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Abstract
Ultrafast pulsed laser of high intensity and high repetition rate is the combined requisite for advancing strong-field physics experiments and calls for the development of thermal-stable ultrafast laser systems. Noncollinear phasing matching (PM) is an effective solution of optimizing the properties of optical parametric chirped pulse amplification (OPCPA) to achieve broadband amplification or to be temperature-insensitive. But as a cost, distinct noncollinear geometries have to be respectively satisfied. In this paper, a noncollinear quasi-phase-matching (QPM) scheme of both temperature- and wavelength-insensitive is presented. With the assistance of the design freedom of grating wave vector, the independent noncollinear-angle requirements can be simultaneously realized in a tilted QPM crystal, and the temperature-insensitive broadband amplification is achieved. Full-dimensional spatial-temporal simulations for a typical 1064 nm pumped mid-IR OPCPA at 3.4 µm are presented in detail. Compared with a mono-functional temperature-insensitive or broadband QPM scheme, the presented QPM configuration shows a common characteristic that simultaneously optimizes the thermal stability and the gain spectrum. Broadband parametric amplification of a ∼40 fs (FWHM) pulsed laser is achieved with no signs of gain-narrowing. Both of the beam profiles and the amplified spectra stay constant while the temperature is elevated by ∼100°C. Finally, influence of the QPM grating errors on the gain spectrum is discussed.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Development of ultrafast pulsed lasers, in terms of longer carrier wavelength, higher intensity, higher repetition rate and the consequent higher average power, is currently of great interest for an ever-growing number of applications: multi-dimensional molecular spectroscopy [1], strong-field physics [2], high-harmonic generation [3] and probe of structural dynamics [4]. In contrast to traditional laser amplification based upon stimulated emission, optical parametric amplification (OPA) gets the advantages of negligible thermal lensing, broad amplification bandwidth, and large wavelength tunability from the visible to the mid-infrared (mid-IR) spectral region [5]. Optical parametric chirped-pulse amplification (OPCPA), a combination of OPA and chirped pulse amplification (CPA), has matured as a promising technique to produce high-intensity, high-average-power and few-cycle laser pulses at any wavelength of interest [6].
Phase-matching (PM) is a crucial prerequisite of the high-efficiency energy transfer in parametric processes. However, PM condition is closely related to ambient parameters, and can only be satisfied at a presupposed wavelength and temperature. Even a moderate wavelength or temperature shifting, may result in a significant conversion degradation. This influence can be respectively evaluated in terms of the gain bandwidth and the temperature bandwidth [7,8]. In recent years, high average power OPCPAs have made great progress, the amplified power is significantly boosted from ∼22 W to ∼100 W [9–11]. Despite the optical parametric processes are commonly claimed to be free of thermal loading due to their quasi-instantaneous energy transfer, heat accumulation in nonlinear crystals is still unavoidable, especially in the mid-IR spectral range. A temperature increase of up to 100°C with respect to the environment has been observed in the mid-IR high average power OPCPAs [11,12]. Temperature gradients will lead to the spatially varying PM conditions and subsequently a reduced conversion efficiency. Additionally, it may modify the amplification characteristic for broadband OPCPAs. Although higher output powers could be obtained if more pump power was available, such thermally induced phase-mismatch sets an inherent limitation on average power scaling. Thermally induced phase mismatch has become an important factor hindering the development of high average power OPCPAs [13,14]. To mitigate these adverse thermo-optical effects, some novel heat management strategies have been put forward to relieve the heat accumulation, at additional cost and complexity [15–17]. It actually helps to reduce the peak temperature, but temperature gradients are still present and the perfect PM can only be ensured at one single certain temperature [18–20]. Making the PM condition less temperature-sensitive is another promising route which can reduce the thermo-optical limitations on nonlinear optical processes, such as the multi-crystal design [21,22] or the phase mismatch compensation method based on electro-optic effect [23]. Generally, gain bandwidth is a key parameter that determines the shortest laser pulse can be efficient amplified, while the temperature bandwidth places a ceiling on the attainable maximum average power density. Thus, to achieve a high average power broadband OPCPA, there is a continual quest for broader gain spectrum simultaneously with better thermal stability.
