1. Introduction

Wavelength tunable femtosecond laser sources are highly important in modern science. Research fields like spectroscopy [1–3], nonlinear imaging [4–6], laser micro processing [7–9] and nonlinear optics [10–13] greatly benefit from high peak and average power wavelength tunable femtosecond pulses, which are often produced using optical parametric amplification (OPA) devices. However, depending on various parameters such as signal wavelength and bandwidth, pump-to-signal conversion efficiency is usually limited to no more than $20\%$ and often substantially less [14]. In typical setups, attempts to improve conversion efficiency by increasing pump intensity or crystal thickness commonly result in drastic degradation of pulse and beam quality, making the source unfit for most applications. Generally, the limiting factor here is the back-conversion process, that (for Gaussian pulsed-beams) starts at nearly full on-axis pump depletion. This can be combated by employing top-hat beam and pulse profiles, which has historically led to the pump-to-signal conversion efficiency of 34% [15]. However, despite the practical difficulties of the spatial-temporal wavepacket shaping, such intensity profiles have an inherent drawback of poor focusability [16]. Another approach is to suppress the back-conversion completely, which can be achieved by eliminating the idler wave from the interaction just before the pump wave is fully depleted. Besides some theoretical suggestions [17–20], this was previously achieved by employing idler second-harmonic generation (SHG) [21], non-collinear pump recycling schemes [22–24] and samarium ($\mathrm {Sm^{+3}}$) doped yttrium calcium oxyborate (Sm:YCOB) nonlinear crystals that strongly absorb the idler wave at infrared wavelengths [25,26], which led to $56\%$ pump-to-signal conversion efficiency and pump depletion of $85\%$. Nevertheless, when compared to solutions employed in typical OPA devices, these approaches tend to either consume a lot of space, demand exotic materials or lack tunability. Furthermore, the researchers of idler elimination-based high conversion efficiency OPA mostly focus on long pulses (ps-ns scale), where temporal walk-off is negligible. Moreover, even though many noteworthy results have been demonstrated, most works do not provide convincing quantitative evaluation of the beam quality (e.g. beam quality factor $M^2$), thus making experimental achievements difficult to compare. In this work we propose a polarization-based idler elimination scheme for the suppression of back-conversion in femtosecond OPA, that is simple, compact and only requires minimal additions to an otherwise completely standard OPA design. Furthermore, our approach preserves the wavelength tunability of the light source. Suppression of the idler wave is achieved by using two consecutive crystals cut for different nonlinear interaction phase matching types (type-I and type-II) in the same amplification stage. The idler wave that is generated in the first crystal is not phase matched for interaction in the second crystal, and therefore does not set off the back-conversion process. Thus, the signal wave can be amplified to a higher energy before reaching the back-conversion regime, avoiding deterioration of amplified beam quality. Unfortunately, at least for the wavelength and crystal combinations used in this work, the use of type-II phase matching limits the gain bandwidth. However, as not all applications require the shortest possible pulses, the achieved duration-energy trade-off may be worthwhile for some applications. We also show how the scheme can be adjusted to increase the energy of the idler wave rather than the signal wave. We support our investigations by numerical simulations and compare the performance of our two-crystal scheme to that of the individual type-I and type-II crystals. By optimizing the lengths of the nonlinear crystals and signal-pump delay we have achieved more than 50 % pump depletion of the femtosecond OPA, while maintaining good $M^2$ of the amplified radiation, nearly throughout the whole OPA tuning range.

