Double frequency modulation spectroscopy: high modulationfrequency with low-bandwidth detectors
David E. Cooper and T. F. Gallagher
In this paper, we describe experimental and theoretical investigations of two variations of frequency modu-lation (FM) spectroscopy that use two electrooptic modulators. In the first variation, both modulators arefrequency modulators (FM-FM), and, in the second, one is a frequency modulator and one is an amplitudemodulator (FM-AM). The essential advantage of FM-FM and FM-AM spectroscopy is that sensitive low-bandwidth detectors, such as photomultiplier tubes, can be used to detect signals generated by the absorp-tion of sidebands displaced from the carrier by frequencies far above the detector cutoff frequency. Thesetwo variations are complementary in the sense that, in situations where optical power is at a premium, theFM-FM scheme is most appropriate, and in situations where modulator drive power is at a premium, theFM-AM scheme is most appropriate. Using either of these variations, we have detected the absorption of700-MHz sidebands with photomultiplier tubes whose cutoff frequencies lie below 100 MHz.
1. Introduction
Frequency modulation (FM) spectroscopy' is a sen-sitive optical spectroscopic technique for measuringabsorption and dispersion in practically any opticalmedium. One of the most promising areas for the ap-plication of FM spectroscopy is in the detection of at-mospheric trace gases and hazardous materials. Ab-sorptions as small as 10-4 have been easily detected withFM spectroscopy using either single-mode1 or multi-mode2 cw lasers. It appears that an optimized (shot-noise-limited) visible wavelength FM system should becapable of detecting an absorption as small as 10-6 witha 1-sec integration time.
The reason the technique is so sensitive becomesapparent if we quickly review the principles of FMspectroscopy. A laser beam of frequency WL is phase-modulated at frequency Q, which' is typically, but notnecessarily, far greater than the linewidth AWL of thelaser, i.e., Q >> AWL. Typical values are Q = 500 MHzand AWL = 1 MHz. In the limit of low-modulationindex, the laser beam acquires sidebands at WL iQ, andwhen the modulated laser beam impinges on a squarelaw detector, such as a photodiode, each sideband beats
David Cooper is with SRI International, Electro-Optics SystemsLaboratory, 333 Ravenswood Avenue, Menlo Park, California 94025,and T. F. Gallagher is with University of Virginia, Physics Depart-ment, Charlottesville, Virginia 22901.
with the carrier to produce a component of the photo-current at Q. However, the two beat signals are 1800out of phase and, therefore, cancel. If prior to photo-detection the modulated beam traverses a mediumwhose complex index of refraction differs for the twosidebands, this sideband cancellation is incomplete, anda photocurrent at Q is produced. One case of practicalinterest is where a differential absorption between thetwo sidebands occurs. Since there is no intrinsic lasernoise at Q for the case where Q >> AWL, the absorptionappears against a background that is in principle shot-noise-limited. Even in cases where Q - AWL, it hasbeen demonstrated 2 that laser noise at Q poses no sig-nificant problems in cw FM experiments because thisnoise bears no fixed phase relationship to the modulatordrive frequency and, therefore, cancels when the pho-tocurrent is heterodyned with the local oscillator in arf mixer.
In the monitoring of an absorption using FM spec-troscopy, optimum sensitivity is obtained when themodulation frequency Q exceeds the absorption line-width. For Doppler-broadened gases, this means Q2 GHz, whereas for atmospheric pressure-broadenedgases this requires Q- 10-20 GHz. In the visiblewavelength region, neither condition poses very seriousproblems, since LiTaO3 modulators 3 and GaAsSchottky barrier photodiodes4 with sufficient band-width have been demonstrated. Although the high-speed GaAs photodiodes do not have the sensitivity ofmost conventional visible wavelength detectors, this isusually not a serious problem, since one can easily putseveral milliwatts of power on the detector with laserlight sources. However, an interesting and promising
1 May 1985 / Vol. 24, No. 9 / APPLIED OPTICS 1327
extension of FM spectroscopy is to the 8-12-,gm atmo-spheric window region, where numerous molecularspecies have strong and characteristic absorption fea-tures, and where carbon dioxide and semiconductordiode laser sources are available. For work in this re-gion, CdTe modulators with 16-GHz bandwidths havebeen constructed.5 However, similarly fast and sensi-tive detectors are unavailable. Sensitive HgCdTe de-tectors are limited to frequencies below -2 GHz,6 andultrafast 8-10-GHz pyroelectric detectors suffer fromvery low sensitivity.