Noncollinear PM configuration has been widely utilized to obtain a broadband gain spectrum [24,25]. Taking advantage of its feasibility in manipulating PM characteristics, the noncollinear PM scheme can also be employed to construct temperature-insensitive OPAs [26,27]. Based on a specified noncollinear configuration, 6 times larger temperature bandwidth has been successfully obtained. Obviously, it is an intuitive and concise method to realize the temperature-insensitive broadband PM provided that the independent temperature-insensitive and wavelength-insensitive noncollinear PM configurations can be simultaneously realized in a compatible one. But unfortunately, it usually cannot be achieved due to their respective requirements to noncollinear angles. To implement that temperature-insensitive broadband OPCPA, combined methods have been proposed relying on a basic temperature-insensitive noncollinear PM configuration, such as, introducing proper angular dispersions, delicately designing the operation temperature and the pump wavelength [27,28].
In this paper, we propose and theoretically verify a versatile quasi-phase matching (QPM) scheme capable of temperature-insensitive broadband parametric amplifications. Benefiting from the design freedom of grating wave vector, the independent temperature-insensitive and wavelength-insensitive noncollinear PM configurations are handily combined in a tilted periodically poled crystal. Full-dimensional simulations have been performed to confirm its temperature-dependent amplification characteristics. Compared with a mono-functional broadband or temperature-insensitive QPM design, the presented temperature-insensitive broadband QPM (TBQPM) scheme enables the generation of steady broadband spatial-spectral profiles across a markedly temperature range. Finally, influence of the QPM grating errors on gain spectrum and the subsequent optimization is discussed.
2. Underlying principles
For high-intensity laser drivers, a higher repetition rate is beneficial for a reduced integration time and an improved signal-to-noise ratio, but will also lead to a higher average power. The combination requirement for ultrafast pulse duration and high average power presents a tremendous challenge for the development of OPCPA systems. Not only is it essential to provide the broadest gain bandwidth, the gain spectrum should be also immune to temperature fluctuations due to the heat accumulation in nonlinear crystals.
Noncollinear configuration is a routine method to manipulate the PM conditions. Figure 1(a) shows a typical noncollinear broadband PM geometry. Normally, group-velocities of the signal and idler waves should be equal along the propagation direction of signal, which can be expressed as that [29]
Where νi and νs respectively present group velocities of the idler and the signal waves, and β denotes the noncollinear angle. It should be noted that, arising from the contribution of the crystal birefringence, the Poynting vector S and the propagation vector k may not be parallel for extraordinary waves, resulting in the directions of the group velocity vectors are noncollinear with those of corresponding wave-vectors [30]. In consideration of the QPM scheme we will employ, where the angle θ between the propagation direction and the optic axis is fixed at 90° then the walk-off effect is completely negligible, this walk-off effect has not been included here.
Fig. 1. With the assistance of a devisable grating wave vector (kg), (a) the group-velocity matching and (b) the temperature-insensitive PM can be simultaneously realized in a noncollinear QPM geometry (c). (d) The sketch of the proposed tilted periodically poled crystal.
Likewise, noncollinear PM configuration can also be employed to improve the temperature bandwidth, provided that another constrained noncollinear geometry is satisfied [26]. On this occasion, as shown in Fig. 1(b), analogously, projections of the first wave-vector derivatives along the propagation direction of idler should be phase matched.
Equations (1) and (2) have respectively presented the clear mathematical criterions for the noncollinear broadband PM geometry and the noncollinear temperature-insensitive PM geometry. Intuitionally, the noncollinear angles of α and β satisfying both of that given noncollinear geometries seemingly can be directly obtained by solving the combined equations of Eqs. (1) and (2). However, a basic PM premise that Δk = 0 still need to be fulfilled. Unfortunately, restricted in such a constrained noncollinear geometry, the wave vectors hardly happen to form a closed vector triangle for phase-matching.
Compared with the birefringence-based bulk crystals, QPM is a feasible technique offering an extra degree of freedom similar to that of the signal-pump noncollinear angle to construct the desired noncollinear PM configuration, but without constraining the interaction geometry [31,32]. To meet a QPM condition, the pump (kp), signal (ks), idler (ki) wave vectors and the grating wave vector (kg), should satisfy that
As shown in Fig. 1(c), based on the required noncollinear geometry, the remaining phase-mismatch of Δk can be perfectly compensated only if an appropriate tilted grating wave vector kg is included. Then, the noncollinear QPM configuration of both temperature- and wavelength-insensitive may be finally achieved. For this purpose, a tilted periodically poled crystal as presented in Fig. 1(d) should be employed. Λ = 2π/kg represents the grating period of the periodically poled crystal, and τ is defined as the deviated angle between the ks and the grating wave vector kg.