2. Experiment

In our experiments a temporally stretched white light continuum (WLC) was pre-amplified to $\lessapprox$1.1 $\mathrm {\mu J}$ within 630 nm - 990 nm spectral range and then further boosted in the collinear OPA. The optical setup was pumped by the second-harmonic (515 nm and $\approx$212 $\mathrm {\mu J}$) of an Yb:KGW femtosecond pump laser (Carbide, Light Conversion), that provides 80 W of average power, 400 $\mu$J pulse energy and 300 fs pulse duration. The pump pulse was not stretched in our experiments and its’ duration after the second-harmonic generation was estimated to be around the same value of 300 fs. The pulse duration of a signal wave after the pre-amplification stage was estimated to be around 120 fs. The optical parametric booster amplifier, shown in Fig. 1, consisted of type-I and type-II beta barium borate ($\mathrm {\beta -Ba(BO_2)_2}$ - BBO) crystals, with an additional third type-II BBO crystal in between to compensate the group velocity walk-off between pump and signal waves in the first crystal, used solely for its birefringence, rather than any nonlinear properties. The group delay was adjusted by tuning the crystal polar angle $\theta$, at which (estimated $\theta \approx 35^{\circ }$) there were no phase-matched nonlinear processes for the wavelengths involved. With 515 nm pumping, type-II BBO can be phase matched so that either signal or idler wave is in the o or e polarization. We exploit this property to enhance the amplification of the idler. This is achieved by rotating the type-II amplification crystal to satisfy the phase-matching conditions for o-polarized idler wave. This way the signal wave from the first crystal is eliminated from the interaction in the second crystal, meaning that the second crystal is seeded only by the idler wave. After the amplification stage, dichroic mirrors were used to filter out the output wave of interest. The $1/\mathrm {e^2}$ level diameters for both seed and pump beams were about $2.4$ mm on the first crystal, corresponding to an estimated peak pump intensity of 30 $\mathrm {\frac {GW}{cm^2}}$. We used several commercial diagnostic devices to characterize the output radiation. A calibrated power meter (Ophir) was employed for parametric conversion efficiency measurements. For spectral measurements a spectrometer employing silicon (Si) linear image sensor was utilized (Qmini, Broadcom). Pulse duration was evaluated by a SHG autocorrelator (Geco, Light Conversion), employing 0.05 mm and 0.1 mm thick BBO crystals. Finally, the beam quality factor $M^2$ was evaluated by using an ISO 11146 compliant beam profiler (BeamSquared, Ophir-Spiricon). Both Si and indium galium arsenide (InGaAs) CCD cameras were utilized for beam profile measurements, depending on the wavelength of interest.

 

Fig. 1. Booster amplification stage of the experiment. DM - dichroic mirror. Electric field projections to ordinary o and extraordinary e polarization axes are also illustrated after type-I and type-II nonlinear interactions.

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3. Results and discussion

In this study we have searched for experimental conditions that allow for the enhancement of parametric energy conversion, while still maintaining the values of the amplified beam quality factor $M^2$ below 1.4. We have found that for the pump peak intensity of 30 $\mathrm {\frac {GW}{cm^2}}$ the optimum lengths of the crystals are 1.5 mm for the type-I crystal and 3 mm for the type-II. The length of the delay crystal was chosen to be 2 mm. Using this setup we can cover the whole spectral range from 630 nm to 990 nm. The polar angle of the delay crystal was adjusted for the best pump-to-signal conversion efficiency at 730 nm and wavelength tuning was achieved by only adjusting the booster amplifier crystals’ polar angles and optimizing the delay between signal and pump waves before the first crystal. The measured spectra are illustrated in Fig. 2(a). Here one can observe that they have a Gaussian-like shape, however, some minor distortions and asymmetry emerges in the periphery. Average spectral width was measured to be around 100 $\mathrm {cm^{-1}}$. The results of pulse duration measurements, presented in Fig. 2(b)., show nearly-Gaussian autocorrelation function profiles, corresponding to the pulse durations of <300 fs throughout the whole tuning range. No additional pulse compression scheme was employed. Output beam profiles for signal wavelengths of 730 nm and 850 nm are shown in Fig. 2(c),d. Their cross sections are smooth and nearly-Gaussian, however, the beam shape is slightly elliptical. We suspect that the ellipticity could have emerged from a misalignment of telescope lenses, as well as birefringent walk-off in the amplification crystals.

