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Abstract
We propose a method for multi-pass non-collinear optical parametric chirped pulse amplification (MNOPCPA) based on two geometries, tangent phase-matching (TPM) and Poynting vector walk-off compensation (PVWC), which optimize the performance of optical parametric chirped pulse amplification (OPCPA). A feasible design scheme is also presented for use in implementing this approach. Employing this design, we construct and perform a numerical simulation, showing that back-conversion from the signal and idler to the pump can be inhibited, and that the conversion efficiency can be boosted dramatically, approaching the theoretical limit of ~64%, when amplification is nearly saturated at full bandwidth. In the MNOPCPA scheme, the output signal has a wider spectrum and a corresponding shorter Fourier-limited pulse duration with the pump being continuously depleted. A barycenter shift of the signal spot results from a spatial walk-off effect due to the pump, which can be offset and corrected well. To the best of our knowledge, this is the first demonstration of a multi-pass non-collinear OPCPA method employed the scheme of regenerative amplification.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical parametric chirped pulse amplification (OPCPA) has the potential to reach several petawatts peak power, and consequently has been one of the most important ultra-short, ultra-intense laser amplification techniques available in recent years [1–6]. The advantages of OPCPA over traditional chirped pulse amplification (CPA) are significant, including its excellent abilities to support a wide gain bandwidths, provide high gain in a single-pass, minimize the B-integral, and be immune to thermal loading effects [7–9]. In order to achieve a higher peak power laser by OPCPA, the key issue is that improving the gain bandwidth for obtaining short compression pulse durations while boosting the pump-to-signal conversion efficiency for increasing output pulse energy [7,9–12]. For this purpose, several ultra-broadband phase-matching methods have been proposed to achieve ultra-short pulses of several femtoseconds, i.e. using a broadband pump beam [13], controlling the angular dispersion of the signal beam [14,15], and employing a two-beam-pumped non-collinear OPCPA [16]. But these methods still have low conversion efficiencies, impeding the ability to increase single-pulse energy. To deal with the issue of conversion efficiency, spatial-temporal flat-top pump pulses have been suggested to flatten the nonlinear drive over the temporal profile, as illustrated in [9,10,12,17–19]. This validity was also shown experimentally [1–4,6,20,21]. In 2005, Bagnoud et al. employed a very flat pump pulse with a spatiotemporal Gaussian profile, achieving the highest-yet pump-to-signal conversion efficiency of 34%, at 1053 nm with a full bandwidth of ~10 nm [21]. However, the limited gain bandwidth hindered the generation of ultra-short pulses, implying that gain bandwidth and conversion efficiency cannot be improved simultaneously [7,9,10,12].
It seemed that the traditional single-pass construction of OPCPA was no longer advantageous for improving the performances. Thus, some researchers kept an eye on CPA structure, and a kind of multipass structure for non-collinear OPCPA emerged as the times required [22–24]. In 2005, Stepanenko et al. proposed that making the signal pass repeatedly through the same one crystal within a long pump pulse in chronological order by using different quasi-phase matching angles, and consequently, they successfully made the multipass noncollinear optical parametric chirped pulse amplifier an attractive alternative to Ti:sapphire CPA systems [22]. This scheme was well applied and improved in low energy [23,24]. But these earlier multipass experiments were aimed at obtaining high gain by OPCPA, which is still of no avail for improving the conversion efficiency. Therefore, the conversion efficiency of OPCPA, as yet, has always been a challenge because of the large phase mismatch in the wings of the signal spectra and the back-conversion from signal and idler to pump [7,9–13,18].
Leveraging the absorption of the doped nonlinear crystal Sm3+:YCOB of the generated idler during OPCPA, Ma et. al. inhibited the back-conversion and increased the conversion efficiency from the pump to signal up to 41% [25]. This study also showed that inhibiting the idler being amplified can boost the conversion efficiency dramatically, approaching the theoretical-limit of 66%, if the crystal was sufficiently long. However, this was also no longer the traditional OPCPA technique, as the tradeoff of increasing the efficiency came at the expense of increasing thermal effects which would result in severe spatial aberration. Additionally, the signal saturation was slowed, requiring a correspondingly long crystal. However, a too-lengthy crystal led to worsening spatial coupling of the three beams and a drift in the center of gravity of the output signal spot caused by the spatial walk-off effect of the pump [26,27]. As a result, the conversion efficiency decreased. Therefore, a novel method is required, which can both inhibit an idler being amplified while maintaining the spatiotemporal coupling efficiency of the three waves. This crucial breakthrough will significantly improve high peak power lasers.
