1044 J. Opt. Soc. Am. B/Vol. 21, No. 5 /May 2004 Zhang et al.

Single-beam noise characteristics ofquantum-correlated twin beams

Yun Zhang, Katsuyuki Kasai, and Kazuhiro Hayasaka

Kansai Advanced Research Center, National Institute of Information and Communications Technology,588-2 Iwaoka, Nishi-ku, Kobe, 651-2492 Japan

Received July 29, 2003; revised manuscript received December 9, 2003; accepted February 4, 2004

We investigated the intensity noise spectra of a single beam of a pump-enhanced continuous-wave optical para-metric oscillator (OPO), which was used to generate quantum-correlated twin beams, as a function of the pumppower. With a triply (pump-, signal-, and idler-) resonant cavity, the oscillation threshold of our OPO was8.5 6 1.3 mW and the measured slope conversion efficiency was 0.72 6 0.02. Twin beams with a power of 240mW were generated at a pump power of 350 mW. The relaxation oscillation frequencies, which depend on thepump power, were observed when the pump power of the OPO was 12.5–28 mW. The experimental resultsconfirm the predicted increase in OPO relaxation frequency with pump power. We experimentally inferredsqueezing of the single-beam intensity, for the first time to our knowledge, by exploiting the nature of quantumnoise that is dependent on loss. © 2004 Optical Society of America

OCIS codes: 270.2500, 190.4970, 190.4410, 270.6570.

1. INTRODUCTIONContinuous-wave (cw) optical parametric oscillators(OPOs) are efficient and widely tunable sources of coher-ent light1 and nonclassical states.2–11 Degenerate cwOPOs have been used to produce single-mode quadrature-squeezed light.2 Quantum-correlated twin beams with asqueezed intensity difference fluctuation and a two-modequadrature-squeezed vacuum state of light have beengenerated from nondegenerate OPOs operating below andabove the oscillation threshold, respectively.3,4 The en-tangled state, with quantum entanglement between thequadrature phase amplitudes of spatially separated sig-nal and idler beams, has been experimentally generatedfrom a nondegenerate OPO operating below the oscilla-tion threshold.5 Twin beams generated by OPOs havebeen observed for almost two decades in a number of ex-periments with type II phase-matching devices.3,4,6–11

Since then, twin beams have been used in high-sensitivityand quantum-nondemolition measurements12 as well asin high-sensitivity spectros-copy.13,14

Pump-enhanced OPOs, also referred to as triply reso-nant OPOs, are significant sources of twin beams. Com-pared with singly and doubly resonant OPOs, they havelow thresholds and provide stable single-frequency out-put. Low-threshold OPOs are of interest for investigat-ing the quantum properties of beams generated in thehigh-pump-power regime (i.e., for pump powers of at leastfour times threshold), especially the single-beam noisecharacteristics of twin beams. Until now, most reportedmeasurements of cw twin-beam correlation were carriedout with low pump power (for pump powers less than fourtimes the threshold), and most focused only on the corre-lation between the signal and the idler beams. Further-more, the output power of the twin beams of these deviceswas low, several dozen milliwatts. All these factors havelimited the application of laserlike twin beams. The high

0740-3224/2004/051044-06$15.00 ©

pump regime11 is of critical importance for use of OPOs assources of cw tunable laserlike radiation for making high-sensitivity spectroscopic measurements. In addition totheir tunable character, these devices offer the unique po-tential of providing high-power twin beams and of facili-tating the investigation of single-beam noise characteris-tics of twin beams.

Pump-enhanced OPOs exhibit several unique proper-ties. The intensity noise spectrum of the output singlebeam of a cw triply resonant OPO is similar to the noisespectrum of a laser oscillator, which exhibits relaxationoscillation. Recently Lee et al.15 observed relaxation os-cillations in the intensity noise spectrum of a single beamemitted by a nondegenerate OPO pumped by a diode la-ser, and Porzio et al.11 observed relaxation oscillations inthe single-beam spectra of twin beams output from a tri-ply resonant OPO for pump powers of as much as approxi-mately 15 times the threshold value. The relaxation os-cillation frequency shifts to higher values as the pumppower is increased; in working with our OPO we observeda similar property in the single-beam spectra. Anotherimportant property of triply resonant OPOs is that the in-tensity noise in a single beam of twin beams can be re-duced below the shot-noise limit. In theory, it was pre-dicted that this intensity noise will fall below the shot-noise limit when the pump power is above four times theoscillation threshold in a bandwidth of the order of thecavity bandwidth.16 Ideally, the intensity noise in asingle beam of twin beams is reduced to half of the shot-noise limit at high pump powers. Recently Porzio et al.developed a complete model for explaining the noisesource that influences an OPO.7 In this paper we studyin detail the intensity-difference noise between the signaland the idler beams and the intensity noise of singlebeam in a high pump range.