 

Fig. 2. Output properties. a) Signal wave spectra; b) Autocorrelation functions and their corresponding Gaussian pulse durations at different wavelengths; c, d) - output beam profiles and their central cross sections at 730 nm and 850 nm, respectively.

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The main efficiency and output beam quality characteristics of the proposed booster amplifier are presented in Fig. 3. Here pump-to-signal conversion efficiency $\eta _{\mathrm {ps}}$, measured pump depletion after the DM2 and $M^2=\sqrt {M^2_x\cdot M^2_y}$ are plotted on the same frequency (wavelength) axis throughout the whole tuning range. The measurements of $M^2$ were limited to $\approx$1.7 $\mathrm {\mu m}$ due to the drop of sensitivity of our InGaAs sensor. Also, we were not able to get the data on the enhanced idler amplification at wavelengths longer than 2000 nm due to insufficient crystal aperture and non-optimal cut orientation. Besides that, the linear absorption of the BBO crystals for wavelengths above 2000 nm could have an effect on the overall performance. The highest pump-to-signal energy conversion of $\eta _{\mathrm {ps}}=40\%$ was obtained at 730 nm, that corresponds to $M^2=1.25$. At full repetition rate and peak pump-to-signal conversion efficiency we have measured 17 W of signal average power (85 $\mathrm {\mu J}$ pulse energy at 200 kHz repetition rate). However, in order to be sure that the results are not influenced by, for example, thermal lensing in atmospheric air due to absorption of specific idler wavelengths by water vapor [27] and focus the investigation purely on the nonlinear optics involved in the two-crystal amplification stage, the laser was pulse-picked to a 20 times lower repetition rate during beam characterization while keeping the pulse energy the same. Nevertheless, at least for most wavelengths, the full average power should not significantly change the measured parameters of the radiation, as measurements with a thermal camera did not show a significant temperature increase on any of the dual-crystal OPA components. This is consistent with other research reporting no thermal distortions in BBO pumped at 515 nm at pump powers significantly exceeding the maximum $\approx$42 W pump power used in our experiments [28]. The maximum pump depletion value of 68% with corresponding $M^2=1.37$ was achieved at 850 nm. The rest of the $M^2(\lambda )$ curve qualitatively follows the pump depletion. The degree of the 68% pump depletion can be observed in the beam profile relay-imaged onto the camera from the last surface of the second amplification crystal (inset of Fig. 3). Overall, Fig. 3. favorably illustrates the capability to achieve $\eta _{\mathrm {ps}}\geq 30\%$ in the spectral range between 700 nm and 920 nm.

 

Fig. 3. Pump-to-signal conversion efficiency, pump depletion and $M^2$ as a function of wavelength and frequency. The most strongly depleted pump beam is displayed in the inset.

