We report, for the first time to our knowledge, on picosecond-pulse optical phase conjugation using photorefractive Sn2P2S6 crystals. For 7.2-ps pulses at 1.06 μm, we have achieved phase-conjugate reflectivities of up to 45% with very fast build-up times, about 15 ms at an intensity of 23 W/cm2 using Te-doped Sn2P2S6. We furthermore demonstrate aberration-free 5 W optical output of 8-ps pulses at 1.06 μm from a side pumped Nd:YVO4 amplifier using the Sn2P2S6-based phase-conjugate feedback.
© 2010 Optical Society of America
Picosecond laser sources with a high average output power are interesting for several applications, for example laser ablation, nonlinear optics, two-photon absorption, spectroscopy, second-harmonic microscopy, laser displays and others. For many of these applications, a good beam quality in terms of a narrow spectral width and a low beam propagation factor M 2 are required, which is in general very challenging for short-pulse lasers having a high average output power. A powerful technique to generate high-power laser outputs is to use doped crystals as amplifying media for an incident low-power beam. One of the very often used configurations for such amplifiers is the side-pumped bounce geometry, since it allows for easy pumping and power scaling, as well as very high repetition rates. Nd-doped yttrium vanadate Nd:YVO4 crystals are very promising for such amplification at the technologically important wavelength of 1.06 μm, due to the very large stimulated-emission cross section and a strong absorption for diode frequencies in comparison with a conventional Nd:YAG. Nd:YVO4 crystals can therefore generate high-power outputs with a very high conversion efficiency .
In recent years, highly efficient outputs from Nd:YVO4 side-pumped amplifiers have been successfully demonstrated in both cw and pulsed regimes. However, side-pumped vanadate amplifiers, in which high density population inversion is produced in a shallow absorption depth near the pump face (~1 mm), exhibit strong thermal lensing and aberration at high-power operation, which results in a degradation of beam quality (higher M 2 factor) and considerably limits the power scaling .
Volume holographic gratings produced in photorefractive crystals can be very efficiently exploited to dynamically clean high-power laser beams, which can result in very narrow cw spectral profiles [3, 4, 5], as well as diffraction-limited spatial profiles [6, 7]. The photorefractive effect has been shown to be very promising also for correcting thermal lensing effects occurring in Nd:YAG amplifiers [8, 9]. By using a self-pumped optical phase-conjugate mirror in a photorefractive crystal, one can direct back the amplified beam to the crystal to achieve both double-pass amplification and at the same time compensate for beam aberrations. For side-pumped Nd:YVO4 amplifiers, phase-conjugate feedback from a ring self-pumped Rh:BaTiO3 phase conjugator has been shown very promising for aberration corrections and power scaling in both cw  and picosecond [11, 12, 13, 14] operating regime. By power scaling with two Nd:YVO4 amplifiers and a phase-conjugate mirror, more than 70 W average power picosecond output from the Nd:YVO4 laser system has been demonstrated .
The key component for aberration correction of Nd:YVO4 systems with optical phase conjugation is a photorefractive material with a high sensitivity at 1.06 μm. The main material requirements for self-pumped optical phase conjugation are a high photorefractive gain Γ, long interaction length L, low absorption constant α ≪ Γ, as well as a real-time response. The materials should also stand high optical intensities, long-term operation and should exhibit a high environmental stability. From numerous photorefractive materials that have been developed in the last forty years , until recently Rh-doped BaTiO3 has been the only material of choice for applications at 1.06 μm. However, BaTiO3:Rh suffers from domain formation caused by 1.06-μm light  and has a phase transition very close to room temperature at ~ 9° C, therefore a new material is needed for photorefractive applications in this wavelength region . Additionally, the response time of BaTiO3 is very slow, typically in the order of several seconds, which considerably limits the application possibilities of this material.
Recently, Te-doped Sn2P2S6 has been developed with very promising properties for infrared photorefractive applications . Sn2P2S6 is a relatively new photorefractive ferroelectric material  with high photorefractive sensitivity even further in the infrared at 1.55 μm  and very fast response of a phase-conjugate mirror [22, 23, 24], typically two orders of magnitude faster as in BaTiO3:Rh. With 1.06-μm 20-W/cm2 light in the cw regime, phase-conjugate reflectivities of more than 40% have been obtained with 100 ms rise time using Sn2P2S6: Te .
