79

80 OPTICS LETTERS / Vol. 19, No. 2 / January 15, 1994

-60

E --7

-8O -8a3)0(L

0~- -

- 1 0MU

0

-1 1 0

Beat signal power with voltageBeat signal power with no voltage I

10

Received signal power (nW)

Fig. 2. Electrical power at the optical difference fre-quency as a function of optical signal power transmittedthrough the crystal. Shown are the beat signal powerwith and without photorefractive coupling, the peak levelof the noise floor, and the average power of the noisefloor. Photorefractive coupling increased the beat signalby more than 10 dB. For all optical signal levels greaterthan 3 nW, the beat signal is more than 20 dB above theaverage noise floor. The solid lines are least-squares fitsto the data.

the nanowatt range by neutral-density filters. Bothoptical beams were s polarized. The external anglebetween the pump and the signal was 4.3°, whichgave a grating spacing of 14 ,um. The signal beamdiameter at the crystal entrance face was 2 mm.Figure 1 shows the experimental configurationused. The signal was focused through iris 2, whichwas -0.9 mm in diameter. Iris 1 was made assmall as possible without attenuating the intensitythrough iris 2. A separate interferometer providedan independent measurement of the frequencydifference.

The InP:Fe crystal faces were [110], [110], and[001]. An external dc electric field of 6 kV/cm wasapplied in the [001] direction. The optical faces wereantireflection coated, but in the presence of the ex-ternally applied electric field the coatings degraded,which provided the scattering centers. For thermalstability,6 7 the crystal was clamped between water-cooled heat sinks nominally kept at 20 'C. The crys-tal absorption coefficient was 0.5 cm-'. When thetwo lasers were phase locked with a conventionalinterferometer, the signal experienced a photorefrac-tive two-wave mixing intensity gain of -25. Theoptical intensity of the amplified scattered pump lighttransmitted through both irises was typically 2.2 nW.

The photodiode was an IR-enhanced Si avalanchephotodiode, 77 = 35%, with a transimpedence am-plifier with load resistance RL = 800 fl. Thebandwidth was greater than dc to 50 MHz, andthe avalanche photodiode gain was approximately170 ± 30. The amplifier was connected to a Hewlett-Packard HP 8590B spectrum analyzer through a dcblocking capacitor (Picosecond Labs 5550B), whichhad a 10-kHz lower cutoff frequency. The spectrumanalyzer was set for a 10-kHz filter bandwidth.

Figure 2 shows the magnitude of the beat signalversus the optical signal power transmitted throughthe photorefractive crystal. The frequency differ-ence could be tuned to well over 50 MHz with, nosignificant change in the beat signal power. Thedata were collected at a difference frequency of 20 to25 MHz. The deduced heterodyne mixing efficiencywas very low, less than 1%, but was clearly largeenough for the beat signal to be detected. Thelow mixing efficiency is not surprising becauseof the large number of fixed scattering centers,which reduced the spatial coherence of the scatteredlocal oscillator light. The beat signal powers forthe case when the crystal voltage was removedand no significant photorefractive coupling of thescattered pump beams occurred are also shown.The bottom curve in Fig. 2 shows the peaks ofthe spectrum analyzer noise floor. Despite the lowmixing efficiency, the beat signal was easily identifiedabove the noise floor. Photorefractive amplificationof the scattered pump light increased the electricalbeat signal power by 10 dB over the value that wasdue to scattering only.

References

1. K. Nguyen, R. Sanchez, T. K. Gustafson, T. K. Yee, andR. Neurgaonkar, Opt. Lett. 16, 1811 (1991).

2. L. E. Adams and R. S. Bondurant, Opt. Lett. 16, 832(1991).

3. F. M. Davidson and C. Field, IEEE Photon. Technol.Lett. 4, 1295 (1992).

4. L. E. Adams and R. S. Bondurant, in Conference onLasers and Electro-Optics, Vol. 11 of 1993 OSA Tech-nical Digest Series (Optical Society of America, Wash-ington, D.C., 1993), p. 88.

5. F. Davidson and C. T. Field, "Optical phase lock loopwith a photorefractive optical beam combiner," IEEEPhoton. Technol. Lett. (to be published).

6. G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, J. Appl.Phys. 66, 3798 (1989).

7. A. Abdelghani-Idrissi, C. Ozkul, N. Wolfer, P. Gravey,and G. Picoli, Opt. Commun. 86, 317 (1991).

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