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3.1 Detailed investigations

For more detailed characterization of our amplification scheme we have measured the $M^2$ as a function of pump energy at constant beam diameter at 730 nm and 850 nm, i.e. at the wavelengths where the maximum signal energy and pump depletion were observed, respectively. The measurements were performed by employing a waveplate-and-polarizer based attenuator in the 515 nm pump beam. Measurements of the two-crystal scheme were also compared to single crystals of either type-I or type-II. Note that due to the shorter interaction length of the single crystals pump intensity had to be increased to reach saturation. This was achieved by decreasing the pump spot size on the crystal by about 2 times while maintaining the same range of pump energies. We display the $M^2$ values as a function of pump-to-signal conversion efficiency $\eta _{\mathrm {ps}}$ rather than pump intensity for easier comparison between one-crystal and two-crystal results. We have also tested different crystal combinations (type-I + type-II) by performing the $M^2(\eta _{\mathrm {ps}})$ measurements. The results are shown in Fig. 4. It is clear that $M^2$ non-linearly increases with $\eta _{\mathrm {ps}}$. By inspecting the 1.5 mm $+$ 3 mm curve one ought to observe that high amplified beam quality of $M^2<1.1$, which is often deemed sufficient for beam quality-sensitive applications like nonlinear microscopy, can be maintained with pump-to-signal efficiency $\eta _{\mathrm {ps}}$ as high as 34% by reducing the peak pump intensity (down to $\approx$16 $\mathrm {\frac {GW}{cm^2}}$). On the other hand, we were able to reach 46% pump-to-signal conversion efficiency at the expense of reduced beam quality ($M^2=1.57$), when employing 2.5 mm $+$ 3 mm configuration. In contrast, we have managed to get $\eta _{\mathrm {ps}}=30$% and $\eta _{\mathrm {ps}}=40$% at 730 nm for type-I and type-II individual crystals, respectively, which could not be fully replicated at 850 nm (Fig. 4). However, at high efficiencies $M^2$ deteriorates faster, when compared to the two crystal configuration, and reaches noticeably larger values. Therefore, the two crystals scheme is clearly superior. When comparing different crystal combinations at 850 nm it seems, that the beam quality is preserved for higher efficiencies by employing the thinner first crystal. On the other hand, at 730 nm all crystal length variations appear to produce different parts of the same curve. This could be explained by different group velocity mismatches and different delay in the middle crystal. We have noticed that the results could be slightly improved by separately tuning $\theta$ of the delay crystal for each signal wavelength. Here we must note, that in order to balance the amplification system for optimal beam quality and amplification efficiency one must choose the crystal thickness and pump intensity carefully. This is evident when comparing the cases of 2 mm $+$ 3 mm and 2.5 mm $+$ 3 mm, as they provide similar results for 730 nm, yet significantly changes the outcome for 850 nm.

 

Fig. 4. Signal beam quality factor $M^2$ as a function of pump-to-signal conversion efficiency $\eta _{\mathrm {ps}}$ for different crystal combinations and different signal wavelengths: a) 730 nm (peak pump-to-signal conversion), b) 850 nm (peak pump depletion). Single crystal measurements were performed by increasing the peak pump intensity by 4.3 times (from 30$\,\mathrm {\frac {GW}{cm^{2}}}$ to 130$\,\mathrm {\frac {GW}{cm^{2}}}$).

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3.2 Comparison with numerical simulations

The integral beam and pulse measurements, which were carried out in our experiments, can only provide partial information about the full quality of the output pulsed-beam and often supply little explanation about the amplification dynamics within the crystal. Furthermore, there seems to be unanswered questions about the shapes of the $M^2(\eta _{\mathrm {ps}})$ functions in Fig. 4. To tackle these issues we have performed spatiotemporal numerical nonlinear propagation simulations of Gaussian wavepackets of radial symmetry, which included dispersion, diffraction and three-wave mixing with no losses, as described in [20]. The simulations were performed using the effective second-order nonlinear coefficient and Sellmeier equation coefficients of the BBO crystal [29]. Initial conditions were similar to the experimental ones. The $M^2$ of the amplified beam was quantified as described in ISO 11146 standard, by simulating the output signal pulsed-beam propagation after an idealized focusing element. We have performed the numerical evaluation of the $M^2(\eta _{\mathrm {ps}})$ dependency for our main proposed crystal combination: 1.5 mm $+$ 3 mm and compared the results with the experiment. Figure 5. presents the comparison of simulated and measured relation of pump-to-signal conversion efficiency and beam quality. The model suggests slightly better beam quality and conversion efficiency for 850 nm, however, for 730 nm calculations matches the experiment quite well. Overall, the measured and theoretical results are in agreement within the experimental $M^2$ error bounds, which were estimated to be $\pm 5\%$. We suggest, that the differences between experiment and model could be attributed to differences in initial conditions, uncertainties in the effective non-linearity and refractive index dispersion, and absence of losses in the model (in the experiments the transmittance of the booster amplifier was $\mathrm {T}\approx 95\%$ for pump and on average $\mathrm {T}\approx 80\%$ for seed). Nevertheless, the model roughly predicts the conversion efficiency, at which the beam quality begins to degrade and the rate of degradation. Furthermore, the model correctly predicts the fact, that $M^2$ growth is steeper for 850  nm. One significant qualitative inaccuracy can be seen in the shape of the theoretical $M^2(\eta _{\mathrm {ps}})$ function at 730 nm, yet this could be easily caused, among other previously stated sources of error, by non-optimally chosen initial delay between signal and pump. The similar shape can be seen in the experimental results for a different case (Fig. 4(b). - 2 mm $+$ 3 mm). Overall, we are confident that only the basic physical phenomena (dispersion, diffraction and parametric amplification) played a key role in the experiment, which could only support the argument of easy reproducibility.

