By using spectrally noncritical phase-matching in a partially deuterated KDP around its retracing point of phase-matching, we have experimentally and numerically investigated the characteristics of second-harmonic generation (SHG) with femtosecond laser at 1 μm for the first time. This phase-matching configuration can support efficient SHG over 20nm bandwidth of the fundamental laser at 1 μm in a 10-mm-long crystal. Efficiency of harmonic conversion as high as 55% has been demonstrated.
©2004 Optical Society of America
Second-harmonic generation (SHG) is a powerful technique of wavelength extension. It has long been appreciated that the efficiency of phase-matched SHG strongly depends on the matching between the spectral content of the input fundamental light and the spectral acceptance bandwidth provided by doubling crystals . In order to increase the conversion efficiency and to avoid harmonic pulse broadening in the regime of ultrashort lasers, the overall group-velocity mismatch (GVM) between the fundamental and the second-harmonic pulses in the crystal needs to be sufficiently small compared with the fundamental pulse duration, or equivalently in frequency domain the spectral acceptance of the crystal needs to be sufficiently large compared with the fundamental pulse bandwidth. To meet this requirement, very thin crystals must be used , which results in low conversion efficiency in most cases unless these crystals are pumped with very high intensities that will be ultimately limited by the damage thresholds of the crystals and other nonlinear effects such as χ(3) processes. Several approaches have been tried to broaden the effective spectral acceptance bandwidth, which can be divided into two categories. In the first category, special geometries have been adopted, including achromatic phase-matching (APM) [3–5], multicrystal sequence , tilted quasi-phase-matched gratings , Čerenkov phase-matching , etc. While it seems that all these techniques are wavelength-independent and suitable for arbitrary spectral region, they are not likely to be practical due to the complexity and quite strict requirements for alignment of the optics. In the second category, the so-called spectrally noncritical phase-matching was used [9–12], which took the advantage of the fact that there exists a zero-GVM wavelength of SHG for a specific crystal; i.e., the first-order wavelength-sensitivity of wave-vector mismatch vanishes at that wavelength. The spectral acceptance bandwidth is then roughly determined by the second-order wavelength-sensitivity parameter and is inversely proportional to the square-root of the crystal length. In this case, the doubling configuration is just like the conventional one and no modifications of the input light are needed, which makes it more practical in the sense of simplicity, reliability and conversion efficiency. The main problem is the availability of proper crystal for a specific wavelength. Fortunately, several mature crystals were investigated and found to be suitable for broadband SHG at certain wavelengths, such as BBO for 1.5 μm , LBO for 1.3 μm , MgO-doped PPLN for 1.55 μm communication band , partially deuterated KDP for 1.034 μm to 1.179 μm region and potentially KDP analogs for 1.013 μm to 1.278 μm region.  The availability of crystal suitable for broadband SHG at wavelength shorter than 1μm, especially in the 800 nm region, is still a big challenge for material science, though. While the ability of broadband SHG in partially deuterated KDP at 1 μm was indirectly verified, the conversion efficiency could not be evaluated since a tunable narrowband ns light source was used.  In this paper we extended this idea directly to femtosecond laser at 1 μm that is an important wavelength besides the 800 nm Ti:Sapphire laser source, the characteristics of SHG with femtosecond laser were experimentally and numerically investigated for the first time. Efficient SHG with a bandwidth over 20 nm was obtained with efficiency of ~55% in a partially deuterated KDP around its retracing point of phase-matching.
2. Experiments and simulations
As a femtosecond light source in the experiments, we used a lithium niobate based optical parametric amplifier (OPA) pumped by a femtosecond Ti:sapphire regenerative amplifier. The OPA produced pulse energy of 15–25 μj in the vicinity of 1.05 μm, with duration of 180–250 fs. A partially deuterated KDP with deuteration level of ~12% cut at θ=41° for type I phase-matching was used as the doubling crystal. The retracing point (i.e., wavelength) occurs at a specific phase-matching angle for a certain nonlinear crystal. Partially deuterated KDP has the advantage that the retracing point of which can be tuned with deuteration level. We intended to adopt the above deuteration level to obtain the spectrally noncritical phase-matched SHG at 1.054 μm. The crystal length was designed to be 10 mm based on the numerical simulation of the nonlinear coupled-wave equations. It provides an acceptance bandwidth of about 20 nm at the retracing point when the SHG falls into the regime of saturation (efficiencies > 50%). The crystal parameters were obtained by the linear-combination model  and Sellmeier equations for KDP and KD*P. 
To investigate the characteristics of SHG around the retracing point, the OPA was tuned to operate around 1.054 μm with a bandwidth over 35 nm that is larger than the acceptance bandwidth of the crystal. The typical experimental results of the output SHG spectrum with the crystal orientation are shown in Fig.1. By decreasing the angle θ of the crystal, approaching to the retracing point [Figs. 1(a) and 1(b)], two wavelength components within the input spectrum are phase-matched simultaneously, which reflects the retracing characteristics of the phase-matching. When we compare Fig. 1(a) with Fig. 1(b), it can be found that both of the phase-matched peaks move towards the retracing wavelength and the separation of them becomes smaller with the increasing θ. When the retracing point is reached, the two peaks link together and a single phase-matched peak with broader spectrum is formed, which is shown in Fig. 1(c). To observe above phase-matching characteristics, a sufficiently broad bandwidth of input laser is necessary. Only in this situation, the phase-matched and non-phase-matched features will show up simultaneously. This helps us to determine the crystal orientation of the retracing point experimentally, which is crucial for further investigations. The feature of harmonic spectrum evolution also offers an alternative method to determine the value of retracing wavelength. The retracing wavelength deduced from Fig. 1(c) is about 1054 nm that is consistent with our design value.