Although Sn2P2S6 has been shown to be a very efficient photorefractive material, its potential for pulsed-laser applications in the infrared has not been explored yet. A holographic experiment has been performed in the nanosecond regime by Bally et al. at 1.06 μm with a pure Sn2P2S6 crystal exhibiting a strong charge compensating effect . In this case, a very small diffraction efficiency in the order of 10-3 has been achieved for single 3-ns pulses, and practically zero efficiency for repetition rates higher than 100 Hz . Another experiment has been performed in the visible interband regime also with a pure Sn2P2S6 crystal using 50-ns pulses at 532 nm, at the edge of the absorption band of Sn2P2S6 . In this case, diffraction efficiencies strongly diminished for repetition rates higher than 3 kHz. Here we show that Te-doped Sn2P2S6 without strong compensating effects can be a very efficient photorefractive material suitable for picosecond laser pulses. We report on the first photorefractive phase conjugation experiments in a Te-doped Sn2P2S6 in the picosecond regime using a high repetition-rate (100 MHz) ps laser at 1.06 μm wavelength. We first investigate the reflectivity and response time of the Sn2P2S6:Te phase-conjugate mirror in the picosecond regime and furthermore investigate its performance in a double-pass side-pumped Nd:YVO4 amplifier system pumped by a cw diode array.
2. Self-pumped optical phase conjugation of ps pulses in Te-doped Sn2P2S6
One of the most efficient, robust and stable geometries to achieve self-pumped optical phase conjugation in photorefractive materials is the ring-cavity configuration . The set-up we used for the characterization of Sn2P2S6:Te in this geometry is very simple, consisting of a Sn2P2S6 crystal, two cavity mirrors and 4-f imaging optics inside the ring cavity to compensate for diffraction; see Fig. 1(a). We used a picosecond pump laser with a repetition rate of 100 MHz, pulse width of 7.2 ps, and a total average output power of 200 mW at the wavelength of 1.06 μm. The light beams were polarized in the plane of the ring-cavity loop and were almost parallel to the x-axis in the Sn2P2S6 crystal. The angle θ within the cavity was about 30°, corresponding to the optimal angle for two-beam coupling in this material . The Te-doped Sn2P2S6 crystal had the dimensions of x × y × z = 10 mm × 6 mm × 7.44 mm along the main Cartesian axes defined as in Refs. [20, 23] with optically polished z faces. The crystal was coated with a 190-nm thick Al2O3 layer and rotated by about 45° with respect to the direction of the incident beam to reduce reflection losses. The absorption constant of the Sn2P2S6 :Te crystal used at the wavelength of 1.06 μm is low, in the order of α ≃ 0.1 cm-1, while the photorefractive gain is about Γ ≃ 4 cm-1, resulting in the coupling strength of ΓL ≃ 2.9 , i.e. well above the threshold of ΓL = 2 for self-pumped optical phase conjugation in the ring-cavity geometry .
In Figure 1(b) the temporal evolution of the phase-conjugate beam is shown for the maximum used input power. The phase-conjugate reflectivity R is defined by the ratio of the phase-conjugate and input beam average powers (R = P 2/P 3). The phase-conjugate rise time τ is defined as the time needed to reach 90% of the saturated reflectivity from 10%, i.e. τ = τ 90% - τ 10%, which is related to the build-up of the transmission grating without the influence of the grating competition effects occurring at the beginning of the process . Very short rise time τ = 15 ms has been measured for the intensity of I = 23 W/cm2 (see Fig. 1(b)). The initial time needed to start the rise of the phase-conjugate beam depends on many parameters, such as the over-threshold coupling strength, absorption, cavity losses, and scattering. In our case it is in the order of magnitude of the rise time τ.