In this paper, we propose a novel approach of multi-pass non-collinear parametric chirped pulse amplification (MNOPCPA) by focusing on the two key issues of monochrome OPA. In the method, the signal and the pump are used together to pass through a crystal multiple times through a combination of two geometries, tangent phase-matching (TPM) and Poynting vector walk-off compensation (PVWC) [27–31]. We also present a feasible design approach for implementing this technique. A numerical model is constructed, reflecting the design, and detailed simulations of the MNOPCPA approach are performed. The optimized performance of MNOPCPA is highlighted by contrasting it with the output characteristics of the traditional single-pass non-collinear OPCPA. At the end of the article, we make a further discussion for benchmarking the scheme against the earlier multi-pass OPCPAs as well as the single pass OPCPA ones. To the best of our knowledge, this is the first demonstration of a multi-pass non-collinear OPCPA approach by using the design of regenerative amplifier.
2. Underlying principle
In 1990 Armstrong et al. derived Jacobi elliptic integrals as the analytical solution of one dimensional coupling wave equations [32]. We use these solutions to calculate and analyze the OPA process without considering the spatial domain. In order to make the simulation more accurate, we employ a numerical approach using three-dimensional coupled nonlinear wave equations to evaluate the spatiotemporal characteristics of OPCPA.
2.1 Numerical approach
The simulation of OPCPA involves difference frequency generation on the nanosecond timescale, so dispersion and temporal slippage are rather small to be ignored, as illustrated by Ross et al. [11,12]. Thus, under the slowly varying envelope approximation, we have the following coupled three-dimensional wave equations [33–36]:
where the indices s, i and p refer to signal, idler, and pump, respectively. The transverse Laplacian operator describes the beam propagating along the z-axis due to diffraction, where x and y are the transverse Cartesian coordinates in the plane orthogonal to the z-axis. The parameters c, j, χ(2), ω, n and E are the velocity of light, the imaginary number, the effective second-order nonlinear susceptibility, the angular frequency, the refractive index, and the complex amplitude of wavelengths, respectively. The phase mismatch Δk = kp - ks - ki, where k denotes the wave vector. The birefringence walk-off angle of the pump is given by ρp, and the angle between the signal (idler) Poynting vector and the pump wave vector is accounted for ρs (ρi). Since the signal wavelength is variable, ρi varies with ks [12].As indicated in [17,18,20], the combination of spatiotemporal Gaussian signal and flat-top pump beams is generally adequate to improve the conversion efficiency in OPCPA. Thus, the signal intensity is represented as a spatiotemporal Gaussian distribution, and the pump is expressed as a hyper-Gaussian [25]. In this study, the intensities of the signal and pump are assumed to take the following form:
where Ios and Iop refer to the signal and the pump peak intensity, respectively. The parameters ts and tp denote the full width at half maximum (FWHM) of pulse duration of the signal and pump, respectively. The sign σs (σp) is given for the beam size of the signal (pump) at 1/e2. In order to amplify the signal adequately, the pump must wrap the signal in the spatial and time domains. Therefore, we set ts = 0.7 ns, tp = 2 ns, σs = 2 mm, and σp = 3 mm in the simulation for not unduly wasting the pump. The simulation uses a signal wavelength from 750 nm to 850 nm and a pump beam of 527 nm, as this waveband has been used for achieving a high peak power laser employing OPCPA when based on LiB5O3 (LBO) [3,4,6]. The crystal LBO is chosen for its broad angular acceptance, low pump-to-signal walk-off, relatively large effective nonlinear coefficient, and sufficient gain bandwidth centered at 800 nm. The simulations based on LBO also can be extended to other bulk nonlinear crystals, such as YCa4O(BO3)3 (YCOB) and BaB2O4 (BBO), due to their similar characteristics. We use the refractive indices of LBO from the Sellmeier equations in [37]. The pump walk-off angle ρp is 0.46° [38]. For type-I phase matching (o + o → e) in LBO, and because of the non-collinear geometry of OPCPA, the phase matching angles (θ, φ) are chosen to be (90°, 13.81°) and the non-collinear angle ρs = 1.26°, in order ensure zero phase mismatch at 800 nm and the maximum efficiency-bandwidth product can be achieved for the pulses of the hyper-Gaussian pump and Gaussian signal [7,9,12].The solutions of the nonlinear ordinary differential equations in Eqs. (1) - (3) were obtained via using a fourth-order Runge-Kutta (R-K) method. The free-propagation components were obtained by adopting the split-step Fourier (SSF) method. The specific iterative process of numerical calculation was guided by [28,35,36].
