Interferometric nonlinear mixing in

multiple-pass femtosecond optical

parametric amplification

J.M. Fraser and K.C. Hall

Department of Physics, University of Toronto, 60 St. George St.,Toronto, Ontario, Canada M5S 1A7

fraser@physics.utoronto.ca

Abstract: We demonstrate that in multi-stage optical parametricamplifiers, spatial and temporal overlap of all products and pump onsubsequent passes lead to strongly phase-dependent conversion, whichhas important consequences for output noise and beam profile char-acteristics. We verify a simple method to avoid this interferometricprocess.c©1999 Optical Society of AmericaOCIS codes: (190.4970) Parametric oscillators and amplifiers

References

1. J.C. Deak, L.K. Iwaki and D.D. Dlott, ”High-power picosecond mid-infrared optical parametricamplifier for infrared Raman spectroscopy,” Opt. Lett. 22, 1796-1798 (1997).

2. L. Carrion and J.P. Girardeau-Montaut, ”Performance of a new picosecond KTP optical para-metric generator and amplifier,” Opt. Commun. 152, 347-350 (1998).

3. J.Y. Zhang, Z. Xu, Y. Kong, C. Yu and Y. Wu, ”Highly efficient, widely tunable, 10-Hz paramet-ric amplifier pumped by frequency-doubled femtosecond Ti:sapphire laser pulses,” Appl. Opt.37, 3299-3305 (1998).

4. F. Seifert, V. Petrov, and F. Noack, ”Sub-100-fs optical parametric generator pumped by ahigh-repetition-rate Ti:sapphire regenerative amplifier system,” Opt. Lett. 19, 837-839 (1994).

5. M.K. Reed and M.K.S. Shepard, ”Tunable infrared generation using a femtosecond 250 kHzTi:sapphire regenerative amplifier,” IEEE J. Quantum Electron. 32, 1273-1277 (1996).

6. N. Bloembergen, Nonlinear Optics, (W.A. Benjamin Inc., Reading, Massachusetts, 1965).

7. R.W. Boyd, Nonlinear Optics, (Academic Press, San Diego, USA, 1992).

8. A.N. Chudinov, Yu.E. Kapitzky, A.A. Shulginov and B.Ya. Zel’Dovich, ”Interferometric phasemeasurements of average field cube E2ωE

∗2ω ,” Opt. Quantum Electron. 23, 1055-1060 (1991).

9. E. Freysz, J. Plantard, R. Gillet, R.M. Rassoul, P. Grelu and A. Ducasse, ”Automatic timedelay optimization between the pump and seed pulses of a broadly tunable femtosecond opticalparametric amplifier,” Appl. Opt. 37, 2411-2413 (1998).

1. Introduction

Optical parametric amplification provides a means for generating widely tunable ultra-short optical pulses. Picosecond and femtosecond pulses with wavelengths in the mid-infrared are typically generated using parametric down conversion in noncentrosymmet-ric nonlinear crystals, seeded using white light generation or parametric fluorescence.In order to maximize conversion efficiency, a multiple-pass configuration is commonlyemployed in which one compensates for the group velocity mismatch (GVM) and spatialwalk-off between the pump pulses and the infrared signal and idler pulses using separatedelay lines.

(C) 1999 OSA 19 July 1999 / Vol. 5, No. 2 / OPTICS EXPRESS 21#11868 - $15.00 US Received July 09, 1999; Revised July 15, 1999

A number of multiple-pass alignment schemes have been presented in the liter-ature (for example [1-5]). In these works, it is often unclear whether both the signal andidler beams are included in the amplification process on subsequent passes through thenonlinear crystal, and if so, whether the authors have addressed issues relating to thephases of the optical fields. As we will demonstrate, simultaneous overlap of all threebeams on subsequent passes can lead to critical changes in the physical properties ofthe parametric down-conversion process.

In this paper, we report the characterization of the signal output of a commercialdouble-pass optical parametric amplifier(OPA). The design of this system incorporatesdual amplification of the signal and idler in the second stage. Our measurements revealstrong oscillations in amplification efficiency with changes in the phase of the 800 nmpump pulses, consistent with the presence of an interferometric nonlinear mixing pro-cess. These results have significant implications for the design of parametric amplifiers,and we present a discussion of the key considerations in ensuring optimum performancein systems which incorporate multiple stages.