In past decades, QPM has been widely employed benefiting from the rapid developments on QPM crystals [33]. Among which, periodically poled LiNbO3 (PPLN) is the most familiar because of its really large nonlinear coefficient and broadband transparency range, and has been successfully applied in mid-IR ultrafast OPCPAs [34,35]. Owing to its small absorption in the mid-IR spectral region, PPLN gets a less thermal loading compared to the BBO crystal. When the amplified power exceeds 10 W, however, there is still severe thermal effects in the PPLN-based OPCPA systems, which will restrict the conversion efficiency and set an inherent limitation on average power scaling [36,37]. To illustrate the optimized performance of that presented QPM scheme, in this manuscript, a Type-0 PPLN is chosen as the nonlinear media in the following discussions. Although the PPLN crystals are limited in energy-scalability by a low-damage threshold, and the aperture size, it is still a promising candidate for high average power optical parametric amplification. In addition, large-aperture MgO:PPLN crystals (≥ 5 × 5 mm2) have been available [38,39], which also makes them have the potential to perform the energetic optical parametric amplification.
Based on a typical parametric process of the 1064 nm pumped broadband OPCPA at 3.4 µm, the realization of that TBQPM scheme are firstly explored. Figure 2 shows the role of α in manipulating the noncollinear QPM geometry at a PM temperature of T0 = 24.5°C. Based on the temperature-dependent Sellmeier equations of 5% doped MgO:PPLN [40], the noncollinear angle of β, the grating period of Λ, and the deviated angle of τ were successively calculated as a function of α, in a case of the broadband QPM and the temperature-insensitive QPM designs respectively. In the calculations, β was first determined according to the angle requirements of Eqs. (1) and (2), and then the required periodic pattern can be subsequently confirmed in terms of the grating period of Λ and the deviated angle of τ. Clearly, for each mono-functional QPM design, there are unlimited potential noncollinear configurations depending on the noncollinear angle of α. Both of the noncollinear angle β and the required periodic pattern (Λ and τ) exhibit definite trends with the increase of α, and coincide at a specific noncollinear angle of ∼1.5°, implying that the broadband QPM and the temperature-insensitive QPM can be simultaneously achieved in such a noncollinear configuration.
Fig. 2. Dependence of (a) the required noncollinear angle β and the corresponding grating periodic pattern in terms of (b) the grating period of Λ and (c) the deviated angle of τ on the noncollinear angle α between the incident signal and pump waves, for a broadband QPM design and a temperature-insensitive QPM design respectively. Pump and signal wavelengths are respectively set at 1064 nm and 3.4 µm. The referenced cases chosen to make a comparison with the optimized TBQPM configuration are marked.
In addition, for a more versatile application, the required noncollinear angle α and the corresponding grating period Λ are respectively plotted in Fig. 3, as a function of the signal wavelength for various pump lasers at 1064 nm and 1550 nm, and their second harmonics. For each given wavelength-pair of the pump and signal waves, there is only one specified noncollinear geometry can provide that temperature-insensitive broadband QPM. By the choice of a suitable pump wavelength, the presented TBQPM scheme can be realized spanning from the near-IR to the mid-IR spectral regions. The optimized noncollinear geometry simplifies the separately optimization of gain bandwidth and temperature tolerance, and provides a promising wide-spectrum approach to construct high average power broadband OPCPAs immune to the temperature fluctuations.
Fig. 3. The required noncollinear angle α and the corresponding grating period Λ to construct that temperature-insensitive broadband QPM geometry versus the signal wavelength, pumped by (a) the fundamental and (b) the second harmonics of typical pump lasers at 1064 nm and 1550 nm.
3. Proof of principle
For a narrowband parametric process, thermal-induced Δk(T) may primarily lead to a descent in amplification efficiency. As for the high average power OPCPAs, however, thermal effects would also remodel the gain spectrum and eventually destroy the original spectrum of the amplified signal wave. Therefore, possessing a thermal-stable gain spectrum is an essential prerequisite for the high average power OPCPA systems.
In this section, in terms of temperature-dependent gain spectra, we perform a detail discussion on the optimized performance of the proposed temperature-insensitive broadband QPM scheme. A typical parametric process, i.e., the 1064 nm pumped mid-IR broadband OPCPA at 3.4 µm, is taken into account. According to the design parameters given in Fig. 2, to construct that TBQPM configuration, a preset noncollinear angle of α = 1.5° should be arranged, with a specified tilted PPLN crystal of Λ = 3.6 µm and τ = 79.7°.