2.2 Two key issues on the representative wavelengths of the broadband signal
The introduction of a strong chirp temporally stretches the ~28 femtosecond (FWHM) Gaussian seed pulse, dispersing the signal’s spectral profile and transferred it exactly onto the temporal profile [7,9,12]. Each moment in time corresponds to one wavelength, as shown with the red line in Fig. 1(a). OPCPA can thus be regarded as a superposition of monochrome OPA with different phase mismatches, and in order to improve the performance of OPCPA, a fuller understanding of monochrome OPA is thus particularly useful.
Fig. 1 (a) Red line: input temporal and spectral distribution of broadband signal. Green line: temporal input intensity of pump. Black line: phase mismatches ΔkL. Blue, cyan and purple regions are the signal wavelengths at ΔkL = 0, 1 and 2, respectively. (b) OPA process corresponding to signals at ΔkL = 0, 1 and 2, respectively. Is, Ip, and η denote to the intensities of signal and pump, and the conversion efficiency, respectively. The triplets (P1, P2, P3), (P4, P5, P6), and (P7, P8, P9) label the three positions corresponding to ΔkL = 0, 1, and 2, respectively, showing that the signal intensity is higher than the pump intensity. (c) - (e) Signal and pump intensities (left vertical axis) and the conversion efficiency (right vertical axis) as a function of the crystal length for inputting signal and pump spatiotemporal intensities at three positions corresponding to different phase mismatches. Red, brown and gray lines refer to different positions.
In earlier practical experiments [3,4,6], we typically set an input signal-to-pump intensity ratio of ~1% with an average pump intensity of 1.18 GW/cm2. The phase mismatches ΔkL = 0, 1 and 2 at l = lA, shown in the blue, cyan and purple regions of Fig. 1(a), where lA is the interaction length, were chosen to be simulated with their own OPA processes. The pump-to-signal conversion efficiency is
where εs-in and εp-in denote the initial input energy of signal and pump, respectively, and εs-out refers to the output energy of signal. Since the pump energy is consumed and the signal is amplified during OPA, there always exists a state when the signal intensity exceeds the pump intensity near the effective interaction length, as demonstrated in Fig. 1(b). Thus, one key issue worth exploration is whether the conversion from the pump to the signal and idler can proceed when the input signal intensity is higher than that of the pump. In order to investigate this issue, the signal and pump spatiotemporal intensities at three positions each, corresponding to ΔkL = 0, 1 and 2 in Fig. 1(b), were chosen as the input to OPA without the idler. We found that the increasing signal-to-pump intensity ratio gradually slows the increase of the signal. This is shown in Figs. 1(c) - 1(e), with the red line representing greater change than the other two lines, while the ranges of the gray and brown lines are similar. In other words, the variation will not be evident if the intensity ratio exceeds a certain value, but the conversion from the pump to signal still exists whether or not the phase mismatch ΔkL equals zero.For monochrome OPA, only the use of conformal spatiotemporal profiles can achieve full pump-to-signal conversion [39,40]. Owing to this, sufficient pump intensity is retained, even at ΔkL = 0, due to the spatial back-conversion. Yet, increasing signal intensities can be sustained by inputting the signal and pump spatiotemporal intensity information at P3, P6, and P9, which are the positions of maximum conversion efficiency respectively corresponding to ΔkL = 0, 1 and 2, as shown in Fig. 1(b). It is worth noting that the initial idler input in the above simulation is set to zero. Equivalently, the signal can be continuously amplified if we artificially set the generated idler in the OPA return to zero after traversing a specific length Δl. This implies that the pump-to-signal conversion efficiency can be improved by inhibiting the amplification of the idler, as illustrated in [25].