This bandwidth limitation of sensitive photodetectorsis a severe problem in the extension of FM spectroscopyto nonvisible spectral regions and in the visible spectralregion under conditions where optical power levels areconstrained to be low. We discuss here two alternativeFM approaches that circumvent the detector band-width limitation and present experimental results wehave obtained using these approaches in the visiblespectral region. We begin with a theoretical descriptionof double frequency-modulated (FM-FM) light andamplitude-modulated FM light (FM-AM) in Sec. II.Although the case of double frequency-modulated lighthas been treated theoretically in the literature,7 themotivation for that treatment was quite different fromthe one stated here, and in addition the formalism needsto be extended to correspond with the actual experi-mental cases discussed in Sec. III.
11. Theoretical DescriptionWe consider here a description of the electric field
and power spectrum of laser light at frequency WL thatis directed first through a frequency modulator oper-ating at Ql, then through either a second frequencymodulator or an amplitude modulator operating at Q2,and finally through an optical medium that interactsdifferently with the different frequency components ofthe double modulated light. The beam is subsequentlymonitored with a photodetector that generates a pho-tocurrent proportional to the square of the electricfield.
A. FM-FM Light
We first consider the case where both modulators arefrequency modulators, and for convenience we use thenotation of Ref. 7. The electric field for this case canbe written as
where Ml and M2 are the modulation indices of the firstand second modulators, respectively, and the J, (M)factors are Bessel functions of integer order. The effectof the optical medium is represented by a set of complexfrequency-dependent transmission factors, Tpq T(L+ pQ, + qQ2), and the transmitted electric field is,therefore, ET(t) = 1/2ET(t) + c.c. with
ET(t) = Eo Jp(Ml)Jq(M2)T(WL + PQj + qQ2)pq=-+
X expi(WL + PQ + qQ2)t. (2)
The components of the laser power spectrum that areof interest in FM spectroscopy are those at the differ-ence frequency nQ, + mQ 2 given by
- -
Ps(t) = T(t)ER(t)87r
= cEo3 Jp(Ml)Jq(M2)Jp'(M1)Jqd(M2)8wr p,q p',q'
X TpqTtq, expi[(p - p')Ql + (q - q')Q2]t- (3)
We will, for reasons that will become apparent, restrictthis general equation to the special case of Q, = 2W + a,Q2 = c, and (p -p') = ±k, (q - q') = 1. Under theseconditions, the component terms of Eq. (3) that havefrequencies ka occur whenever = 2k and are givenexplicitly by
We will further restrict Eq. (4) to the case where k = 1.The idea here is that W is an arbitrary frequency, chosento be coincident with a particular absorption feature ofinterest, and a is a much smaller frequency, chosen tolie within the passband of the photodetector in use andalso much smaller than the linewidth of the absorptionfeature. Under these conditions Eq. (4) reduces to
Ps(Ut) = CE2Jp(M1)Jq(M2)87r pq
X [Jp-1(Ml)Jq+2(M2)TpqT_lq+ 2 exp(iat)+ Jp+l(M)Jq-2(M2)TpqT;+,q-2 exp(-iat)]
We note that if all the transmission factors Tij are setequal to unity in this expression, a situation corre-sponding to no absorption or dispersion, then with thehelp of Neumann's addition theorem for Bessel func-tions, 8 it is easily shown that PS (at) = 0, as expected.Clearly, when absorption and dispersion are present,many possible ways of generating beat signals at aexist.