Figure 2(a) shows the response rate 1/τ as a function of the input intensity I 3. As predicted by the conventional one-center photorefractive theory, response rate is a linear function of intensity . This indicates that for the investigated intensity range, the saturation effects that are often observed in short-pulse experiments for high peak intensities are not reached yet [30, 31, 32]. Compared with the cw measurements of the self-pumped phase conjugation at 1.06 μm using the same crystal and a very similar set-up , the slope d(1/τ)/dI is four times higher for ps pulses; i.e. the response at the same average intensity is for ps pulses four times faster as for the cw regime. This is rather unusual, since for very short pulses a saturation of the carrier number density is expected, which should decrease the response time in the pulsed regime . This may indicate that additional photorefractive centers become important for Sn2P2S6:Te. Indeed, although the origins of the photorefractive response in Sn2P2S6 are not clearly identified yet, there are several indications for a rather complex charge-transfer mechanism in this material [19, 20, 25, 33, 34]. The higher speed observed in the ps regime could be also due to additional two-photon absorption contribution, since the second-harmonic wavelength 0.53 μm is already at the edge of the absorption band of Sn2P2S6 . A similar enhancement of the response speed attributed to two-photon absorption was recently observed using femtosecond pulses in the visible using oxidized LiNbO3, where the grating-recording speed was enhanced by a factor of 40 compared to the cw case, still leading to a linear dependence of the response speed as a function of intensity . From the applications point of view, self-pumped phase-conjugation results with Sn2P2S6:Te are very positive indicating no detrimental saturation effects and even speeding-up of the effect in the picosecond regime.
In Fig. 2(b) the steady-state phase-conjugate reflectivity is shown as a function of the input intensity. In the investigated intensity range, the reflectivity at high intensities does not start to decrease due to possible electron-hole competition effects . We measured phase-conjugate reflectivities of more than 45 percent, which is in good agreement with the measurements with a cw laser at the same wavelength . The only measured point that deviates considerably is the measurement at the lowest intensity of 2.3 W/cm2. Here the measured phase-conjugate reflectivity is much higher for ps pulses compared to the case for cw lasers, for which the reflectivity at this intensity was already limited by the dark conductivity. This again suggests a more effective charge excitation in Sn2P2S6:Te by ps pulses compared to the cw regime.
3. High-power diode-pumped Nd:YVO4 amplifier using Sn2P2S6:Te phase-conjugate mirror
In this section we report on the performance of the Te-doped Sn2P2S6 phase-conjugate mirror as a feedback mirror in a master-oscillator power amplifier (MOPA) system. We employed a similar experimental set-up as in Ref. , with a diode-pumped amplifier in a bounce geometry, see Fig. 3. The amplifier used was a 1.0 at. % a-cut Nd:YVO4 slab crystal of dimensions a×b×c = 20 mm × 5 mm × 2 mm, with anti-reflection coating for 1 μm and cut at 5° at the end surfaces to prevent self-lasing. The crystal was wrapped in indium foil and sandwiched between two aluminium blocks. The temperature of the blocks was maintained at about 10° C using a water re-circulating cooler. The amplifier was transversely pumped by a cw single-bar diode array emitting at the wavelength around 808 nm. The signal laser used for the amplifier was the same as used for the characterization of the Sn2P2S6:Te phase-conjugate mirror, a commercial diode-pumped cw mode-locked Nd:YVO4 laser with a pulse width of 7.2 ps and a repetition rate of 100 MHz.
In our experiment the average power of the incident signal into the amplifier was 15 mW. At the maximum diode pump power of 46 W, the signal beam was amplified in a single pass to approximately 400 mW. This beam was directed onto the Te-doped Sn2P2S6 crystal to form a self-pumped phase-conjugate mirror in ring cavity scheme. As shown in the previous section, about 45 percent of this power was reflected back as a phase-conjugate beam and amplified in a second pass through the amplifier. The final output power for the maximum pump power is more than 5 W (see Fig. 4). For comparison, we also show the results obtained with an optimized BaTiO3:Rh phase-conjugate mirror. The BaTiO3:Rh crystal with 1000 pm doping level had dimensions of a×b×c = 8 mm × 7 mm × 6 mm, was cut normal to the a axis and antireflection coated for 1 μm; the same crystal was employed in Refs. [13, 14] and also leads to a maximal phase-conjugate reflectivity of about 45%. We see that the amplification of phase-conjugate MOPA is with Sn2P2S6:Te phase-conjugate mirror as good as with BaTiO3:Rh.