2. The Optical Parametric Amplifier

The parametric amplifier used to investigate the interferometric mixing process is aCoherent OPA 9800 [5], although the characteristics under study are not unique to thissystem. The OPA (Fig. 1) is based on type II down conversion (e → e + o) in a 3 mmBeta-Barium Borate (BBO) crystal (θ = 32◦) which is angle tuned for phase matchingin the mid-infrared. The signal pulses are tunable from 1.2 to beyond 1.6 µm, providingidler wavelengths in the range from below 1.6 to 2.4 µm. The parametric process ispumped by 150 fs, 4 µJ pulses, produced at a repetition rate of 250 kHz throughregenerative amplification of the output of a Titanium sapphire oscillator operating ata center wavelength of 803 nm. The down-conversion process is seeded using white lightgeneration (WLG), created by focusing 20% of the 4 µJ pump pulses into a sapphiredisk. The idler and pump have parallel polarizations, while the signal is orthogonal.The system incorporates two amplification stages in which compensation for GVM andspatial walk-off between the pump and infrared beams is provided using a separatevariable delay line for the pump pulses alone (Dl2). Signal and idler share the sameoptical path on second pass. In both pump and midinfrared optical paths, a fused silicalens serves to both colliminate and refocus the beams onto the BBO crystal.

Figure 1. Optical lay-out of OPA9800: Dl1, Dl2- delay lines; Dm1, Dm2- di-electric mirrors; S- 80:20 beamsplitter; WLG- white-light generating crystal; BBO-Beta-Barium Borate crystal; filter- neutral density and long wavelength pass filters;WP- λ/2-waveplate; PBC- polarizing beam cube; D- Ge detector.

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3. Signal Output Characteristics

Measurements were made of the OPA signal power as a function of the delay of the pumppulses (Dl2) and for a range of tuning conditions. The signal beam was attenuated andfocused onto a germanium detector and the output was measured using lock-in detection(optical chopper not shown in Fig. 1). Sub-micron control of delay was achieved throughthe use of a stepper motor with a microstep driver.

Data for OPA signal wavelengths between 1.345 and 1.591 µm as a function ofDl2 appear in Fig. 2. Due to the nature of the tuning process, there is a temporal offsetwhich varies from wavelength to wavelength, and so for comparison purposes, the zeroof delay is set to align the traces in Fig. 2. Strong oscillations in the magnitude of thesignal power are observed as the second pass pump delay is varied across the range ofpulse overlap between the pump and infrared beams (Fig. 2 inset). Analysis using a fastFourier transform shows that the period of the oscillations is 818nm±6nm, suggestingthe presence of an interferometric process dependent on the pump wavelength. Thedata in Fig. 2 also reveal a strong sensitivity to the signal wavelength. A symmetricpattern with maximum fringe visibility was found with the signal tuned to 1.56 µm.With the signal tuned closer to the degeneracy wavelength of 1.6 µm, stronger powermodulations are seen at negative time delays, while tuning to shorter signal wavelengthsleads to more prevalent fringes for positive delays.

0.0

0.5

1.0

-200 0 200

1591

1569

1562

1552

1505

1470

1435

1345

0 5 10 150.00.51.0

OPAoutput(norm.)

Pump delay (fs)

Outp

ut(n

orm

.)

Signal wavelength (nm)

Pump delay (fs)

0 5 10 150.0

0.5

1.0O

PA

outp

ut(n

orm

.)

Pump delay (fs)

Figure 2. Average power of signal as a function of second pass delay betweenpump and midinfrared pulses for various signal wavelengths. Negative delay corre-spond to early arrival of the pump pulses.

In addition to these temporal modulations in average power, the spatial profileof the signal beam showed clear signs of interference fringes. Variations in Dl2 or inany of the second pass mirror orientations was observed to cause these fringes to scanacross the beam profile. Furthermore, the number of fringes within the spatial profileincreased as the alignment of the pump and infrared beams through the BBO wascaused to deviate from collinear. The simultaneous presence of multiple spatial fringes

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corresponded to a reduced temporal fringe visibility. The data in Fig. 2 was obtainedafter the OPA was aligned to maximize output power, which corresponded to a nearcollinear orientation.