Our purpose in the present paper is to present thesingle-beam noise characteristics of twin beams gener-

2004 Optical Society of America

Zhang et al. Vol. 21, No. 5 /May 2004/J. Opt. Soc. Am. B 1045

ated by a triply resonant OPO. The relaxation oscillationfrequencies that depend on the pump power were ob-served when the pump power of the OPO was 12.5–28mW. Experimental results confirmed the predicted in-crease in OPO relaxation frequency with pump power.Squeezing of the single-beam intensity was also experi-mentally studied for the pump powers of more than 60mW when the extra noise was canceled.

The paper is organized as follows: In Section 2 we de-scribe the experimental setup. In Section 3 we describeand discuss the experimental results. The relaxation os-cillation of our OPO and the intensity noise on the singlebeam of twin beams are discussed in detail. In Section 4we present our conclusions.

2. EXPERIMENTAL SETUPThe experimental setup is shown schematically in Fig. 1.The OPO was the same pump-enhanced signal and idler-resonant (triply resonant) OPO as was used in the re-search reported in Refs. 8 and 9 to generate the quantum-correlated twin beams. A diode-pumped Nd:YAG laser(Lightwave Electronics, Model 142) served as the pumpsource of the system. The laser delivered a maximumoutput power of 400 mW at a fixed wavelength of 532 nm,of which 350 mW was available in front of the OPO.Half-wave plate P1 and polarizing beam splitter PBS0were used to adjust the power in front of the OPO. Thetwin beams were produced when the OPO was operatedabove the threshold. The signal and idler beams of thetwin beams were cross polarized. To measure the singlebeam’s noise characteristic we used polarizing beam split-ter PBS1 to separate the twin beams into signal and idlerbeams according to their polarization. The intensitynoise of the signal beam was detected in a balanced ho-modyne detector.17 The detection apparatus was com-posed of half-wave plate P2, polarizing beam splitterPBS2, and two identical high-quantum-efficiency photo-diodes (InGaAs; Epitaxx ETX500) matched to equal-transimpedence low-noise amplifiers. The half-waveplate and the polarizing beam splitter acted to split the

Fig. 1. Experimental setup for a triply resonant cw OPO: D1,D2, photodiodes; PBS0–PBS2, polarizing beam splitters; P1,half-wave plate for 532 nm; P2, P3, half-wave plates for 1064 nm.

beam into two beams with equal intensity. The ac pho-tocurrents of the balanced detector were combined in ahybrid junction to generate sum and difference currentsi1 and i2 , respectively. These currents were input tospectrum analyzers that recorded the noise power. Thesum signal was a measure of the intensity noise of thebeam, whereas the difference signal gave the shot-noiselevel.17

Half-wave plate P3 and polarizer PBS1 were removedto allow us to measure the correlation between the signaland idler beams. As was shown by Heidmann et al.,3

half-wave plate P2, polarizing beam splitter PBS2, andtwo detectors composed the detection system for the twinbeams. To measure the noise of a single beam we in-serted P3 and PBS1. In this case the angle between theaxes of plate P2 and polarizer PBS2 was fixed at 22.5°;the system of P2 and PBS2 acted as a normal 50% beamsplitter. When the angle between the axes of plate P3and polarizer PBS1 is 0°, the transmission light of PBS1is the signal beam; when the angle between the axes ofplate P3 and of polarizer PBS1 is 22.5°, the transmissionlight of PBS1 is mixed light of the signal and the idlerbeams. In this way, the intensity noises of signal beamsand the intensity noises of mixed beam between signaland idler beams can be recorded. The process of detec-tion is described in Subsection 3.D below.