For a double-pass amplifier with a conventional mirror in a similar geometry and amplification as used here, the beam propagation parameter after amplification was about M 2 ~ 3 . The spatial TEM00 output from the double-pass amplifier with the Sn2P2S6:Te phase-conjugate mirror is shown in Fig. 5. The output exhibited beam propagation parameters Mx 2 < 1.33 and My 2 < 1.25. For comparison the figure also shows the spatial form of the original signal beam delivered by the signal laser with M 2 of about 1.2. The signal amplified by about 350 times is not considerably distorted, demonstrating that the double-pass amplifier with the phase-conjugate mirror using Te-doped Sn2P2S6 has a good potential for correction of thermal distortions inside the amplifier.
The duration of the amplified pulse from a double-pass amplifier was investigated by measuring the intensity autocorrelation trace using second harmonic generation in a 5-mm thick KTP (KTiOPO4) crystal. The results are shown in Fig. 6(a). For comparison also the autocorrelation traces for the signal (master) beam and the amplified signal beam after the single pass are shown. The full width at half maximum (FWHM) of the original signal beam is 6.9 ps, obtained by considering a Gaussian-shape pulse. After the first pass through the amplifier the FWHM of the single-pass amplified beam is 8.3 ps. For the amplified phase-conjugate beam (double-pass amplified) the FWHM is 8.6 ps. Therefore, the pulse duration is not considerably broadened after phase conjugation in Sn2P2S6:Te, meaning that the bandwidth of the photorefractive grating is large enough to not induce substantial frequency narrowing effects. The about 20% broadening of the pulse duration of the amplified beam is therefore mainly due to the finite gain-bandwidth of the amplifier, as also observed for the phase-conjugate MOPA system using BaTiO3:Rh . We also measured the spectrum of the signal (master) beam and the phase-conjugate beam from the Sn2P2S6:Te crystal (see Fig. 6(b)), confirming no change in the central wavelength or the spectral narrowing of the phase-conjugate beam.
The important parameters for many applications are the build-up time of the amplification and the switching time for changing the pump power. For BaTiO3:Rh the long build-up time of the phase-conjugate mirror is a serious drawback for most applications, as well as for the alignment and optimization of the set-up. Figure 7(a) shows the build-up dynamics of the mirror without pumping, for both Sn2P2S6:Te and BaTiO3:Rh using 200 mW signal beam (23 W/cm2 average intensity). While in Sn2P2S6:Te the rise time is about 15 ms, for BaTiO3:Rh the reflectivity is still increasing even after 10 minutes of operation, i.e. the measured phase-conjugate response at 1.06 μm in the ps regime is for Sn2P2S6:Te more than four orders of magnitude faster than in BaTiO3:Rh. When the transmission grating responsible for the phase conjugation is already built up, the response after switching the pump power is faster also for BaTiO3:Rh, as shown in Fig. 7(b), however the steady-state is again reached almost in real time for Sn2P2S6:Te, while it takes more than 10 s for BaTiO3:Rh for changing the pump power from 18.5 W to 21 W. The initial fluctuations observed in Fig. 7(b) are due to the thermal fluctuations of the laser diode frequency after switching the driving current.
We have performed the first photorefractive phase conjugation experiments with Sn2P2S6 in the pulsed regime. For the investigation we have used a Te-doped Sn2P2S6 crystal and a high repetition rate 100 MHz ps pulses at 1.06 μm wavelength. For 7.2-ps pulses with 23 W/cm2 average power we have achieved a very fast rise time of about 15 ms and phase-conjugate reflectivity of 45%. We have furthermore used the Sn2P2S6:Te phase-conjugate mirror as a feedback mirror in a double-pass side-pumped Nd:YVO4 amplifier, pumped by a cw 808 nm diode array. From a 15-mW signal beam at 1.06 μm (about 7 ps pulse length and 100 MHz repetition rate) we have obtained an almost diffraction limited output with 5 W average power, without considerable distortions of the pulse length and frequency. We have demonstrated that the amplification with Sn2P2S6:Te is as good as with an efficient BaTiO3:Rh crystal, however the response rate is increased by more than four orders of magnitude (miliseconds compared to minutes) for starting the operation. This makes Sn2P2S6:Te a very promising material for corrections of aberrations in high-power picosecond amplifiers at 1.06 μm.
This work was supported by the Swiss National Foundation (200020-119961) and a Scientific Research Grant-in-Aid (16032202, 18360031). T. Bach acknowledges the support from the International co-operation project by the Swiss National Foundation (IZAJZ0-123463) and the Japan Society for the Promotion of Science (JSPS/RCI-2/08040 ID No. RC 20830002).
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