Another key result, as can be seen in Fig. 2(a), is that the conversion efficiency can be dramatically improved by periodically setting the idler to zero. An extreme situation is assumed: when Δl is set to near zero, or we keep the idler at zero, the pump can almost completely convert to signal and idler due to the absence of back-conversion. Also, a longer crystal is needed for larger ΔkL, in order to achieve maximal pump-to-signal conversion efficiency in OPA. Since the simulation is limited to the spot size chosen and a non-collinear configuration, it can only be used for certain cycles, and with shorter Δl, more cycles can be achieved. Additionally, the output signals and residual pump spots at different phase mismatches are shown in Figs. 2(b), 2(d) and 2(f), and Figs. 2(c), 2(e) and 2(g), respectively. The spatial regions of the pump occupied by the signal are almost depleted, showing that the pump can be exhausted in spite of the existence of the phase mismatching and un-conformal spatiotemporal distribution. However, returning the idler to zero may contribute to a worsening shift of the signal spot center of gravity in the pump walk-off direction because of a longer transmission distance for the single geometry [26]. With these two key points from monochrome OPA in hand, we demonstrate here a method of multi-pass, non-collinear OPCPA (MNOPCPA) based on different geometries. With this approach, the pump and signal can pass repeatedly through the same crystal with the idler being released entirely after each OPCPA process, and while the impact of spatial walk-off of the pump on the signal spot can be eliminated.
Fig. 2 (a) Conversion efficiency as a function of crystal length with the idler periodically returning to zero. (b), (d) and (f) Output signal spots corresponding to ΔkL = 0, 1 and 2, respectively. (c), (e) and (g) Residual pump spots corresponding to ΔkL = 0, 1 and 2, respectively.
3. MNOPCPA based on two geometries
For non-collinear OPCPA, the two geometrical configurations used are TPM and PVWC. The output characteristics of both are presented in detail in [27,28,30]. Since the index ellipsoids of the bulk nonlinear crystal, i.e. LBO, YCOB, BBO, are axisymmetric, axisymmetric phase matching must exist [37]. In addition, the energy flow of the pump deviates from the crystal wave vector as a result of the asymmetry of the refraction index for extraordinary light orthogonal to the wave vector direction [37,38]. The pump walk-off direction must also be axisymmetric. In Section 3.1, we propose a feasible design scheme for MNOPCPA on the basis of rotational symmetry. In the scheme, a numerical model of MNOPCPA is described, and the results of the simulations performed are discussed in Section 3.2. In order to highlight the optimized performance of this multi-pass approach, we contrast and analyze the output characteristics of MNOPCPA and traditional single-pass non-collinear OPCPA in Section 3.3.
3.1 Design scheme of MNOPCPA
We present the schematic diagram of axisymmetric type-I phase matching in crystal LBO with the design scheme of MNOPCPA in Fig. 3. MNOPCPA can be implemented as follows. First, we describe the functions of the optical elements needed. As shown in Fig. 3(b), the objects labeled M1 (M9) to M8 (M12) are reflecting mirrors on the signal (pump). The Dichroic mirror-1 and Dichroic mirror-2 reflect the pump while transmitting the signal. The Half-wave plate-1 and Half-wave plate-2 rotate the signal and pump polarization states 90°, respectively. The objects labeled Pockels-1 to Pockels-4 are electro-optical modulators that can rotate the beam polarization state 90 ° when provided with 1/2λ voltages. Pockels-1 and Pockels-2 act on the signal, while Pockels-3 and Pockels-4 act on the pump. Polarizer-1 and Polarizer-4 are polarizing mirrors that reflect p-polarized light while transmitting s-polarized light, and Polarizer-2 and Polarizer-3 reflect s-polarized light while transmitting p-polarized light. The paths of the signal and pump can be summarized as follows.