3. EXPERIMENTAL RESULTSA. Steady OperationA calibrated thermal powermeter was employed for boththe pump-power (Pp) and the output-power (Pout) mea-surements. Figure 2 shows the results of measurementsmade over a range of pump powers from 18 to 350 mW.We varied the input power by rotating half-wave plate P1of the power adjustment system. In particular, at apump power of 350 mW an output power of 240 mW wasobtained. From these measured powers we computedconversion efficiency h 5 Pout /Pp , obtaining 0.68 6 0.04for the frequency downconversion from 532 to 1064 nm.The linear fit is also shown in Fig. 2 (dotted line), whichyields an OPO threshold of Pth 5 9.0 6 1.8 mW and aslope conversion efficiency of 0.72 6 0.02.

Solving the equations of evolution in the cavity and us-ing the boundary condition at the output coupler, we canexpress the output power as the square root of the pumppower or as a function of the threshold factor16:

Pout 5 2e~APthPp 2 Pth! or pout 5 2e~As 2 1 !,(1)

where pout [ Pout /Pth and s [ Pp /Pth are the normalizedoutput power and the normalized pump power, respec-tively. Constant parameter e represents the power slopeefficiency of the output beam at threshold. We used Eq.(1) to fit the experimental data, to determine thresholdPth , and thus to express the measured pump powers withthe threshold factors. We used a two-parameter least-squares fit of Eq. (1) to the experimental data in Fig. 2,where e and Pth were used as the fitting parameters (solidcurve). From the good agreement (Fig. 2, inset) in thelow-pump-power range (pump powers less than 13 timesthe pump threshold), the fit yielded a pump power at

1046 J. Opt. Soc. Am. B/Vol. 21, No. 5 /May 2004 Zhang et al.

threshold of Pth 5 8.5 6 1.3 mW, which is near thethreshold value of the linear fit of all experimental data,and an s power slope efficiency of e 5 1.2 6 0.1. Unfor-tunately, the output power fell short of the theoreticallyexpected value in the high-pump-power range. In Fig. 2the output power is higher than the expected value. Pos-sible reasons for this discrepancy include increased sub-harmonic loss and decreased pump loss because of upcon-version, absorption of the OPO fields in the crystal, andthermally induced changes in the crystal’s refractive in-dex. All these reasons will induce changes in the pumpthreshold and in the power slope efficiency and, in turn,in the output power of the OPO. These issues will haveto be carefully addressed in the future.

Note that during each increment of the pump power weobserved several axial mode hops of the subharmonicwave, which yielded different output powers. Such modehops are probably induced by absorption of the OPO fieldsin the crystal. This absorption leads to thermally in-duced changes in the crystal’s refractive index and tospectral clustering.1,18 The difference in output powercan be interpreted as a varying threshold or thresholdfactor. Reliable operation of the OPO at a chosen thresh-old factor thus required careful adjustment of the cavitylength. For a reproducible measurement of output powerversus pump power we fine tuned the cavity length dur-ing cw OPO resonant operation. We did this by applyinga manually adjustable offset voltage to the piezoelectrictransducer. For each pump-power setting the voltagewas adjusted to produce the maximum output power.

B. Intensity Correlation MeasurementsThe measured intensity difference spectrum of the twinbeams, which is generated by a nondegenerate OPO, isexpressed as

S~V! 5 1 2 $hehd /@1 1 ~V/G!2#%, (2)

where V is the analysis frequency, G is the cavity line-width, he 5 T2 /(T2 1 T1 1 a) is the cavity escape effi-ciency, T2 5 5% is the transmission of the output mirror,T1 , 0.1% is the transmission of the high-reflectivityfacet of the crystal, and a , 0.3% is the extra loss. Thetotal detection efficiency, hd , is ;90%. The detection ef-

Fig. 2. Output power of OPO measured as a function of pumppower. The fit yields an OPO threshold of 8.5 6 1.3 mW and aslope conversion efficiency of h 5 0.72 6 0.02.

ficiencies in our experiment were measured with ;92%photodetector quantum efficiency and ;98% propagationefficiency.

Figure 3 shows the best intensity difference noise re-duction of the twin beams generated by our OPO. Thefrequency range in the figure is 1–50 MHz. The maxi-mum noise reduction was 27.2 6 0.3 dB (80%) below theshot-noise limit at an analysis frequency of 3 MHz. Thetotal output power of 26 mW (13 mW per beam) was ob-tained when the pump power was ;40 mW (approxi-mately four times the threshold). The values predictedby Eq. (2) (solid curve) with the experimentally measured

Fig. 3. Intensity difference noise reduction versus frequency ata pump power of ;40 mW. Resolution bandwidth, 100 kHz;video bandwidth, 100 Hz.