 

Fig. 5. Signal beam quality factor as a function of pump-to-signal conversion efficiency for different signal wavelengths (a - 730 nm; b - 850 nm) in the case of both real life and numerical experiments. Here 730 nm denotes peak pump-to-signal conversion efficiency and 850 nm denotes peak pump depletion.

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In the experiment, final conversion efficiency optimization was performed by adjusting the delay between signal and pump waves. Therefore, we have decided to evaluate this adjustment to understand its impact on the beam quality. The simulations (presented in Fig. 6) showed that, in the case of interest, beam quality is slightly dependent on the initial delay and, unsurprisingly, $\eta _{\mathrm {ps}}$ has a maximum value at a certain delay between signal and pump. The conversion efficiency peak, at least in this case, corresponds to a satisfactory $M^2$ value, which is somewhat insensitive to small delay perturbations. By observing the output wavepackets, presented in the inset of Fig. 6, one can reach an expected conclusion that the high $M^2$ value of the OPA output indicates spatiotemporal distortions. It seems, that with low delay values the parametric interaction is inefficient. On the other hand, when delay is high enough, the amplification can reach back-conversion point within shorter propagation distances, when compared to the ones at the conditions of peak $\eta _{\mathrm {ps}}$. It is plausible that this optimal delay is intensity dependent, thus, the irregular behavior of $M^2(\eta _{\mathrm {ps}})$ (e.g. 2 mm $+$ 3 mm configuration at 850 nm in Fig. 4(b).) could be caused by the fact that in our experiments the initial delay between signal and pump was optimized for the best conversion efficiency at peak pump energy and the delay crystal was optimized for only one configuration.

 

Fig. 6. Simulated influence of the initial delay between signal and pump pulse peaks on the pump-to-signal conversion efficiency and $M^2$ for 730 nm wavelength in case of 1.5 mm $+$ 3 mm crystal configuration. Positive delay values correspond to the leading pump pulse. Simulated output signal wavepackets are also presented.

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Moving on, there are clues, indicating that using high peak intensities with a single crystal can also provide substantial $\eta _{\mathrm {ps}}$ with reasonable beam quality, therefore, we have looked into this matter, too. In Fig. 7. we present the numerical results of the OPA modeling for 730 nm signal output in cases of single crystal and double crystal configurations, obtained at the highest conversion efficiency. The simulation results show that the polarization-based idler elimination helps to achieve $\approx 40\%$ pump-to-signal conversion efficiency before entering the substantial back-conversion regime. Even at the highest experimental intensity levels only a slight pump back-conversion on the beam axis is observable. In contrast, in the single crystal OPA, employed in the high conversion efficiency regime, several forward- and back-conversion cycles are present in both type-I and type-II cases, thus degrading the overall quality of the wavepacket. The difference between type-I and type-II crystals underlines the importance of back-conversion in parametric amplification. Both experimental and simulation results show that in type-I crystal pumped by high intensity pulses the $\eta _{\mathrm {ps}}$ can reach $30\%-35\%$, however, pulse and beam quality is very poor. Somewhat surprisingly, in case of type-II crystal the high conversion efficiency can be achieved, while maintaining imperfect, yet still reasonable beam quality, much better than when using a single type-I crystal, which can be explained by the high temporal walk-off between idler and pump pulses (see supplemental document for more details). The aforementioned effect coincidentally quite optimally manifests itself at around our pump pulse duration of 300 fs, meaning that these superior results in 3 mm thick type-II crystal can be achieved only in a limited range of pump pulse durations. Furthermore, the requirement of several back-convertion cycles signifies, that such amplifier is sensitive to the input pulsed-beam conditions. These problems are not present in the two-crystals approach, thus, our scheme produces better quality wavepackets and could be applied to OPAs with a wider range of pump pulse durations.