Fig. 3 (a) Schematic diagram of the axisymmetric type-I phase matching using LBO. XC and YC are the crystallographic coordinate axes. ks, ki, and kp refer to the signal, idler, and pump wave vectors, respectively. Sp is the pump Poynting vector. The two small block diagrams show the two non-collinear geometries used. The parameters ρs, ρi, and ρp have the same meaning as described in Section 2.1. (b) Design scheme of MNOPCPA. Red and green refer to the signal and pump paths, respectively. M1 to M12 are reflecting mirrors. Dichroic mirror-1 and Dichroic mirror-2 reflect the pump and transmit the signal. Half-wave plate-1 and Half-wave plate-2 are used for rotating the polarization states of the signal and pump by 90 °, respectively. Pockels-1, Pockels-2, Pockels-3 and Pockels-4 are electro-optical modulators, and can rotate the polarization state of the beams by 90 ° when they are given ½λ voltages, where Pockels-1 and Pockels-2 (Pockels-3 and Pockels-4) act on signal (pump). Polarizer-1 and Polarizer-4 reflect p-polarized light and transmit s-polarized light, while Polarizer-2 and Polarizer-3 reflect s-polarized light and transmit p-polarized light.
In order, the incident signal passes through or by M1, M2, Polarizer-1, Pockels-1, Polarizer-2, Half-wave plate-1, Pockels-2, M3, Dichroic mirror-1, LBO, Dichroic mirror-2, M4, and M5. After being reflected by M6, the signal returns. During the process, the polarization state of the signal is rotated 90 °, from s-polarized light to p-polarized light, by Half-wave plate-1 when Pockels-1 and Pockels-2 do not operate. This ensures that the incoming signal can pass through the crystal four times with p-polarized light. When the signal arrives at Pockels-2 a second time, one of two paths can be chosen:
- (A) Continuous oscillation for another cycle. Providing a 1/2λ voltage to Pockels-2 causes no change to the polarization state of the signal, due to the combined function of Pockels-2 and Half-wave plate-1. Subsequently, the signal can be transmitted to Polarizer-2 and return after being reflected by M7. Keeping the voltage on Pockels-2 ensures that the signal can be transmitted for a new cycle.
- (B) Output the signal. Removing Pockels-2 from operation, and providing a 1/2λ voltage to Pockels-1, the signal is changed from p-polarized to s-polarized light by Half-wave plate-1. This allows the signal to be reflected by Polarizer-2. Because of Pockels-1, the signal is changed back to p-polarized light and can be reflected by Polarizer-1. Finally, the signal is output from M8.
Like the signal, the incident pump passes through or by M9, M10, Polarizer-3, Pockels-3, Polarizer-4, Half-wave plate-2, Pockels-4, Dichroic mirror-1, LBO, and Dichroic mirror-2. The pump is reflected by M11. During the process, the pump polarization state is rotated 90 ° from p-polarized to s-polarized light by Half-wave plate-2 when Pockels-3 and Pockels-4 are not used. This ensures the incoming pump can pass through the crystal two times with s-polarized light. When the pump arrives at Pockels-4 the second time, there are again two paths are available:
- (C) Continuous oscillation for another cycle. Providing a 1/2λ voltage to Pockels-4 causes no change to the pump polarization state, due to the combined function of Pockels-4 and Half-wave plate-2. Subsequently, the pump can be transmitted to Polarizer-4 and return after being reflected by M12. Keeping the voltage on Pockels-4 ensures that the pump can be transmitted again.
- (D) Output the pump. Removing Pockels-4 from operation and providing a 1/2λ voltage to Pockels-3, the pump is changed from s-polarized to p-polarized light by Half-wave plate-2. This allows the pump to be reflected by Polarizer-4. Due to Pockels-3, the pump is changed back to s-polarized light and can be dumped from Polarizer-3.
