Interferometric nonlinear mixing in multiple-pass femtosecond optical parametric amplification.

doi:10.1364/OE.5.000021

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Interferometric nonlinear mixing in multiple-pass femtosecond optical parametric amplification.

James Fraser and Kimberley Hall »View Author Affiliations

Optics Express, Vol. 5, Issue 2, pp. 21-27 (1999)
http://dx.doi.org/10.1364/OE.5.000021

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Abstract

We demonstrate that in multi-stage optical parametric amplifiers, spatial and temporal overlap of all products and pump on subsequent passes lead to strongly phase-dependent conversion, which has important consequences for output noise and beam profile characteristics. We verify a simple method to avoid this interferometric process.

[Optical Society of America ]

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 noncentrosymmetric nonlinear crystals, seeded using white light generation or parametric fluorescence. In order to maximize conversion efficiency, a multiple-pass configuration is commonly employed in which one compensates for the group velocity mismatch (GVM) and spatial walk-off between the pump pulses and the infrared signal and idler pulses using separate delay lines.

A number of multiple-pass alignment schemes have been presented in the literature (for example [1

J.C. Deàk, L.K. Iwaki, and D.D. Dlott, “High-power picosecond mid-infrared optical parametric amplifier for infrared Raman spectroscopy,” Opt. Lett. 22, 1796–1798 (1997). [CrossRef]

–5

M.K. Reed and M.K.S. Shepard, “Tunable infrared generation using a femtosecond 250 kHz Ti:sapphire regenerative amplifier,” IEEE J. Quantum Electron. 32, 1273–1277 (1996). [CrossRef]

]). In these works, it is often unclear whether both the signal and idler beams are included in the amplification process on subsequent passes through the nonlinear crystal, and if so, whether the authors have addressed issues relating to the phases of the optical fields. As we will demonstrate, simultaneous overlap of all three beams on subsequent passes can lead to critical changes in the physical properties of the parametric down-conversion process.

In this paper, we report the characterization of the signal output of a commercial double-pass optical parametric amplifier(OPA). The design of this system incorporates dual amplification of the signal and idler in the second stage. Our measurements reveal strong oscillations in amplification efficiency with changes in the phase of the 800 nm pump pulses, consistent with the presence of an interferometric nonlinear mixing process. These results have significant implications for the design of parametric amplifiers, and we present a discussion of the key considerations in ensuring optimum performance in systems which incorporate multiple stages.

2. The Optical Parametric Amplifier

The parametric amplifier used to investigate the interferometric mixing process is a Coherent OPA 9800 [5

M.K. Reed and M.K.S. Shepard, “Tunable infrared generation using a femtosecond 250 kHz Ti:sapphire regenerative amplifier,” IEEE J. Quantum Electron. 32, 1273–1277 (1996). [CrossRef]

], although the characteristics under study are not unique to this system. The OPA (Fig. 1) is based on type II down conversion (e→e+o) in a 3 mm Beta-Barium Borate (BBO) crystal (θ=32°) which is angle tuned for phase matching in the mid-infrared. The signal pulses are tunable from 1.2 to beyond 1.6 µm, providing idler wavelengths in the range from below 1.6 to 2.4 µm. The parametric process is pumped by 150 fs, 4 µJ pulses, produced at a repetition rate of 250 kHz through regenerative amplification of the output of a Titanium sapphire oscillator operating at a center wavelength of 803 nm. The down-conversion process is seeded using white light generation (WLG), created by focusing 20% of the 4 µJ pump pulses into a sapphire disk. The idler and pump have parallel polarizations, while the signal is orthogonal. The system incorporates two amplification stages in which compensation for GVM and spatial walk-off between the pump and infrared beams is provided using a separate variable delay line for the pump pulses alone (Dl2). Signal and idler share the same optical path on second pass. In both pump and midinfrared optical paths, a fused silica lens 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- dielectric 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.

3. Signal Output Characteristics

Measurements were made of the OPA signal power as a function of the delay of the pump pulses (Dl2) and for a range of tuning conditions. The signal beam was attenuated and focused 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 through the use of a stepper motor with a microstep driver.