 

Fig. 7. Numerically calculated output signal radiation properties comparing single crystal and double crystal regimes at 730 nm. a) - spatial-temporal intensity profiles, b) - on-axis pulse intensity profiles, c) - temporally integrated beam cross sections. Evaluations were performed for three different cases: 1) - 2.5 mm thick type-I crystal: $\eta _{\mathrm {ps}}=35\%$, $M^2 = 2.07$, pump $I_0 = 131\mathrm {\frac {GW}{cm^2}}$ ; 2) - 3 mm thick type-II crystal: $\eta _{\mathrm {ps}}=47\%$, $M^2 = 1.43$, pump $I_0 = 131\mathrm {\frac {GW}{cm^2}}$; 3) - 1.5 mm type-I crystal combined with 3 mm type-II crystal: $\eta _{\mathrm {ps}}=42\%$, $M^2 = 1.22$, pump $I_0 = 30\;\mathrm {\frac {GW}{cm^2}}$.

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Finally, we would like to note that although we have demonstrated the concept in a BBO-based OPA pumped at 515 nm, we are confident that this approach could be successfully applied to other spectral ranges and crystal combinations. While the tuning range would not be very broad, the idea could be directly translated to the infrared by pumping with the laser fundamental, whilst still using type-I and type-II BBO crystals. Alternatively, we envision that our scheme could be of the highest utility in complex multi-level nonlinear optical setups, e.g., those involving difference- or sum- frequency or harmonic generation stages after an OPA. In this case, the improved efficiency of the OPA stage could be expected to substantially improve the overall efficiency of a multi-step scheme, because maintaining the wavepacket free of spatiotemporal distortions should ensure that subsequent wavelength conversion steps are also as efficient as possible.

4. Conclusion

In this work the concept of employing a combination of type-I and type-II nonlinear crystals in series within an optical parametric amplifier was presented. We have demonstrated experimentally in a 515 nm pumped femtosecond setup that the proposed scheme enables one to achieve polarization-based idler elimination, which may greatly increase the conversion efficiency of narrow-bandwidth short-pulsed light by suppressing the back-conversion process. The two-crystal amplifier can be successfully tuned throughout a wide wavelength range with sub-300 fs pulse durations, enhanced conversion efficiency of $>40\%$ and up to $\geq 68\%$ pump depletion. Rigorous experiments and numerical analysis revealed, that the proposed amplification regime does not suffer the significant beam and the whole wavepacket quality degradation, which is not the case for the single crystal optical parametric amplifier employed at the comparable conversion efficiency. Furthermore, significantly higher peak pump intensity is required in the high conversion efficiency single crystal amplification regime, which means that the two crystals approach is longer serving and can be used with higher average pump power. Superior conversion efficiency results could be achieved by employing the super-Gaussian pump beam intensity profile at the expense of beam quality factor, while still avoiding spatial-temporal couplings. In general, such two-crystal booster amplifier is cost-effective, could be applied in the long-pulse regime and may serve as a convenient tool in many future nonlinear applications.