4. Theory and comparison to results

Optical parametric amplification exploits the noncentrosymmetry in a crystalline mediumto allow for the transfer of energy between fields at different frequencies. The paramet-ric mixing process is described by a solution of Maxwell’s equations in the nonlinearmedium of the BBO crystal, as clearly outlined in Bloembergen and co-worker’s semi-nal work [6]. On the first pass, when collinear signal and pump beams are incident ona transparent crystal of length L, using the slowly-varying amplitude approximationand in the limit of negligible pump depletion and zero phase mismatch, the intensity ofsignal (ωs) and idler (ωi) beams at the output face of the crystal can be shown to be:

Is =nsc

2π

[(As (0)

)2cosh2 κL

](1a)

Ii =nic

2π

[(ωi

ωs

)2ks

ki

(As (0)

)2sinh2 κL

](1b)

Here we have followed the notation of Boyd [7], in which the electric fields are denotedby Ei (z, t) = Ai (z) e

i(kiz+ωit)+complex conjugate, where we have defined Ax (z) =Ax (z) e

iφx so that Ax is a real value, nx and kx are the refractive index and wavevectormagnitude of the beam at frequency ωx, κ =

8πωsωidc2√kskiAp, and d is the effective nonlinear

coefficient determined by the crystal type, frequencies and experimental geometry. Thissolution corresponds to exponential amplification of the signal seed and generation andamplification of the idler.

On second pass, for the case in which all three beams are present at the entranceto the nonlinear crystal, the intensity of signal (ωs) and idler (ωi) beams at the outputface of the crystal can be shown to be:

Is =nsc

2π

[(As (L)

)2cosh2 κL+

(ωs

ωi

)2ki

ks

(Ai (L)

)2sinh2 κL

+2ωs

ωi

√ki

ksAs (L)Ai (L) coshκL sinhκL sin (φs + φi − φp)

](2a)

Ii =nic

2π

[ (Ai (L)

)2cosh2 κL+

(ωi

ωs

)2ks

ki

(As (L)

)2sinh2 κL

+2ωi

ωs

√ks

kiAs (L)Ai (L) coshκL sinhκL sin (φs + φi − φp)

](2b)

where we have defined z=L to be at the entrance of the nonlinear crystal on second pass.Though this simple analysis cannot fully describe OPA behavior, it provides direct quan-tifiable results and suggests certain qualitative features without resorting to numericalmethods. Instead of simple exponential amplification of signal and idler beams, Eq. 2predicts that the direction of energy transfer will correspond to either up conversion (sig-nal and idler depletion) or down conversion (signal and idler amplification) dependingon the relative phases of the beams. Small changes in delay between the three beamswill therefore lead to large variations in the total power in the signal and idler after

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the second stage of amplification. These oscillations are superimposed onto a smoothbackground due to the first two terms in Eq 2.

We have written Eq. 2 to specifically highlight its interferometric nature. Anequivalent interpretation of these results is that on second pass, mixing between signaland pump generates a new idler beam that interferes with the beam generated on firstpass. Mixing between idler and pump generates a new signal beam that interferes withthe original signal beam. This phenomenon is closely related to the work of Chudinov etal. [8], who, in the case of second harmonic generation, demonstrated that two cascadedmixing processes can lead to phase sensitive output intensities.

The phase dependency of the output intensities described by Eq. 2 are consistentwith the oscillations seen in Fig. 2: the oscillatory period of (818±6) nm is <2% from thecenter wavelength of the pump pulses. The sensitivity of the shape of the fringe patternto variations in tuning conditions may be accounted for through consideration of thecombined effects of GVM in the BBO crystal and in the various glass elements throughwhich the signal and idler travel (including the lens and Dm2 shown in Fig. 1). Asdiscussed above, in order to observe interferometric amplification, both the signal andidler must simultaneously have nonzero amplitudes in the BBO crystal, and thus thepulse amplitudes must be overlapped in time and space. Far from degeneracy, the GVMin the glass causes the idler pulse to be delayed in time relative to the signal. One cansee from the data in Fig. 2 that individual pulse envelopes are beginning to be resolvedalready at 1.345 µm (As discussed in Section 5. and shown in Fig. 3(right), the left peakis due to the signal alone.) The rapid reduction in the fringe visibility observed as thesignal and idler begin to separate in time is likely enhanced by a small amount of chirppresent both in the pump and infrared pulses. This arises from imperfect compressionof the regeneratively amplified pulses in conjunction with additional chirp inherent tothe white light generation process.

As the signal wavelength is tuned close to the degeneracy wavelength of 1.6 µm,the glass induced-GVM reduces to zero. In this case, the GVM in the BBO crystal, whicharises due to the birefringence of the material, becomes the dominate source of pulsewalk-off and has an opposite sign to that in glass. As a result, one expects the signalpulse envelope to trail that of the idler for signal wavelengths near 1.6 µm. This isconsistent with the observation of stronger fringes for negative delays with the signalwavelength tuned longer than 1.56 µm.

For a general OPA signal wavelength, therefore, one observes the competingeffects of the two sources of GVM. The observation of maximum fringe visibility withthe signal tuned to 1.56 µm, accompanied by a symmetric fringe pattern with respectto delay, indicates that the GVM in the glass is compensated by the BBO GVM, cor-responding to minimum pulse walk-off. The importance of the interferometric mixingprocess for OPA signal wavelengths near 1.56 µm is of particular relevance to researchersinterested in accessing standard optical communications wavelengths around 1.5 µm.