Gain spectrum is a key property to evaluate the OPCPA performance, and can be treated as a combination of the parametric gain of each individual signal wavelength. Neglecting the pump depletion and under a plane-wave approximation, the small-signal gain can be estimated [5]:
Dependence of the gain spectrum on temperature was calculated based on published Sellmeier equations [40]. The results are depicted in Fig. 4, in comparison with those of the broadband QPM and the temperature-insensitive QPM configurations. Theoretically, there are unlimited noncollinear QPM configurations capable of either wavelength- or temperature-insensitive. As shown in Fig. 2, two particular designs away from the intersection one are chosen as the references. The perfect PM temperature is set at a room temperature of 24.5 °C and the length of the 5% doped MgO:PPLN crystal (L) is 5 mm. Then, a pump intensity of ∼0.5 GW/cm2 is chosen for all of the simulated cases. A comparable parametric gain of ∼1500 can be achieved in the perfect PM situation. The other essential crystal parameters are all listed in Table 1.
Fig. 4. Evolution of the gain spectrum versus an increasing deviated temperature of ΔT in (a) a temperature-insensitive QPM, (b) a TBQPM and (c) a broadband QPM configuration respectively. (d) Temperature-dependent small-signal parametric gain at the central wavelength of 3.4 µm for the TBQPM configuration, and (e, f) the gain spectra near the edge of its acceptable temperature boundary. The perfect PM temperature (ΔT = 0) is set at 24.5 °C. The gain spectra were respectively normalized to the maximum values of each QPM configuration at the central wavelength and perfect PM temperature.
Table 1. Nonlinear Crystal Parameters for the 5% doped MgO:PPLN at 24.5°C (λp=1064 nm, λs=3.4 µm, λi = 1.55 µm)
For a conventional noncollinear broadband OPCPA shown in Fig. 4(c), since the noncollinear temperature-insensitive PM geometry is not satisfied, despite an ultrabroad gain bandwidth of ∼520 nm (full width at half-maximum, FWHM) can be achieved at the perfect PM temperature, the severe overall reduction of the gain spectrum with an increasing temperature indicates its terrible thermal stability. Particularly, the maximum gain decreased by more than 90% at a moderate deviated temperature (ΔT = 40 °C). In addition, the elevated temperature would also give rise to a thermal-induced spectrum narrowing, resulting in a gain bandwidth of only ∼220 nm. For the other extreme case of the temperature-insensitive QPM design shown in Fig. 4(a), compared with the other counterparts, it exhibits a significantly narrowed gain spectrum at the initial set PM temperature. Nevertheless, it shows an extraordinary ability in improving the thermal stability that stabilized gain spectra can be obtained. It is clear that, neither the temperature-insensitive PM design nor that conventional broadband PM configuration can provide a thermal-stable broadband gain for the development of high-repetition and high-intensity OPCPA systems. In contrast, the proposed TBQPM configuration, combining both of the advantages of the above noncollinear configurations, exhibits not only an ultrabroad gain bandwidth of ∼520 nm, but also an excellent thermal stability, as shown in Fig. 4(b). To explore the limitation of the TBQPM scheme for high average power optical parametric amplification, temperature-dependent parametric gain at the central wavelength of 3.4 µm, and the gain spectra near the edge of its acceptable temperature boundary are presented. As it shows, the broadband gain spectrum is nearly unaffected even when the temperature gets an elevation by 100 °C, indicating the thermal-induced phase mismatch will no longer be a limiting factor at the current power level.
It should be noted that, the noncollinear configurations capable of realizing the temperature-insensitive parametric amplification, should follow a clear geometric equation which was mathematically deduced at central wavelengths, as presented in Eq. (2). So, even though Eq. (2) is satisfied in a TBQPM scheme, for a broadband parametric process, in principle, it still cannot ensure the PM conditions for the other deviated spectral components of the signal and the idler waves can also be temperature-insensitive and thus realize the thermal-stable broadband amplification. From another perspective, group velocity matching angle Ω is temperature-dependent due to the temperature-dependent group velocities, defined by Ω(T) = Arccos[vs(T)/vi(T)]. It is a basic requirement for a temperature insensitive broadband PM scheme that the initially set noncollinear angle β can be always approximate to Ω(T) at various operation temperature. Nonetheless, temperature has little effect on the group velocity and the resulting group velocity matching angle, then the Ω(T) ≈ Ω(T0) =β is approximately achieved. As a consequent, as long as the PM condition is temperature-insensitive at the central wavelengths, i.e, Δk ≈ 0 is always satisfied at the central wavelengths, it can be concluded that the broadband gain spectrum should be also reserved for various operation temperature, as Fig. 4(b) predicted.