To proceed further, one needs to specify whichtransmission factors differ from unity. We will assumethat the modulation index of the first modulator issmall, Ml < 1, so that all terms other than p = 0, +1 arenegligible. In addition, we will consider the case ofdifferential absorption and dispersion between side-band groups centered at +W. These sideband groupsare the triplets (W, W + a, co - ) and (-co, -co + , -co- a), respectively. Hence in this case the correspondingnonunity transmission factors appearing in Eq. (5) are(To1, T,,, T. 3 ) and (To-, T-1 , T,_ 3). With theseapproximations, the beat signal appearing at a is givenby
In deriving this expression, we have written Tpq = exp- (6pq + ipq) and assumed a weak interaction limitbetween the medium and the optical field. In writingthe absorption and phase terms, we have replaced thenumerical subscripts by their corresponding frequen-cies. The essential features of this result are similar tothose for conventional FM spectroscopy. The inphase(cosat) term arises from a differential between weightedaverages of the absorptions of the upper and lowertriplet groups. The quadrature (sinat) term arises fromdifferentials between the average phase shifts of upperand lower sideband pairs. In the limit where a- is smallrelative to the linewidth of the absorption feature ofinterest, and for the case where the absorption is probedby the upper sideband triplet, we may write
t3-w-cr s-so = -w+c r b,
4 -co-e = = = ' -(-w = b
where 6 and 4 are the constant background absorptionand phase shift, respectively. Our signal then reducesto
P 8(Tt) = 8 2MJW(M 2 )A6 cosot, (7)
where A(3 = (+ - ). The inphase term in this ex-pression is identical to that obtained in conventionalFM spectroscopy with the exception of the factor2J2(M 2 ). Note, however, that no quadrature signalarises from the anomalous dispersion. If the secondmodulator is driven with M2 1.8, then J1(M2 ) takeson its maximum value yielding 2J (1.8) = 0.67. It isthus possible to obtain signals in FM-FM spectroscopycomparable with those in conventional FM spectros-copy, provided the second modulator is driven at highmodulation index.
The origin of the heterodyne beat signals appearingat a in FM-FM spectroscopy becomes clear if we con-sider the effect of both modulators in the frequencydomain, as illustrated in Fig. 1. The FM light from thefirst modulator is shown in Fig. 1(a); the upper andlower sidebands are separated from the laser frequencyWL by 2 + a; and we have drawn the sideband ampli-
tudes assuming M1 1. The effect of the second fre-quency modulator on this FM spectrum is shown in Fig.1(b). For convenience, we have taken M 2 2.4, whichcorresponds to the first zero of Jo. Consequently, thesecond modulator shifts all the optical power from thefirst modulator to different frequencies; i.e., there arenow no components at WL, and WOL 1 (2 + ). Thepresence of these components, however, does not changethe heterodyne signal obtained by the absorption fea-ture located at co, since no J(Ml)JO(M 2 ) or J(Ml)-JO(M2 ) factor appears in Eq. (6). Figure 1 shows clearlythat beat signals at a- arise from the sideband products
1:
0
0
-2.-. - 0 0 c
RELATIVE FREQUENCY
2.+1a
Fig. 1. Optical power spectrum of (a) pure FM light at frequency2w + and modulation index M1, and (b) the light produced by di-recting this FM light through a second frequency modulator operating
at frequency w and modulation index M 2.
JO(M1 )Jl(M 2) J1 (M1)JA(M2) and J(Ml)J(M 2)J1 (Ml)J3 (M2 ). These are exactly the factors appearingin Eq. (6).
B. FM-AM Light
Let us now consider the case in which the secondmodulator is an amplitude modulator, constructed by,placing a frequency modulator between linear polarizerscrossed at 1450, so that no light is transmitted if thesecond modulator is not driven. (For modulators withbirefringent crystals, a bias voltage must be used.) Inthis case, the electric field can be written9
- Z Jp(Mj) expi(WL + P%)tJ + c.c. (8)This is simply the FM-FM electric field given in Eq. (1)minus the pure FM electric field from the first modu-lator. As a result, in the FM-AM configuration evenwhen M2 is small, the components at WL and WL P Q1are almost completely suppressed, but components atfrequencies WL I p I q 2 with q # 0 are unatten-uated. Thus one obtains a frequency spectrum essen-tially identical with that obtained in the FM-FM con-figuration when M 2 is large. Hence these two config-urations are complementary in that FM-FM is prefer-able when optical power levels are low and the secondmodulator can be driven at high modulation index, andFM-AM is preferable when optical power levels are highand the second modulator is constrained to be drivenat low modulation index.