Additionally, synchronization control is provided by a master clock in order to initially synchronize the signal and pump on arrival at the crystal LBO. The positions of reflecting mirrors M6, M7, M11, and M12 can be adjusted in order to synchronize the two beams. The optical path of the signal (LBO - M4 - M5 - LBO) should equal to the pump (LBO - M11 - LBO). The optical path difference between LBO - M6 (M7) - LBO of the signal and LBO - M12 - LBO of the pump should be exactly zero.
In this design approach, the signal and pump can be made to go through the crystal LBO with an integral multiple of four and two times, respectively, by providing varying periodic 1/2λ voltages on Pockels-1, Pockels-2, Pockels-3, and Pockels-4. Therefore, the occurrence of OPCPA relies on the design for the pump oscillation, that is, OPCPA can occur at an integral multiple of two via the free combination of options (A) - (D). Moreover, one of the most important characteristics of the design is that the idler can be released entirely before each pass. This scheme also combines the features and advantages of TPM and PVWC geometries, and it can offset and correct the deficiencies of OPCPA that are due to the use of a single geometry. This will be illustrated in detail in Section 3.3.
3.2 Numerical model and simulations of MNOPCPA
To create a numerical model for MNOPCPA, we simplify the design scheme described in Section 3.1 by placing identical, mirror-image crystals repeatedly, as shown in Fig. 4. The incoming pump is vertical to the crystal, and the spatial walk-off symmetrically redirects the direction of the Poynting vector. Similarly, the signal passes through the crystals with different geometries. The idler is forced to zero at the end face of each crystal.
Fig. 4 Numerical model of MNOPCPA based on the design scheme in Section 3.1. Green and red lines refer to the pump and signal beams. The dashed green line is the direction of the pump Poynting vector in the crystal. The purple region is the interaction of OPCPA among the three beams, signal, idler, and pump. The crystals arranged at the even number are placed as mirror images. The geometry configurations of neighboring groups are inversed, and each group includes two crystals.
An intensity ratio of ~1% between the Gaussian signal and hyper-Gaussian pump is employed to simulate the process of MNOPCPA. In the simulation, for the two TPM and PVWC geometries, the definitions of the angles ρs, ρi, and ρp, come from [27,28,30]. By using dichotomy, we optimize the crystal lengths corresponding to different numbers of MNOPCPA passes in order to output conversion efficiency maxima as shown in Table 1. For fixed input intensity ratio and spatiotemporal pulse shapes, the crystal length is unique for the maximum conversion from the pump to signal which is similar to a traditional single-pass non-collinear OPCPA. Table 1 also shows the maximum output conversion efficiencies for 2 - 20 MNOPCPA passes. A key result is that the pump-to-signal conversion efficiency can be greatly improved as the number of passes increases. If the number of passes increases to infinity, the conversion may achieve the theoretical limit with nearly complete pump depletion. For the collinear OPA with the same beam sizes of 800 nm signal and 527 nm pump, the theoretical limit for conversion efficiency is ~66%. However, due to the non-collinear geometry here, the spatial walk-off effect, and the given spatiotemporal duty ratio between the signal and the pump, the theoretical limit of the simulation only nears 64%.
Table 1. Optimized crystal lengths for increasing MNOPCPA passes, showing conversion efficiency maxima.
In Fig. 5, we show the conversion efficiency as a function of the cumulative crystal length for different numbers of MNOPCPA passes. With the data in Table 1, we see that the optimized crystal length decreases when eight or fewer passes are performed, because longer crystals may cause worse back-conversion. By contrast, more passes can flatten the jitter in the conversion efficiency. As shown, from the eighth to the twentieth pass, the output conversion efficiencies exceed 60%, and the curves become smoother.
Fig. 5 Conversion efficiency as a function of the cumulative crystal length for different numbers of MNOPCPA passes.