4. Full-dimensional simulations
In terms of small-signal gain spectrum, the preliminary results have clearly demonstrated that temperature-insensitive broadband OPCPA can be realized in a specific noncollinear QPM geometry. Next, full-dimensional numerical simulations were carried out to clarify the potential applications of the TBQPM scheme on high average power ultrabroadband OPCPAs. A Gaussian laser is assumed throughout this letter that I(x, t) = I0·exp[−2(x ∕σ0)2]·exp[−2(t ∕τ0)2], when the intensity distribution on y-axis is ignored. I0 = n·c·ɛ0·E02/2 represents the peak intensity and σ0 (τ0) is the beam radius (pulse duration) in half-width at 1/e2 maximum of the radial intensity distribution. Including the full spatial and temporal dependence, the coupled-wave equations that govern the evolution of the three parametrically interacting waves can be written as [41]
In our simulations, an initial ∼40 fs (FWHM) pulsed laser at 3.4 µm, i.e., the case of τ0 = 35 fs, is temporally stretched to ∼12 ps by 300 times. Accordingly, the 1064 nm narrowband pump laser is 1.5 times longer with a duration of ∼18 ps. Beam radius is taken to be 0.5 mm that σ0 = 0.5 mm for both of the pump and the signal waves. A pump intensity of ∼450 MW/cm2 is chosen and the initial Gaussian signal intensity is 1/300 of that of the pump wave. Likewise, various noncollinear configurations of the temperature-insensitive QPM, the broadband QPM and the TBQPM schemes are comparably studied. In the meantime, identical MgO:PPLN crystals as those given in Fig. 4 are employed.
The coupled-wave equations of Eqs. (7)–(9) were numerically solved by a standard split-step method based on the same parameters listed in Table 1. The calculated spatial-spectral profiles for various QPM configurations are respectively demonstrated in Fig. 5, along with that of the original seeding signal wave. In general, the simulated results show consistent performance as that temperature-dependent gain spectra presented in Fig. 4. Attributed to the similar noncollinear broadband PM conditions, both of the broadband QPM and the TBQPM configurations are able to produce nearly unrestricted amplified spectra with broad bandwidth of ∼390 nm and ∼380 nm respectively and a comparative conversion efficiency of ∼40% at the perfect PM temperature (T = 24.5 °C, ΔT = 0 °C). In comparison, the original signal spectral bandwidth is ∼420 nm. We attribute this moderate spectrum narrowing to the non-uniform Gaussian envelopes of both of the signal and the pump waves. In contrast, a considerably narrowed amplified spectrum of only ∼185 nm is predicted for the temperature-insensitive case with a synchronously reduced conversion efficiency of ∼20%.
Fig. 5. Calculated spatial-spectral profiles of the amplified signal waves in (a, d, g) a temperature-insensitive QPM, (b, e, h) a TBQPM and (c, f, i) a broadband QPM configuration respectively. Inset: the initial spatial-spectral profiles of signal. The slight spatial distortion along the x-axis is ascribed to the utilization of noncollinear OPA configurations.
At high average power operations, however, thermal absorption in nonlinear crystals and the subsequent inhomogeneous crystal heating may lead to longitudinal temperature gradients across the crystal, as well as the radial ones around the optical axis. The resulting temperature difference within crystal varies depending on the absorption coefficient, the thermal conductivity and the aperture size. Since the perfect PM can only be ensured at one single certain temperature, to achieve a more robust energy transfer, larger temperature acceptance is required. In this paper, we mainly focus on the enhancement of the spectrum output and the improvement of the thermal stability against temperature fluctuation, so only the cases of global temperature variations are discussed.
The resulted spatial-spectral profiles are respectively placed in Figs. 5(d)–5(f) and Figs. 5(g)–5(i), provided that the crystal temperature gets a global elevation from 24.5 °C, i.e., the initial PM temperature, to 64.5 °C (ΔT = 40 °C) and 124.5 °C (ΔT = 100 °C). Compared with the performance at a PM temperature, there is almost no difference in both of the conversion efficiency and the amplified spectra, for whether the temperature-insensitive QPM configuration or the presented TBQPM design. As it presents, the temperature-insensitive broadband QPM scheme can not only provide a sufficiently broad gain spectrum to support the effective amplification of the ∼40 fs pulsed laser, but also be temperature-insensitive, which is promising to construct high-repetition few-cycle OPCPA systems. In contrast, the conversion efficiency of the mono-functional broadband QPM configuration gets a severe reduction from ∼42% to ∼12% when ΔT = 40 °C. And synchronously, the spectral bandwidth decreases from ∼390 nm to ∼210 nm, showing a considerable thermal-induced gain- narrowing effect. As the ΔT gets a further increase to 100 °C, nearly no signs of parametric amplification can be observed.