The effect of an optical medium on the FM-AMelectric field is again represented by a set of complexfrequency-dependent transmission factors T and thetransmitted field can be written ET(t) = 2[ET(t) -eT(t)] + c.c. with ET(t) given by Eq. (2) and T(t) givenby
1 May 1985 / Vol. 24, No. 9 / APPLIED OPTICS 1329
J0 (Ml)
t, (Ml)
(a}1(
J-1 (M1 > _ J1 (M1)J1 (M2 ) Absorption
-J1 (M, )J 3 (M2 ) Feature
Jo( Jj(
(b) _ _ I i I _
J(MI J-1(M2)
l l ~~J-1 (M1 XJ1(M2)J.(M) J-1 (2)
I ,a 1 .1 I1
PolarizingBeam
Lens Splitter
Fig. 2. Experimental configura-tion used for FM-AM spectrosco-py and for FM-FM spectroscopywhen no dc bias voltage is appliedto the second modulator crystaland the polarizers are removed.
eT(t) = Eo Jp(Ml)T(WL + Pil) expi(wOL + PQI)t- (9)
The power spectrum of this FM-AM light at the variousbeat frequencies of interest is given by P, (t) ETET -
(EWT + ET) + jTeT It is straightforward to showthat with the same conditions used to treat the FM-FMcase, only the ETE' term gives rise to beat signals at a.Hence P, (at) for FM-AM light is identical to that forFM-FM light and given by Eq. (6).
111. Experimental Results
We have investigated experimentally both FM-FMand FM-AM spectroscopy in the visible spectral regionusing two LiTaO3 electrooptic modulators driven atfrequencies in the 500-1500-MHz range. In both cases,signals were recovered using either photomultipliertubes or semiconductor photodiodes. We obtained thehighest SNRs in the FM-AM configuration by drivingthe amplitude modulator cw and detecting the signal,with a photodiode.
A. FM-AM Experiments
The schematic of our experimental configuration forFM-AM spectroscopy is given in Fig. 2. The laser is aSpectra-Physics 102 He-Ne laser operating at 632.8 nm,which has a power of 2 mW and a cavity mode spacingof 641 MHz. A single cavity mode with -1 mW ofpower is selected from this laser by means of a linearpolarizer. The laser beam is gently focused through thefirst electrooptic modulator, which is driven cw at fre-quency 2W + a = 1460 MHz by a Hewlett Packard (HP)8620 sweep oscillator and a solid-state power amplifiercapable of 10-W output. The drive power is adjustedto put 15% of the optical power in each of the two side-bands, corresponding to a modulation index M1 0.8.Figure 3 shows a typical power spectrum of this pureFM light. The optical beam is next focused gentlythrough a second electrooptic modulator, which isplaced between two linear polarizers crossed at ±450.This modulator is driven at frequency w = 700 MHz byan EPSCO PG5kB pulsed cavity oscillator with a
w
0~-J
-)0
-1460 0 1460
RELATIVE FREQUENCY (MHz)
Fig. 3. Optical power spectrum of pure FM light with a 1460-MHzmodulation frequency.
250-Hz pulse repetition frequency and 50-,usec pulsewidth. The rf power level is adjusted to give a modu-lation index of M2 - 1. Due to the natural birefringenceof LiTaO 3 , a dc bias voltage of up to 200 V must be ap-plied to the crystal to ensure that the transmitted beamis extinguished when no rf is applied to the modulator.The resulting frequency-amplitude modulated beamnext impinges on a piezoelectrically scannable Spec-tra-Physics 410 etalon of 30-GHz FSR and 600-MHzbandwidth. We observe the retroflection from theetalon, which decreases as the etalon is scanned throughthe laser frequency, mimicking a 25% absorption.
1330 APPLIED OPTICS / Vol. 24, No. 9 / 1 May 1985
Lens Lens Lens
CO-J
V/)
U-
-700 700
RELATIVE FREQUENCY (MHz)
Fig. 4. FM-AM signal at 60 MHz resulting from absorption ofsidebands at 700 MHz obtained with 65 nW of optical power incident
on an RCA 931 PMT biased at 900 V.