Data for OPA signal wavelengths between 1.345 and 1.591 µm as a function of Dl2 appear in Fig. 2. Due to the nature of the tuning process, there is a temporal offset which varies from wavelength to wavelength, and so for comparison purposes, the zero of delay is set to align the traces in Fig. 2. Strong oscillations in the magnitude of the signal power are observed as the second pass pump delay is varied across the range of pulse overlap between the pump and infrared beams (Fig. 2 inset). Analysis using a fast Fourier transform shows that the period of the oscillations is 818nm±6nm, suggesting the presence of an interferometric process dependent on the pump wavelength. The data in Fig. 2 also reveal a strong sensitivity to the signal wavelength. A symmetric pattern with maximum fringe visibility was found with the signal tuned to 1.56 µn. With the signal tuned closer to the degeneracy wavelength of 1.6 µm, stronger power modulations are seen at negative time delays, while tuning to shorter signal wavelengths leads to more prevalent fringes for positive delays.

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

In addition to these temporal modulations in average power, the spatial profile of the signal beam showed clear signs of interference fringes. Variations in Dl2 or in any of the second pass mirror orientations was observed to cause these fringes to scan across the beam profile. Furthermore, the number of fringes within the spatial profile increased as the alignment of the pump and infrared beams through the BBO was caused to deviate from collinear. The simultaneous presence of multiple spatial fringes corresponded to a reduced temporal fringe visibility. The data in Fig. 2 was obtained after the OPA was aligned to maximize output power, which corresponded to a near collinear orientation.

4. Theory and comparison to results

Optical parametric amplification exploits the noncentrosymmetry in a crystalline medium to allow for the transfer of energy between fields at different frequencies. The parametric mixing process is described by a solution of Maxwell’s equations in the nonlinear medium of the BBO crystal, as clearly outlined in Bloembergen and co-worker’s seminal work [6

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

]. On the first pass, when collinear signal and pump beams are incident on a transparent crystal of length L, using the slowly-varying amplitude approximation and in the limit of negligible pump depletion and zero phase mismatch, the intensity of signal (ω_s ) and idler (ω_i ) beams at the output face of the crystal can be shown to be:

I_{s} = \frac{n_{s} c}{2 π} [{({\bar{A}}_{s} (0))}^{2} \cosh^{2} κ L]

(1a)

I_{i} = \frac{n_{i} c}{2 π} [{(\frac{ω_{i}}{ω_{s}})}^{2} \frac{k_{s}}{k_{i}} {({\bar{A}}_{s} (0))}^{2} \sinh^{2} κ L]

(1b)

Here we have followed the notation of Boyd [7

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

], in which the electric fields are denoted by

E_{i} (z, t) = A_{i} (z) e^{i (k_{i} z + ω_{i} t)}

complex conjugate, where we have defined

{\overset{}{A}}_{x} (z) = {\bar{A}}_{x} (z) e^{i ϕ_{x}}

so that Ā_x is a real value, n_x and k_x are the refractive index and wavevector magnitude of the beam at frequency

ω_{x}, κ = \frac{8 π ω_{s} ω_{i} d}{c^{2} \sqrt{k_{s} k_{i}}} \bar{A_{p}},

, and d is the effective nonlinear coefficient determined by the crystal type, frequencies and experimental geometry. This solution corresponds to exponential amplification of the signal seed and generation and amplification of the idler.

On second pass, for the case in which all three beams are present at the entrance to the nonlinear crystal, the intensity of signal (ω_s ) and idler (ω_i ) beams at the output face of the crystal can be shown to be:

I_{s} = \frac{n_{s} c}{2 π} [{({\bar{A}}_{a} (L))}^{2} \cosh^{2} κ L + {(\frac{ω_{s}}{ω_{i}})}^{2} \frac{k_{i}}{k_{s}} {({\bar{A}}_{i} (L))}^{2} \sinh^{2} κ L

+ 2 \frac{ω_{s}}{ω_{i}} \sqrt{\frac{k_{i}}{k_{s}}} {\bar{A}}_{s} (L) {\bar{A}}_{i} (L) \cosh κ L \sinh κ L \sin (ϕ_{s} + ϕ_{i} - ϕ_{p})]

(2a)