3.3 Comparison and analysis between MNOPCPA and traditional single-pass non-collinear OPCPA
To explore the process of MNOPCPA, we select eight passes because the output conversion efficiency no longer increases dramatically with additional passes, and the simulation on eight-pass non-collinear OPCPA is adequate to represent the evolution of the signal and pump. In order to smooth the curve shown in Fig. 6, no back-conversion should be allowed to appear in each OPCPA process. Thus, we decrease the optimized crystal length from 6.1 mm to 5.5 mm. To highlight the advantages of MNOPCPA, the simulations are also performed on the traditional non-collinear single-pass OPCPA, also based respectively on TPM and PVWC configurations under the same conditions and with the same input. Figure 6(a) shows how the conversion efficiency changes with cumulative crystal length. The maximum conversion efficiencies of the traditional OPCPA are ~32%, whereas for MNOPCPA they reach 60.89%. Although the crystal length is not optimal, the output conversion efficiency is sufficient, and shows that MNOPCPA is less sensitive to crystal length and injection ratio. Figures 6(b) and 6(c) show the evolution of the signal spectrum and pump residual time domain waveform for every pass of MNOPCPA. The signal spectrum flattens as the pump is gradually consumed. The output spectrum is a near-perfect hyper-Gaussian, and the pump can be almost fully depleted without back-conversion.
Fig. 6 (a) Comparison of the conversion efficiency between MNOPCPA and traditional OPCPA. (b) and (c) Evolution of the signal spectrum and the residual pump.
A comparison of the MNOPCPA and traditional single-pass non-collinear OPCPA spectra is given in Fig. 7(a), where the black line shows the output spectrum of MNOPCPA, and the red and cyan lines refer to the spectrum of traditional OPCPA, based on TPM and PVWC geometries at the maximum conversion efficiency, respectively, as shown in Fig. 6(a). In contrast to traditional OPCPA, the wings of the MNOPCPA output spectrum are greatly amplified, widening the spectrum. In other words, the full bandwidth can be nearly saturated amplification. This allows a shorter pulse duration after compression, as seen in the black line of Fig. 7(b). The FWHM of the Fourier-limit pulse from MNOPCPA is 20.99 fs, which is nearly 3 fs shorter than the two generated from traditional OPCPA. Figure 7(a) also shows the spectral phases. Since the variation of the signal phase caused by the OPA amplifier is irrelevant to the initial phases [11,12], the phase of signal spectrum is assumed to be zero in the beginning, and we only consider the spectral phases gained during amplification. We find that the phase aberration at the wings of the spectrum in MNOPCPA is larger than from OPCPA. This is obvious, because the phase mismatch is rather large, and the cumulative crystal length of MNOPCPA is nearly four times larger than that of traditional OPCPA. However, the phases of the central wavelengths are in agreement.
Fig. 7 Black, red, and cyan express the curves came from MNOPCPA, OPCPA based on TPM, and OPCPA based on PVWC, respectively. (a) Solid and dashed lines refer to the spectrum intensity and phases, respectively. (b) Fourier-limit pulses corresponding to (a).
Because of non-collinear angles in OPCPA, in the spatial domain the beam sizes of the signal and the pump are not the same, leading to a portion of the pump that cannot be utilized. Fortunately, the proposed scheme of MNOPCPA detailed here remedies this. It makes the non-collinear configuration approach collinear by combining the two geometrical configurations, so that the pump can be squeezed. This is reflected in the spots of the residual pump [Figs. 8(h) and 8(j)]. Significant pump remains after traditional OPCPA due to spatial saturation, and the most marginal region of the pump cannot be employed, as shown in Figs. 8(e) and 8(f). In comparison, the pump is nearly depleted in MNOPCPA as the number of passes increases, and in the spatial domain, only a rather small region is remained. Additionally, for the spatial distribution of the input shown in Figs. 8(a) and 8(d), there is a shift in the output signal spots from traditional OPCPA when based on the single geometry, as seen in Figs. 8(b) and 8(c). Thus, the MNOPCPA scheme can offset and correct the shifting of the center of gravity in the output spot of the signal caused by the spatial walk-off effect. As shown in Figs. 8(g) and 8(i), the output signal is no longer deflected by using the MNOPCPA scheme. Instead, it is much more homogeneous just like the input pump.