We should note that the light sources used in those references were narrow-band ns pulses [11–12] the retracing characteristics and the ability of broadband SHG were manifested by scanning the input wavelength at a certain orientation or temperature setting of the crystals. Different wavelengths were experimentally independent. By using femtosecond lasers, however, there are χ(2) nonlinear couplings among different frequency components and dispersion effects, which makes the output spectrum fundamentally different. All these features cannot be revealed in the scanning narrow-band cases. Standard nonlinear coupled wave equations in time domain were applied to study SHG of femtosecond laser around the retracing point. In the simulations, dispersions up to the second order were included, while all the transverse effects such as diffraction and walk-off were simply neglected. Detailed numerical calculations of the output SH spectrum including these effects are shown in Fig.2, where ΔKL (ΔK times L), an equivalent measure of the crystal orientation angle θ, is the phase-mismatch at the retracing wavelength (i.e., 1.054 μm). Sufficiently broad input fundamental spectrum (Δλ=150 nm, corresponding to 10 fs pulse duration) was assumed in the calculations. The two main peaks in Fig. 2(a) and (b) correspond to the phase-matched components, while other minor peaks can be attributed to those spectral components where phase-mismatch are odd multiple of π. With the decreasing of ΔKL, i.e., θ approaches to the retracing point, the two phase-matched peaks move to the retracing wavelength symmetrically, and link together to form a single peak when ΔKL=0 is exactly reached, as shown in Fig. 2(c). The spectral width of this peak is much broader than those of the individual peaks, indicating that the spectrally noncritical phase-matching is satisfied. Several side lobes still appear on the SH spectrum since the input fundamental spectrum is sufficiently broad.
The predicted evolution behavior of the SH spectrum agrees well with the experimental results qualitatively. In Figs. 1 and 2, the laser spectrum was centered to the retracing wavelength of 1.054 μm. If the fundamental wavelength deviated slightly from the retracing value, we observed similar features but with asymmetric SH spectra. Figures 1 and 2 have suggested that spectral bandwidth is the most important parameter in SHG at the retracing point. This SHG process is basically independent on the pulse chirp and/or duration, since GVM vanishes at the retracing point. Thus, the obtained results can be valid for broadband lasers with various pulse durations from tens femtosecond to nanosecond.
In order to match the acceptance bandwidth at the retracing point of the crystal used and to expect high SHG conversion efficiency, we spectrally filtered the output from the OPA. We obtain a bandwidth of 23 nm centered at 1.054 μm, and the pulse energy was reduced to ~10 μj. This pulse was with some chirp, and its duration was measured to be ~250 fs. Figure 3 shows the output SH spectrum, and the input fundamental spectrum is given in the inset. The bandwidth of the SH pulse as broad as 17 nm was obtained. In addition, pulse-to-pulse stability of the SH pulses is ~±5%. The corresponding autocorrelation trace of the SH pulse is shown in Fig. 4, which gives a pulse duration of ~200 fs. Though the autocorrelation traces are with some unusual asymmetry due to the unsatisfactory power-driver of the optical delay-line, the measurements suggest that the laser bandwidth is not beyond the acceptance bandwidth of the crystal. When the crystal setting deviated from its retracing point, multi-peak features as Fig. 1 were not observed in this bandwidth-matched case. Only single peak of SH spectrum was obtained, and its width was maximized at the retracing point. These experimental results are basically consistent with the theoretical estimations. As a comparison, SH bandwidth of ~8 nm (not given) was obtained with a 10-mm-long KDP at its phase-matching angle, under the same input conditions used for the KD*P crystal.
The conversion efficiencies at different input intensities are shown in Fig. 5. The input fundamental beam was telescoped down to a diameter of ~ 1 mm, and its intensity was varied by a neutral density filter. Conversion efficiency as high as 55% was obtained at about 5 GW/cm2, saturation and back conversion were observed at higher input intensities. As a comparison, a numerically simulated curve was also plotted in the figure, where Gaussian beam and pulse shapes were assumed. Parameters corresponding to the experimental conditions were used in the simulations. The conversion efficiency decreases at higher intensity due to wavelength-dependent phase-mismatching caused by the second-order dispersion (i.e., GVD). The measured conversion efficiencies are in good agreement with the theoretical predictions. The deviation can be attributed to the non-ideal beam collimation, non-Gaussian pulse shape and spatial walk-off. Nevertheless, the experimental results have manifested directly the ability of efficient second harmonic generation of broadband femtosecond pulses with a partially deuterated KDP in the noncritical phase-matching configuration.
In conclusion, we have studied second harmonic generation of femtosecond pulses in a partially deuterated KDP around its retracing point vicinity both experimentally and numerically. The characteristics of the generated SH pulses and its intensity-dependent conversion efficiencies were investigated in detail, which have shown that this spectrally noncritical phase-matching configuration can support efficient SHG over 20 nm bandwidth of the fundamental pulses in the 10-mm-long crystal. Efficiency as high as 55% has been obtained in a single-pass scheme, which makes this approach attractive.
This work was partially supported by the Natural Science Foundation of China (grant Nos. 10376009, 10276012, and 10104006).
References and links
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