I_{i} = \frac{n_{i} c}{2 π} [{({\bar{A}}_{i} (L))}^{2} \cosh^{2} κ L + {(\frac{ω_{i}}{ω_{s}})}^{2} \frac{k_{s}}{k_{i}} {({\bar{A}}_{s} (L))}^{2} \sinh^{2} κ L

+ 2 \frac{ω_{i}}{ω_{s}} \sqrt{\frac{k_{s}}{k_{i}}} {\bar{A}}_{s} (L) {\bar{A}}_{i} (L) \cosh κ L \sinh κ L \sin (ϕ_{s} + ϕ_{i} - ϕ_{p})]

(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 quantifiable results and suggests certain qualitative features without resorting to numerical methods. Instead of simple exponential amplification of signal and idler beams, Eq. 2 predicts that the direction of energy transfer will correspond to either up conversion (signal and idler depletion) or down conversion (signal and idler amplification) depending on the relative phases of the beams. Small changes in delay between the three beams will therefore lead to large variations in the total power in the signal and idler after the second stage of amplification. These oscillations are superimposed onto a smooth background due to the first two terms in Eq 2.

We have written Eq. 2 to specifically highlight its interferometric nature. An equivalent interpretation of these results is that on second pass, mixing between signal and pump generates a new idler beam that interferes with the beam generated on first pass. Mixing between idler and pump generates a new signal beam that interferes with the original signal beam. This phenomenon is closely related to the work of Chudinov et al. [8

A.N. Chudinov, Yu.E. Kapitzky, A.A. Shulginov, and B.Ya. Zel’Dovich, “Interferometric phase measurements of average field cube $E_{ω}^{2}$ $E_{2 ω}^{*}$ ,” Opt. Quantum Electron. 23, 1055–1060 (1991). [CrossRef]

], who, in the case of second harmonic generation, demonstrated that two cascaded mixing processes can lead to phase sensitive output intensities.

The phase dependency of the output intensities described by Eq. 2 are consistent with the oscillations seen in Fig. 2: the oscillatory period of (818±6) nm is <2% from the center wavelength of the pump pulses. The sensitivity of the shape of the fringe pattern to variations in tuning conditions may be accounted for through consideration of the combined effects of GVM in the BBO crystal and in the various glass elements through which the signal and idler travel (including the lens and Dm2 shown in Fig. 1). As discussed above, in order to observe interferometric amplification, both the signal and idler must simultaneously have nonzero amplitudes in the BBO crystal, and thus the pulse amplitudes must be overlapped in time and space. Far from degeneracy, the GVM in the glass causes the idler pulse to be delayed in time relative to the signal. One can see from the data in Fig. 2 that individual pulse envelopes are beginning to be resolved already at 1.345 µm (As discussed in Section 5. and shown in Fig. 3(right), the left peak is due to the signal alone.) The rapid reduction in the fringe visibility observed as the signal and idler begin to separate in time is likely enhanced by a small amount of chirp present both in the pump and infrared pulses. This arises from imperfect compression of the regeneratively amplified pulses in conjunction with additional chirp inherent to the 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, which arises due to the birefringence of the material, becomes the dominate source of pulse walk-off and has an opposite sign to that in glass. As a result, one expects the signal pulse envelope to trail that of the idler for signal wavelengths near 1.6 µm. This is consistent with the observation of stronger fringes for negative delays with the signal wavelength tuned longer than 1.56 µm.

For a general OPA signal wavelength, therefore, one observes the competing effects of the two sources of GVM. The observation of maximum fringe visibility with the signal tuned to 1.56 µm, accompanied by a symmetric fringe pattern with respect to delay, indicates that the GVM in the glass is compensated by the BBO GVM, corresponding to minimum pulse walk-off. The importance of the interferometric mixing process for OPA signal wavelengths near 1.56 µm is of particular relevance to researchers interested in accessing standard optical communications wavelengths around 1.5 µm.