Fig. 4. Normalized single-beam noise versus frequency whenthe pump power increases from 12.5 to 28 mW. Resolutionbandwidth, 100 kHz; video bandwidth, 100 Hz.

Fig. 5. Normalized single-beam noise versus frequency whenthe pump power increases from 28 to 55 mW. Resolution band-width, 100 kHz; video bandwidth, 100 Hz.

Zhang et al. Vol. 21, No. 5 /May 2004/J. Opt. Soc. Am. B 1047

Fig. 6. Intensity noise in a single beam versus frequency at various pump powers. Resolution bandwidth, 100 kHz; video bandwidth,100 Hz.

parameters (he , hd , and G) are shown for comparison.The experimental results agree with the theory very well.The output power of the twin beams increased with pumppower. Because of the detection saturation of the detec-tor, we did not detect the best correlation between the sig-nal and the idler modes. However, part of the twinbeams was measured with our detection system; the cor-relation between the signal and the idler mode was al-ways retained (the correlation between signal and idlerdecreased owing to the low detection efficiency), even withthe output power of 240 mW. The noise reduction of at-tenuated twin beams with power of 100 mW is shown inthe inset of Fig. 3. The noise reduction was 21.26 0.3 dB below the shot-noise limit because the attenua-tion was induced. This means that twin beams with apower of 240 mW were generated with our OPO.

C. Relaxation OscillationWe measured the intensity noise in a single beam of theOPO output by using balanced detection to detect a singlebeam of twin beams. Examples of the recorded normal-ized single-beam intensity noise as a function of noise fre-quency are shown in Fig. 4 for the OPO operating atpump powers of 12.5, 18, 23, and 28 mW. At high pumppowers the noise spectra were different and clearlyshowed a broad noise peak with a nonzero center fre-quency, which is called the relaxation oscillation fre-quency. This frequency shifts to higher values as thepump power is increased. However, an unpredicted ex-perimental result was observed when the pump thresholdfactor increased further. Figure 5 shows the normalizedintensity noise in a single beam versus frequency for

pump powers of 28 to 55 mW. The intensity noise of sig-nal beams decreased with increasing pump power, differ-ently from the previous case.11,15 The intensity noise de-creased with increasing pump power, indicating theinherent noise character of the single beam generated byan OPO. This behavior is like that predicted by Fabreet al.16 and was recently studied theoretically in detail byPorzio et al.19 The reduction in the single-beam intensitynoise indicates a possibility of using our triply resonantOPO to generate sub-Poissonian light at high pump pow-ers.

D. Single-Beam Noise SpectraExcept for the relaxation oscillation, it is more attractiveto generate the sub-Poissonian light from an OPO operat-ing above threshold. In the absence of pump excess,squeezing should appear in the single-beam spectrum of aperfectly triply resonant OPO for pump powers well abovefour times the threshold value.16,19 To reach such a re-gime it is necessary to lower the threshold of the OPO andto shift the relaxation oscillation frequency to a highvalue as quickly as possible while increasing the pumppower. In our OPO, because of the large pump excessnoise and the relaxation oscillation tail, the squeezedsingle beam of the twin beams was not obtained. How-ever, we did show, for the first time to our knowledge,squeezing of the single beam by exploiting the nature ofquantum noise that is dependent on loss when the pumppower is more than four times the pump threshold. Toshow the squeezing we separated the detected intensitynoise into classical excess noise and quantum noise in thesingle beam as follows:

1048 J. Opt. Soc. Am. B/Vol. 21, No. 5 /May 2004 Zhang et al.

Vd 5 Vex 1 Vq , (3)

where Vd is the detected noise, Vex is the classical excessnoise, which is above the shot-noise limit, and Vq is quan-tum noise, which is either below the shot-noise limit ornot. If the noise is below the shot-noise limit, it will behighly sensitive to loss and any loss will induce extranoise (shot noise) in the system, i.e., Vout 5 mV in 1 (12 m)VSNL , where VSNL is the shot noise and m is the lossefficient. However, if the noise is classical noise therewill be no extra noise (shot noise) added to system owingto the loss, i.e., Vout 5 mV in . Thus it is possible to dis-tinguish the quantum noise and the classical noise byadding the loss to the system. In our experiment themeasurement process consisted of two steps. In the firststep the intensity noise of the single beam without loss(the intensity noise of the signal beam) was measuredwith a homodyne detector. This means that the sum ofexcess noise and quantum noise was recorded. In thesecond step the intensity noise of mixed light (which weachieved by rotating half-wave plate P3), which was com-bined with half of the signal and half of the idler, wasmeasured with the homodyne detector. In this case thesum of excess noise and quantum noise after loss (the lossefficiency was 1/2) was recorded. Comparing these twonoise powers yields the quantum noise of a single beam.Suppose that the quantum noise Vq 5 SsVSNL , where Ssis squeezing; the sum of excess noise and quantum noiseafter loss can be written as Vd(m) 5 mVex 1 m@mSs 1 (12 m)#VSNL . Thus the detected noises in our first- andsecond-step measurements are Vd(I) 5 Vex 1 SsVSNL andVd(II) 5 Vd(0.5) 1 Vd(0.5) 5 Vex 1 1/2 SsVSNL 1 1/2 VSNL ,respectively, when the system is balanced just as for ourOPO. The squeezing can be written as

Ss 5 1 2 2FVd~II!

VSNL2

Vd~I!

VSNLG . (4)

Thus the difference between two measurements indicatessqueezing of the quantum noise directly. Examples of in-tensity noise as a function of analysis frequency areshown in Fig. 6 for the OPO operating at different pumppowers. When the pump power was below four times theoscillation threshold there was no difference in the inten-sity noise with and without loss. This result indicatesthat the quantum noise of the single beam is above orequals the shot-noise limit. At high pump powers [Figs.6(b)–6(d); more than four times threshold], the intensitynoise powers with and without loss were different andclearly show squeezing of the single beam. To our knowl-edge, the squeezing in a single beam output from an OPOwas not observed experimentally before. To confirm thatsuch is the case we compared our experimental resultswith the theoretical prediction. In the absence of pumpexcess, the spectrum of the single beam can be writtenas16

SS~V! 5 H 1 2heAs~As 2 2 !

2@1 1 ~V/G!2#@~As 2 1 !2 1 ~V/G!2#J .

(5)

Figure 7 shows the quantum noise versus normalizedpump power; the solid curve was calculated from Eq. (5)

at an analysis frequency of 35 MHz, and the filled circleswith error bars show the measured quantum noise of thesingle beam. The good agreement between theoreticalprediction and experimental measurement shows that wehave indeed achieved squeezing of a single beam.

4. CONCLUSIONSIn conclusion, we have investigated the intensity noise ofthe single beam of a pump-enhanced cw OPO, which weused to generate quantum-correlated twin beams, as afunction of pump power. With a triply resonant cavitythe oscillation threshold of our OPO was 8.5 6 1.3 mWand the conversion efficiency was 0.72 6 0.02. Twinbeams with a power of 240 mW and a quantum correla-tion of 80% (27.2 dB) at an analysis frequency of 3 MHzwere generated. Relaxation oscillation frequencies,which depend on the pump power, were observed whenthe pump power of the OPO was 12.5–28 mW. The in-tensity noise of the single beam was also investigated at ahigh pump power (more than four times threshold). Al-though we did not obtain sub-Poissonian light, to ourknowledge we have directly shown squeezing of a singlebeam of twin beams.

Y. Zhang’s e-mail address is zhangyun@crl.go.jp.

REFERENCES1. R. C. Eckardt, C. D. Nabors, W. J. Kozlovsky, and R. L.

Byer, ‘‘Optical parametric oscillator frequency tuning andcontrol,’’ J. Opt. Soc. Am. B 8, 646–667 (1991).

2. L. A. Wu, H. J. Kimble, J. L. Hall, and H. F. Wu, ‘‘Genera-tion of squeezed states by parametric down conversion,’’Phys. Rev. Lett. 57, 2520–2523 (1986).

3. A. Heidmann, R. J. Horowitz, S. Reynaud, E. Giacobino, C.Fabre, and G. Camy, ‘‘Observation of quantum noise reduc-tion on twin laser beams,’’ Phys. Rev. Lett. 59, 2555–2557(1987).