The retroflected beam is directed through two neu-tral-density filters having a combined transmittance of3% onto a RCA 931 photomultiplier tube with 600-900V applied across the dynode chain. Under these con-ditions, the PMT bandwidth is <100 MHz, and theaverage incident optical power is -65 nW. A significantadvantage to driving the amplitude modulator with apulsed rf oscillator is that the light is only incident onthe PMT during the rf pulse. Thus the PMT may beexposed to much higher light levels than it would be ableto stand on a cw basis, thereby improving the shot noiselimit of the signal. The detector photocurrent is am-plified 20 dB using a HP461A amplifier and fed into therf port of a Mini Circuits ZFM-3 mixer. The local os-cillator (LO) port of the mixer is driven by 5 mW of peakpower at frequency a = 60 MHz. This signal is gener-ated by mixing part of the sweep oscillator output witha doubled portion of the pulsed cavity oscillator output.The mixer and doubler used here are Mini Circuitsmodels ZFM-150 and FK-5, respectively. The mixeroutput is amplified to a 5-mW peak using a HP 462Aamplifier. The intermediate frequency (IF) output ofthe ZFM-3 mixer is monitored by a PAR 162 boxcarsignal averager triggered by pulses from the cavity os-cillator. FM spectra are recorded by driving an X- Yrecorder with the output of the boxcar as the frequencyof the etalon is scanned.
Figure 4 shows a FM-AM signal obtained with 65 nWof optical power incident on the PMT biased at 900 V.This signal exhibits the asymmetric feature of a normalFM signal with the two peaks separated by 1400 MHz,twice the drive frequency of the amplitude modulator.The signal is exactly what is obtained in a normal FMconfiguration using a 700-MHz frequency modulatorand a 1-GHz photodetector, but it has been recoveredin our experiment by use of an additional amplitudemodulator and a 100-MHz PMT. Although our signalprocessing is far from optimum, we estimate from theobserved SNR (100) that an absorption as small as 2.5X 10-3 could be measured in this configuration. Thisis an impressive sensitivity given the small amount ofoptical power incident on the detector.
We also performed FM-AM experiments using asemiconductor photodiode and a cw rf driver for theamplitude modulator. For these experiments, thefrequency modulator is driven at 1060 MHz by the HP8620 sweep oscillator, and the amplitude modulator isdriven at 500 MHz by a General Radio 1209B oscillatorand Boonton 230A amplifier. The rf drive to the am-plitude modulator is again adjusted to give a modulationindex M2 - 1. The detector used is a HP 4220 PINphotodiode having a bandwidth in excess of 1 GHz.The IF signal at 60 MHz is again detected using theZFM-3 mixer. However, to improve the SNR, we me-chanically chop the laser beam at 100 Hz and detect themixer output with a lockin amplifier referenced to thechopping frequency. FM spectra are recorded bydriving an X- Y recorder with the lockin output as thefrequency of the etalon is scanned.
Figure 5 shows the FM-AM signal obtained with -0.5mW of average power incident on the HP 4220 photo-diode. As before, the signal exhibits the asymmetrycharacteristic of a normal FM signal with the two peaksseparated by 1000 MHz, twice the drive frequency of theamplitude modulator. From the observed SNR, weestimate a minimum detectable absorption of 2.5 X10-4. This is comparable with the minimum detectableabsorptions reported using conventional FM spectros-copy.
B. FM-FM Experiments
The FM-FM experiments are performed using theconfiguration illustrated in Fig. 2 with the exceptionthat the two linear polarizers are removed from thebeam path and no dc bias voltage is applied to the sec-ond LiTaO3 crystal. The first frequency modulator isdriven cw at 2W + a = 1410 MHz with M1 - 0.8, and thesecond frequency modulator is driven with the EPSCOoscillator at frequency W = 700 MHz. Thus the offsetfrequency is = 10 MHz in this case. The rf powerlevel of the pulsed cavity oscillator is adjusted to givea modulation index of M2 - 2 maximizing the opticalpower in first sidebands. Figure 6 shows the powerspectra of pure FM light from the second modulator forvarious settings of the rf power level. Figure 6(a) is thespectrum with no rf power applied [i.e., Fig. 6(a) showsthe laser carrier spectrum], and Figs. 6(b), 6(c), and 6(d)are the observed power spectra corresponding to mod-
1 May 1985 / Vol. 24, No. 9 / APPLIED OPTICS 1331
I I
I1:0
(0
zV)
AL
-500 500RELATIVE FREQUENCY (MHz)
Fig. 5. FM-AM signal at 60 MHz resulting from absorption ofsidebands at 500 MHz obtained with 0.5 mW of optical power incident
on a HP 4220 photodiode.