5. Design Considerations

The incorporation of interferometric mixing into an OPA design affords the possibility of obtaining higher output power than would be possible if dual amplification of the signal 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 for an interferometrically stable configuration. Power stability will be limited by vibrations from all environmental sources. Experiments in which lock-in detection techniques are employed will be especially sensitive to slow power drifts due to variations in ambient temperature or air flow. In addition, the strong sensitivity of the signal characteristics to wavelength tuning is undesirable. Separation of signal and idler into individual delay lines would provide a way to compensate for GVM, but necessitates the use of a more complicated geometry. The mode quality of the OPA output beams is also vulnerable to minor misalignment of the optical set-up, as any deviation from non-collinearity will introduce 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 large changes to the relative phase, alignment is more challenging for an OPA which incorporates phase-sensitive mixing than for a non-interferometric setup. Though not a serious concern in our manual system, this would have important repercussions if part or all of the alignment procedure is automated [9

E. Freysz, J. Plantard, R. Gillet, R.M. Rassoul, P. Grelu, and A. Ducasse, “Automatic time delay optimization between the pump and seed pulses of a broadly tunable femtosecond optical parametric amplifier,” Appl. Opt. 37, 2411–2413 (1998). [CrossRef]

In order to evaluate the impact of these issues, the system was modified to eliminate the interferometric mixing process in the second stage of amplification. This was accomplished by selectively filtering out the idler power from the infrared beam following 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 amplification stage 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 of the signal power as a function of the second pass delay (Dl2) with the signal tuned to 1552 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 filtered out, the 0.8 µm fringes disappear. The reduction in power with the idler removed is less than what might be predicted by Eq. 1 and 2; this is likely due to limitations of this simple 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 idler removed after first pass (black) and not removed for 1552 nm (left, purple) and 1345 nm (right, blue).

Other characteristics of the system are improved by the removal of the idler before the second amplification stage. The noise characteristics of the OPA output are improved, as verified by an oscilloscope and spectrum analyzer both with and without the polarizing cube present. Removal of the idler, furthermore, eliminates the spatial fringes from the beam profile, leading to a dramatic improvement in mode quality and stability. 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, in which both signal and idler beams are subjected to amplification on the second pass through the nonlinear crystal. We observe strong oscillations in the OPA signal power as a function of phase changes in the pump beam, as predicted from a simple coupled amplitude equation analysis. Inclusion of the interferometric process can lead to improved conversion efficiency, but at the cost of increased output noise, alignment sensitivity and reduced mode quality. In order to assess the effects of these difficulties, we selectively filtered out the idler energy before the second pass using a polarizing beam cube. This led to a decrease in signal power, but with improved noise characteristics and spatial mode.

The relative impact of dual amplification of signal and idler on subsequent passes will vary with amplifier configuration. Group velocity mismatch and spatial walk-off will often separate signal and idler pulses, leading to a phase-independent output signal. For situations in which signal and idler group delays match, however, interferometric 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 possible interferometric dependencies in the design of a multiple-pass parametric amplifier.

References

1.	J.C. Deàk, L.K. Iwaki, and D.D. Dlott, “High-power picosecond mid-infrared optical parametric amplifier for infrared Raman spectroscopy,” Opt. Lett. 22, 1796–1798 (1997). [CrossRef]
2.	L. Carrion and J.P. Girardeau-Montaut, “Performance of a new picosecond KTP optical parametric generator and amplifier,” Opt. Commun. 152, 347–350 (1998). [CrossRef]
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). [CrossRef]
4.	F. Seifert, V. Petrov, and F. Noack, “Sub-100-fs optical parametric generator pumped by a high-repetition-rate Ti:sapphire regenerative amplifier system,” Opt. Lett. 19, 837–839 (1994). [CrossRef] [PubMed]
5.	M.K. Reed and M.K.S. Shepard, “Tunable infrared generation using a femtosecond 250 kHz Ti:sapphire regenerative amplifier,” IEEE J. Quantum Electron. 32, 1273–1277 (1996). [CrossRef]
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 phase measurements of average field cube $E_{ω}^{2}$ $E_{2 ω}^{*}$ ,” Opt. Quantum Electron. 23, 1055–1060 (1991). [CrossRef]
9.	E. Freysz, J. Plantard, R. Gillet, R.M. Rassoul, P. Grelu, and A. Ducasse, “Automatic time delay optimization between the pump and seed pulses of a broadly tunable femtosecond optical parametric amplifier,” Appl. Opt. 37, 2411–2413 (1998). [CrossRef]

OCIS Codes
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

ToC Category:
Research Papers

History
Original Manuscript: July 12, 1999
Published: July 19, 1999

Citation
James Fraser and Kimberley Hall, "Interferometric nonlinear mixing in multiple-pass femtosecond optical parametric amplification.," Opt. Express 5, 21-27 (1999)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-5-2-21