5. Design Considerations

The incorporation of interferometric mixing into an OPA design affords the possibilityof obtaining higher output power than would be possible if dual amplification of thesignal and idler was not used, as is clear from Eq. 2. This power advantage, however,comes at some cost. The use of a phase-sensitive generation process obviates the need foran interferometrically stable configuration. Power stability will be limited by vibrationsfrom all environmental sources. Experiments in which lock-in detection techniques areemployed will be especially sensitive to slow power drifts due to variations in ambienttemperature or air flow. In addition, the strong sensitivity of the signal characteristicsto wavelength tuning is undesirable. Separation of signal and idler into individual delay

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lines would provide a way to compensate for GVM, but necessitates the use of a morecomplicated geometry. The mode quality of the OPA output beams is also vulnerableto minor misalignment of the optical set-up, as any deviation from non-collinearity willintroduce multiple fringes in the spatial profile. Small variations in the beam phases,furthermore, will shift these fringes, causing large changes to the spatial mode. Finally,since a small adjustment to the orientation of any optic after first pass results in largechanges to the relative phase, alignment is more challenging for an OPA which incorpo-rates phase-sensitive mixing than for a non-interferometric setup. Though not a seriousconcern in our manual system, this would have important repercussions if part or all ofthe alignment procedure is automated [9].

In order to evaluate the impact of these issues, the system was modified to elim-inate the interferometric mixing process in the second stage of amplification. This wasaccomplished by selectively filtering out the idler power from the infrared beam follow-ing first pass using a polarizing beam cube (PBC) inserted into the signal/idler beam(see Fig. 1). With the idler removed, the initial conditions for the second amplificationstage are similar to those for the first pass, and the final output power is not phase-dependent, as predicted by Eq. 1. Fig. 3(left) contains the results of a measurement ofthe signal power as a function of the second pass delay (Dl2) with the signal tuned to1552 nm with and without the polarizing beam cube inserted into the infrared beam.Results are similar for all wavelengths under study. As expected, with the idler filteredout, the 0.8 µm fringes disappear. The reduction in power with the idler removed is lessthan what might be predicted by Eq. 1 and 2; this is likely due to limitations of thissimple analysis resulting from the omission of pump saturation and walk-off effects.

Figure 3. Average power of signal as a function of second pass delay, with idlerremoved after first pass (black) and not removed for 1552 nm (left, purple) and1345 nm (right, blue).

Other characteristics of the system are improved by the removal of the idlerbefore the second amplification stage. The noise characteristics of the OPA output areimproved, as verified by an oscilloscope and spectrum analyzer both with and withoutthe polarizing cube present. Removal of the idler, furthermore, eliminates the spatialfringes from the beam profile, leading to a dramatic improvement in mode quality andstability. Since the output power depends smoothly on individual mirror orientations,the second-pass alignment procedure is also simplified.

6. Conclusions

In this work, we have investigated interferometric mixing in a double-pass OPA, inwhich both signal and idler beams are subjected to amplification on the second pass

(C) 1999 OSA 19 July 1999 / Vol. 5, No. 2 / OPTICS EXPRESS 26#11868 - $15.00 US Received July 09, 1999; Revised July 15, 1999

through the nonlinear crystal. We observe strong oscillations in the OPA signal power asa function of phase changes in the pump beam, as predicted from a simple coupled am-plitude equation analysis. Inclusion of the interferometric process can lead to improvedconversion efficiency, but at the cost of increased output noise, alignment sensitivity andreduced mode quality. In order to assess the effects of these difficulties, we selectivelyfiltered out the idler energy before the second pass using a polarizing beam cube. Thisled to a decrease in signal power, but with improved noise characteristics and spatialmode.

The relative impact of dual amplification of signal and idler on subsequentpasses will vary with amplifier configuration. Group velocity mismatch and spatial walk-off will often separate signal and idler pulses, leading to a phase-independent outputsignal. For situations in which signal and idler group delays match, however, interfero-metric mixing will be present and will have a strong impact on amplifier characteristics.The conclusions of this work thus demonstrate the need for careful consideration of pos-sible interferometric dependencies in the design of a multiple-pass parametric amplifier.

(C) 1999 OSA 19 July 1999 / Vol. 5, No. 2 / OPTICS EXPRESS 27#11868 - $15.00 US Received July 09, 1999; Revised July 15, 1999