ulation indices of 1.7, 2.2, and 3.2, respectively. Wehave, in fact, obtained modulation indices in excess of4 using the EPSCO driver. In Figs. 6(b) (c) and (d), thecarrier peak is more pronounced than expected becausethe light incident on the second modulator is depolar-ized by the natural birefringence of the LiTaO3 crystalin the first modulator, and this depolarized componentis not affected by the second modulator.
FM-FM spectra are measured using either an EMI9558 PMT biased between 600 and 1000 V and gated onduring the rf pulse to the second modulator or an un-gated EG&G FND 100 photodiode. Under these biasconditions, the PMT bandwidth is -20 MHz. Thebandwidth of the photodiode is -1 GHz. Figure 7shows the FM-FM signal recovered with -16 nW ofoptical power incident on the 9558 PMT biased at 1000V. The detector photocurrent signal at 10 MHz isamplified 20 dB by the HP 461A amplifier and fed intothe rf port of the ZFM-3 mixer. The LO signal to theZFM-3 is generated in a fashion identical to that de-scribed in the FM-AM experiments. The IF output ofthe ZFM-3 is monitored by the PAR 162 boxcar
0-JI
U1
C-
1 I I I I
-1400 -700 0 700 1400
RELATIVE FREQUENCY ( MHz)
Fig. 6. Optical power spectra of (a) unmodulated laser light and FMlight from the second modulator ( = 700 MHz) with rf drive poweradjusted to give modulation indices of (b) 1.7, (c) 2.2, and (d) 3.2,
respectively.
triggered by the cavity oscillator. As expected, thesignal peaks are separated by 2W = 1400 MHz, and theobserved SNR (-150) implies a minimum detectableabsorption of -1.7 X 10-3, comparable with the SNRobserved in the corresponding FM-AM case of Fig. 4.
The FM-FM signal recovered with the EG&G pho-todiode is shown in Fig. 8. Again the peaks are sepa-rated by 2co = 1400 MHz, and, as is the case in ourFM-AM measurements, the observed SNR is largerthan obtained with a PMT. This is largely because, forthe diode measurements, the average optical powerincident on the detector is in the milliwatt (rather thanthe nanowatt) range.
IV. Conclusions
We have demonstrated two variations of FM spec-troscopy that use two electrooptic modulators. TheFM-FM configuration uses two frequency modulators,and the FM-AM configuration uses one frequency and
1332 APPLIED OPTICS / Vol. 24, No. 9 / 1 May 1985
(b)
I I I I I
l
-J
CDC/)
LL
CL
-700 700RELATIVE FREQUENCY (MHz)
Fig. 7. FM-FM signal at 10 MHz resulting from absorption ofsidebands at 700 MHz obtained with 16 nW of optical power incidenton a EMI 9558 PMT biased at 1000 V and gated on during the rf
pulse.
one amplitude modulator. In either configuration, thefirst modulator is driven at frequency i 1 = 2W + a andthe second at Q2 = W. The signal of interest is theFourier component of the photocurrent at frequency a.The great advantage of FM-FM and FM-AM spec-troscopy is that W can be any frequency, chosen tocoincide with an absorption feature of interest, subjectto constraints on modulator design. The frequency ais chosen to lie within the bandpass of the detector usedand be much smaller than the absorption linewidth.We have shown that the inphase signal in FM-FM andFM-AM spectroscopy is simply the product of 2J (M 2 )with the inphase signal obtained in conventional FMspectroscopy. A penalty that one pays in FM-FM andFM-AM spectroscopy is the necessity of using twomodulators, one of which must operate at a frequencytwice the frequency of a comparable single-modulatorFM system.