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References

J. C. Deàk, L. K. Iwaki and D. D. Dlott, "High-power picosecond mid-infrared optical parametric amplifier for infrared Raman spectroscopy," Opt. Lett. 22, 1796-1798 (1997). [CrossRef]
L. Carrion and J.P. Girardeau-Montaut, "Performance of a new picosecond KTP optical parametric generator and amplifier," Opt. Commun. 152, 347-350 (1998). [CrossRef]
J. Y. Zhang, Z. Xu, Y. Kong, C. Yu and Y. Wu, "Highly effcient, widely tunable, 10-Hz parametric amplifier pumped by frequency-doubled femtosecond Ti:sapphire laser pulses," Appl. Opt. 37, 3299-3305 (1998). [CrossRef]
F. Seifert, V. Petrov, and F. Noack, "Sub-100-fs optical parametric generator pumped by a high-repetition-rate Ti:sapphire regenerative amplifier system," Opt. Lett. 19, 837-839 (1994). [CrossRef] [PubMed]
M. K. Reed and M. K. S. Shepard, "Tunable infrared generation using a femtosecond 250 kHz Ti:sapphire regenerative amplifier," IEEE J. Quantum Electron. 32, 1273-1277 (1996). [CrossRef]
N. Bloembergen, Nonlinear Optics, (W.A. Benjamin Inc., Reading, Massachusetts, 1965).
R. W. Boyd, Nonlinear Optics, (Academic Press, San Diego, USA, 1992).
A. N. Chudinov, Yu. E. Kapitzky, A. A. Shulginov and B. Ya. Zel'Dovich, "Interferometric phase measurements of average field cube E2wE*2w," Opt. Quantum Electron. 23, 1055-1060 (1991). [CrossRef]
E. Freysz, J. Plantard, R. Gillet, R. M. Rassoul, P. Grelu and A. Ducasse, "Automatic time delay optimization between the pump and seed pulses of a broadly tunable femtosecond optical parametric amplifier," Appl. Opt. 37, 2411-2413 (1998). [CrossRef]

Other

J. C. Deàk, L. K. Iwaki and D. D. Dlott, "High-power picosecond mid-infrared optical parametric amplifier for infrared Raman spectroscopy," Opt. Lett. 22, 1796-1798 (1997). [CrossRef]
L. Carrion and J.P. Girardeau-Montaut, "Performance of a new picosecond KTP optical parametric generator and amplifier," Opt. Commun. 152, 347-350 (1998). [CrossRef]
J. Y. Zhang, Z. Xu, Y. Kong, C. Yu and Y. Wu, "Highly effcient, widely tunable, 10-Hz parametric amplifier pumped by frequency-doubled femtosecond Ti:sapphire laser pulses," Appl. Opt. 37, 3299-3305 (1998). [CrossRef]
F. Seifert, V. Petrov, and F. Noack, "Sub-100-fs optical parametric generator pumped by a high-repetition-rate Ti:sapphire regenerative amplifier system," Opt. Lett. 19, 837-839 (1994). [CrossRef] [PubMed]
M. K. Reed and M. K. S. Shepard, "Tunable infrared generation using a femtosecond 250 kHz Ti:sapphire regenerative amplifier," IEEE J. Quantum Electron. 32, 1273-1277 (1996). [CrossRef]
N. Bloembergen, Nonlinear Optics, (W.A. Benjamin Inc., Reading, Massachusetts, 1965).
R. W. Boyd, Nonlinear Optics, (Academic Press, San Diego, USA, 1992).
A. N. Chudinov, Yu. E. Kapitzky, A. A. Shulginov and B. Ya. Zel'Dovich, "Interferometric phase measurements of average field cube E2wE*2w," Opt. Quantum Electron. 23, 1055-1060 (1991). [CrossRef]
E. Freysz, J. Plantard, R. Gillet, R. M. Rassoul, P. Grelu and A. Ducasse, "Automatic time delay optimization between the pump and seed pulses of a broadly tunable femtosecond optical parametric amplifier," Appl. Opt. 37, 2411-2413 (1998). [CrossRef]

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