As discussed in previous sections, TBQPM is realized by virtue of the extra grating wave vector provided by a tilted periodically poled crystal (Λ, τ). However, in a practical application, due to the limited processing precision or the inaccurate refractive index, bits of grating error is normally inevitable between the actual periodic pattern (Λ’, τ’) and the designed one (Λ, τ). For the proposed TBQPM scheme, grating errors in either the tilted angle τ or the grating period Λ may result in a considerable influence in PM conditions and the gain spectra. Obviously, such deviations in τ can be simply corrected by tilting the crystals, as shown in Fig. 6(a).
Fig. 6. (a) Schematic diagram of the modulation of τ by tilting the periodically poled crystal. Dependence of small-signal parametric gain on (b) the signal wavelength at a PM temperature and (c) the temperature at a central wavelength with various grating period deviations (ΔΛ). By introducing an appropriate tilted angle of Δτ, such deteriorations on both of (d) the gain spectrum and (e) the temperature response can be considerably compensated. The original design of that tilted MgO:PPLN is presented in Table. 1 with Λ = 3.6 µm, and τ = 79.7°.
Finally, in view of the gain bandwidth and the temperature bandwidth, sensitivity of the temperature-dependent gain spectrum on grating period errors is discussed. Based on the identical parametric process and parameters as those presented in Fig. 4, dependence of small-signal parametric gain on the signal wavelength and the temperature were calculated with various grating period deviations (ΔΛ), and the results are contrastively shown in Figs. 6(b) and 6(c), respectively. Similar to previous discussions, in our calculations, only the parallel wave vector mismatch is considered that Δk(T, λs) = kp(T, λp)·cosα - ks(T, λs) - ki(T, λi)·cosβ - kg·cosτ, while the vertical kp(T, λp)·sinα + ki(T, λi)·sinβ = kg·sinτ is always satisfied. The noncollinear angle of α between the pump and the signal waves is fixed at 1.5°. As presented, as the grating period deviates from its optimum value, significant distortion appears on both of the gain spectrum and the temperature response, which is not conducive to the application of the TBQPM scheme. Thus, we try to optimize its performance by tilting the MgO:PPLN crystal and the consequent grating wave vector. α remains unchanged in this process. As shown in Figs. 6(d) and 6(e), by introducing an appropriate tilted angle, such deteriorations on both of the gain spectrum and the temperature response can be considerably compensated, except that the gain spectra get slightly shifted. As a conclusion, moderate deviation in grating period is endurable for the TBQPM scheme.
5. Conclusion
In summary, we have demonstrated a versatile noncollinear QPM scheme capable of temperature-insensitive broadband parametric amplification. By virtue of the design freedom of an extra grating wave vector, the separate broadband noncollinear PM geometry and temperature-insensitive noncollinear PM geometry are handily combined in a tilted periodically poled crystal. To verify the amplification properties of that TBQPM scheme, full dimensional numerical simulations have been performed in comparison with its mono-functional broadband PM and temperature-insensitive PM counterparts. As predicted, it can provide steady broadband gain spectrum immune to temperature fluctuations. For a typical mid-IR parametric process of the 1064 nm pumped broadband OPCPA at 3.4 µm, broadband parametric amplification of that chirped signal with an original ∼40 fs (FWHM) transform-limited pulse duration is achieved with no signs of gain-narrowing. What is more, the exporting beam profiles and amplified spectra stay constant while the temperature is elevated by ∼100°C. Considering the possible grating errors in practical applications, the influence of period deviation in gain spectra was exploited. And the results show that such deteriorations on both of the gain spectrum and the temperature response can be considerably compensated as long as an appropriate tilted angle is introduced. The proposed TBQPM scheme provides a promising approach for the development of high repetition-rate few-cycle OPCPAs beyond the current level. It is almost free from the limitations of the laser wavelength. Given the existing various kinds of periodically poled crystals and the multiple QPM types, it can be potentially applied to any parametric process.
Funding
National Natural Science Foundation of China (61505113); Science and Technology Planning Project of Shenzhen Municipality (JCYJ20180305124930169, ZDSYS201707271014468).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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