We have conducted experiments in both configura-tions and verified that indeed one can use narrowband
N
I0
-J
CDU/)
U-
U-
-700 700
RELATIVE FREQUENCY (MHz)
Fig. 8. FM-FM signal at 10 MHz resulting from absorption ofsidebands at 700 MHz obtained with 0.5 mW of optical power incident
on an EG&G FND 100 photodiode.
detectors to monitor absorption of sidebands displacedfrom the carrier by frequencies far above the detectorcutoff. The two configurations are complementary inthat FM-FM spectroscopy is most appropriate whenoptical power levels are low and available rf drive powerto the second modulator is high, and FM-AM spec-troscopy is most appropriate when optical power levelsare high, and available rf drive power to the secondmodulator is low. Considering the signals we haveobtained using only a few tens of nanowatts on a PMT,a very attractive future application of FM-FM andFM-AM spectroscopy is a sensitive visible wavelengthabsorption spectrometer using non-laser light sources,such as xenon or mercury-vapor lamps. In addition, theFM-AM configuration should prove invaluable in the9-11-Atm CO2 laser region, where optical power levelsare high, but where detector bandwidths are low, andavailable crystal halfwave voltages preclude easy at-tainment of high modulation index in the secondmodulator.
The authors wish to thank G. C. Bjorklund for use ofone of the LiTaO3 modulators and J. P. Watjen forgenerous loans of microwave equipment. This workwas supported by SRI International IR&D funds.
References1. G. C. Bjorklund, "Frequency-Modulation Spectroscopy: A New
Method for Measuring Weak Absorptions and Dispersions," Opt.Lett. 5, 15 (1980).
2. D. E. Cooper and T. F. Gallagher, "Frequency-Modulation Spec-troscopy with a Multimode Laser," Opt. Lett. 9, 451 (1984).
3. N. H. Tran, R. Kachru, P. Pillet, H. B. van Linden van den Heuvell,T. F. Gallagher, and J. P. Watjen, "Frequency-Modulation Spec-troscopy with a Pulsed Dye Laser: Experimental Investigations
1 May 1985 / Vol. 24, No. 9 / APPLIED OPTICS 1333
of Sensitivity and Useful Features," Appl. Opt. 23, 1353 (1984).4. S. Y. Wang, D. M. Bloom, and D. M. Collins, "20-GHz Bandwidth
GaAs Photodiode," Appl. Phys. Lett. 42, 190 (1983).5. G. M. Carter, "Tunable High Efficiency Microwave Frequency-
Shifting of Infrared Lasers," Appl. Phys. Lett. 32, 810 (1978).6. D. L. Spears, "Theory and Status of High-Performance Hetero-
dyne Detectors," Proc. Soc. Photo-Opt. Instrum. Eng. 300, 174(1981).
7. H. Lotem, "Extension of the Spectral Coverage Range of Fre-quency Modulation Spectroscopy by Double Frequency Modula-tion," J. Appl. Phys. 54, 10 (1983).
8. M. Abramowitz and I. A. Stegun, Eds., Handbook of MathematicalFunctions with Formulas, Graphs, and Mathematical Tables(NBS Applied Math. Series 55, Dec. 1972).
9. A. Yariv, Quantum Electronics (John Wiley & Sons, New York,1975).
Electrooptics continued from page 1326
terminal equipment, using a return fiber. This enables the mea-surement to be made independent of the instabilities associated withthe optical source and the feed fiber.
The system has been tested and showed outstanding performance.Planned work concerns development of techniques for multiplexingseveral of the sensors to a single optical fiber link.
The second project addresses a special niche in the area of opticalfiber communication. Currently, for long-distance optical commu-nication, infrared systems with a 1.1- to 1.6-/im wavelength are used.Short-haul optical communication (such as within a factory or largenaval vessel) has not been adequately addressed by using appropriatemethods and realizations to fulfill special needs. This is the needSenior wants to respond to. He uses 0.8-Am radiation and concen-trates on special criteria: low noise and a truly remarkable dynamicrange (23 dB) receiver. The novelty consists in inserting a logarithmicstage in the amplifier. By two-stage transistor action the signal isthen strongly compressed. The entire receiver is realized on a hy-bridized printed circuit, about 1-square-inch large.
ConclusionIt appears that the scientists in Manchester are engaged in a variety
of (somewhat unconnected) areas of opto-electronic and micro-elec-tronic research which are attracting notable industrial interest.
The Laser Radar Report will be published in a subsequentissue.