Fig. 8 (a) and (d) Input spots of signal and pump. (b) and (e) ((c) and (f)) Spots of the output signal and the corresponding residual pump in traditional OPCPA based on TPM and PVWC configurations at the maximum conversion efficiency in Fig. 6(a), respectively. (g) and (h) ((i) and (j)) Evolution of signal and pump spots after each pass.
4. Further discussion
Traditional single-pass OPCPA technique is mainly subject to its instantaneous nature, because the nonlinear crystals cannot store energy, which need the pump and signal to synchronously pass through the medium with phase matching angle in time and space domain when performing amplification. Combining with the large phase mismatch in the wings of the signal spectra and the spatiotemporal back-conversion from signal and idler to pump, one can hardly have a good practical applicability and stability. In order to reduce the influence of the synchronization and phase mismatch fluctuation, the earlier multipass noncollinear OPCPA schemes [22–24] have made a great improvement. The signal is requested to pass repeatedly through the same one crystal in chronological order within one pump pulse by using different quasi-phase matching angles, so that the amplification of signal is no longer limited by the time scale of pump. In lower energy, the earlier multipass schemes are more suitable, because the pump energy is adequate. They are more cost-efficient for obtaining high gain, and meanwhile, other performance, i.e. beam quality and spectra, can be improved over the ones based on single-pass structure. However, this structure has a low pump energy efficiency, because the long pump pulse is necessary for the amplification.
Comparably, the proposed MNOPCPA scheme based on the two geometrical configurations is more advantageous in high peak power laser systems. The pump, together with the signal, can be well controlled to oscillate between the cavity-like mirrors, increasing the energy utilization. Due to the release of idler and the combination of two geometrical configurations, the performance of OPCPA, i.e. the conversion efficiency, the amplified signal spectrum, and the beam quality, can be improved simultaneously. In theory, this scheme is adequate to impact the traditional single-pass structure. However, there are still some limitations. For example, the large number of electro-optical modulators may pose B-integral problem of short pulses which leads to uncompressible diphase distortions, especially for employing one as the final amplifier of a high peak power laser system; or the pulse contrast can be influenced by the limited polarization extinction of the polarizers. To solve these possible problems under real experimental conditions, we offered a simplified MNOPCPA scheme, as shown in Fig. 9. But one can only work at the expense of reducing the pass number. Even though, the fancy price of the large-aperture electro-optical modulators also impedes the development of the technique. It seems that the design scheme of MNOPCPA is much fitter as a power amplifier. Anyhow, we will continue to optimize the design scheme further, and experimentally verify its validity step by step in the near future.
Fig. 9 The simplified scheme of MNOPCPA. The meaning of the signs and the principle of operation are same to Fig. 3(b).
5. Conclusion
We propose a novel theoretical scheme for multi-pass non-collinear OPCPA (MNOPCPA) that optimizes the performance of OPCPA, by focusing on the amplification characteristics of monochrome OPA. We present the design approach of MNOPCPA that utilizes a combination of two geometries, TPM and PVWC. In the design, the signal and the pump are guided to pass through the crystal together multiple times, with the generated idler during the process of OPCPA released entirely after each pass. Following the design, we constructed a numerical model of MNOPCPA and performed simulations. Key results for the optimized performance of MNOPCPA were highlighted, by contrasting it with traditional single-pass OPCPA. Because of the continuous inhibition of the idler, the maximum conversion efficiency of MNOPCPA can approach the theoretical limit with the pump being nearly depleted. For a signal with a full bandwidth of 100 nm centered at 800 nm, the FWHM of the output spectrum was wider than in traditional OPCPA, with the central portion flattened due to the absence of back-conversion in MNOPCPA. This leads to a shorter duration of the corresponding Fourier-limit pulse. In the spatial domain, the MNOPCPA scheme can offset and correct the shifting of the center of gravity of the output signal spot caused by the spatial walk-off effect, providing a homogeneous signal spot to be obtained.
Funding
National Natural Science Foundation of China (NSFC) (Nos. 61378030 and 61521093).
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