4. K. C. Peng, Q. Pan, H. Wang, Y. Zhang, H. Su, and C. D.Xie, ‘‘Generation of two-mode quadrature-phase squeezingand intensity-difference squeezing from a cw-NOPO,’’ Appl.Phys. B 66, 755–758 (1998).

5. Y. Zhang, H. Wang, X. Y. Li, J. T. Jing, C. D. Xie, and K. C.Peng, ‘‘Experimental generation of bright two-modequadrature squeezed light from a narrow-band nondegen-erate optical parametric amplifier,’’ Phys. Rev. A 62, 023813(2000).

Fig. 7. Quantum noise in a single beam versus normalizedpump power. Solid curve, theoretical prediction; filled circles,experimental results.

Zhang et al. Vol. 21, No. 5 /May 2004/J. Opt. Soc. Am. B 1049

6. J. Teja and N. C. Wong, ‘‘Twin-beam generation in a triplyresonant dual-cavity optical parametric oscillator,’’ Opt. Ex-press 2, 65–71 (1998), http://www.opticsexpress.org.

7. A. Porzio, C. Altucci, P. Aniello, C. de Lisio, and S. Solimeno,‘‘Resonances and spectral properties of detuned OPOspumped by fluctuating sources,’’ Appl. Phys. B 75, 655–665(2002).

8. Y. Zhang, K. Kasai, and M. Watanabe, ‘‘Investigation of thephoton-number statistics of twin beams by direct detec-tion,’’ Opt. Lett. 27, 1244–1246 (2002).

9. Y. Zhang, K. Kasai, and M. Watanabe, ‘‘Experimental inves-tigation of the intensity fluctuation joint probability andconditional distributions of the twin-beam quantum state,’’Opt. Express 11, 14–19 (2003), http://www.opticsexpress.org.

10. J. R. Gao, F. Y. Cui, C. Y. Xue, C. D. Xie, and K. C. Peng,‘‘Generation and application of twin beams from an opticalparametric oscillator including an alpha-cut KTP crystal,’’Opt. Lett. 23, 870–872 (1998).

11. A. Porzio, F. Sciarrino, A. Chiummo, M. Fiorentino, and S.Solimeno, ‘‘Twin beams correlation and single beam noisefor triply resonant KTP OPOs,’’ Opt. Commun. 194, 373–379 (2001).

12. H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, andK. C. Peng, ‘‘Experimental realization of a quantum mea-surement for intensity difference fluctuation using a beamsplitter,’’ Phys. Rev. Lett. 82, 1414–1417 (1999).

13. H. B. Wang, Z. H. Zhai, S. K. Wang, and J. R. Gao, ‘‘Gen-eration of frequency tunable twin beams and its applicationin sub-shot noise FM spectroscopy,’’ Europhys. Lett. 64,15–21 (2003).

14. H. Souto Ribeiro, C. Schwob, A. Matre, and C. Fabre, ‘‘Sub-shot-noise high-sensitivity spectroscopy with optical para-metric oscillator twin beams,’’ Opt. Lett. 22, 1893–1895(1997).

15. D.-H. Lee, M. E. Klein, and K.-J. Boller, ‘‘Intensity noise ofpump-enhanced continuous-wave optical parametric oscil-lators,’’ Appl. Phys. B 66, 747–753 (1998).

16. C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud,‘‘Noise characteristics of a non-degenerate optical paramet-ric oscillator—application to quantum noise reduction,’’ J.Phys. (Paris) 50, 1209–1225 (1989).

17. K. Schneider, R. Bruckmeier, H. Hansen, S. Schiller, and J.Mlynek, ‘‘Bright squeezed light generation by a continuous-wave semimonolithic parametric amplifier,’’ Opt. Lett. 21,1396–1398 (1996).

18. T. Debuisschert, A. Sizmann, E. Giacobino, and C. Fabre,‘‘Type-II continuous-wave optical parametric oscillators:oscillation and frequency-tuning characteristics,’’ J. Opt.Soc. Am. B 10, 1668–1680 (1993).

19. A. Porzio, C. Altucci, P. Aniello, A. Chiummo, C. de Lisio,and S. Solimeto, ‘‘Spectral properties of the single beamsgenerated by an optical parametric oscillator,’’ J. Opt. BQuantum Semiclassical Opt. 4, S313–S317 (2002).