Advances in Condensed Matter Physics

Volume 2018, Article ID 5731938, 7 pages

https://doi.org/10.1155/2018/5731938

## Numerical Simulations of Transfer of Spatial Beam Aberrations in Optical Parametric Chirped-Pulse Amplification

^{1}School of Electronic Information and Electrical Engineering, Changsha University, Changsha, 410003, China^{2}Key Laboratory for Micro-/Nano-Optoelectronic Devices of Ministry of Education, School of Physics and Electronics, Hunan University, Changsha 410082, China

Correspondence should be addressed to Guobao Jiang; moc.361@oabougdna and Lulu Wang; nc.ude.uscc@wll

Received 21 June 2018; Accepted 30 August 2018; Published 1 October 2018

Academic Editor: Qinghua Guo

Copyright © 2018 Ying Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In this paper, the spatial characteristics of the optical parametric chirped-pulse amplification (OPCPA) process were numerically studied when initial pump beam was aberrated. Numerical results showed that the spatial walk-off effect transferred phase modulation partly to the signal beam as the pump phase was modulated. Moreover, the modulation amplitude became increasingly severe as the nonlinear length extended. In the absence of phase aberration in the initial input signal, the induced phase aberration in the output signal was assumed as the differential form of the pump beam phase. As the pump beam intensity was modulated, the spatial walk-off effect reduced the influence of pump beam noise on beam quality and the angular spectrum but reduced signal gain simultaneously; thus, it may do more harm than good in the OPCPA process. In the case of a non-diffraction-limited pump beam, the greater the beam quality factor , the lower the conversion efficiency of the output signal in the OPCPA process. These results have important guiding significance for optimized design of an OPCPA system for high power laser.

#### 1. Introduction

High-energy ultrashort solid lasers have comprised a development trend in laser optics in recent decades. In 1986, Strikland et al. suggested the idea of chirped-pulse amplification (CPA) [1], which dramatically reduced the possibility of nonlinear damage to the laser medium and fully leverages gain bandwidth during amplification [2, 3]. Optical parametric amplification (OPA) is an efficient approach of generating tunable pulses from a fixed laser source [4–6], including large energy fiber laser sources [7, 8]. The integration of OPA and CPA into optical parametric chirped-pulse amplification (OPCPA) has rapidly extended the peak power of amplified ultra-short laser pulses to the petawatt level due to unique features of efficient conversion, high gain, and broad bandwidth [9–13].

In strong-field physics applications, laser beam quality and pulse contrast are key issues in OPCPA laser systems [14]. To date, the pulse contrast of OPCPA systems has been studied extensively [15, 16], and various methods have been proposed to increase pulse contrast on a picosecond timescale [17–20]. However, less attention has been paid to beam quality in the OPCPA process, as the OPCPA technique was normally considered capable of ensuring the optical quality of an amplified signal field [16, 21]. This might not be a problem for most low-energy OPCPA systems where the pump laser sources are diffraction-limited or in a type 0 () quasi-phase-matching OPA process without spatial walk-off between interacting waves [22, 23]. However, circumstances are quite different for high-energy OPCPA systems where high-energy pump lasers are typically far below the diffraction limit [24, 25]. Meanwhile, the spatial walk-off effect is always present due to the adoption of birefringent nonlinear crystals.

Several articles have considered beam quality in OPCPA systems [26, 27], mainly by examining the influences of the pump beam-profile and dephasing on OPA gain and signal beam quality. A theoretical model was developed for dephasing effects due to angular deviation from ideal phase matching, and the impact of the angular content of the beam on small signal gain and conversion efficiency in a strongly depleted regime was evaluated numerically [26]. In this paper, the spatial characteristics of the OPCPA process pumped by a spatially aberrated beam are studied theoretically and numerically. Three typical types of spatially aberrated pump beams are discussed, including the phase-modulated pump beam, intensity-modulated pump beam, and non-diffraction-limited pump beam. In the spatial domain, the nonlinear process of OPCPA is identical to that of OPA; thus, most parts of this paper do not differentiate explicitly between OPA and OPCPA.

#### 2. Numerical Model

In this paper, the type I phase-matching OPA process is simulated by nonlinear coupled-wave equations in the spatial domain, implying that all temporal effects in the time domain are ignored. The equations governing the evolution of the envelopes* E*_{p},* E*_{s}, and* E*_{i} of the pump, signal, and idler pulses [28, 29], respectively, arewhere* E*_{j}(*z, x*) is normalized to the input pump field* E*_{0}. For the sake of simplicity, a one-dimensional transverse model is used in simulations; diffraction effects are ignored due to the large beam aperture. A Gaussian pump beam is assumed throughout the paper, although different beam shapes may be involved. The spatial variable* x* is normalized to the radius of the pump beam waist* w*; Δ*k = k*_{s}* + k*_{i}* - k*_{p} is the wave-vector mismatch among the three waves, where wave vector* k*_{j}* = n ω*

_{j}

*/c*. The nonlinear length is defined by as a measure of the pump intensity. The pump beam is considered as the reference beam, thus, walk-off terms only appear in (1) and (2). The signal walk-off length

*L*

_{sp}is defined as

*L*

_{sp}

*= w/*, where

*ρ**is the walk-off angle, and*

*ρ**L*

_{ip}

*= L*

_{sp}in the type-I collinear configuration. The ratio of

*L*

_{sp}to crystal length

*L*indicates the practical walk-off magnitude of the OPA process in the nonlinear crystal. In the calculations, the initial signal wave is assumed to be a Gaussian beam with phase uniformity, and Δ

*k*is set to zero because it primarily affects signal gain and conversion efficiency, which has been thoroughly discussed [22]. Investigation of the walk-off effect in isolation can explicitly clarify its impact on the output signal beam. The standard split-step method and Runge-Kutta algorithm were adopted to solve the nonlinear equations numerically [29–31].

#### 3. Analyses and Discussions

##### 3.1. Pump Beam with Phase Modulation

First, the OPCPA process pumped by a phase-modulated beam is investigated. For simplicity, the pump beam is assumed to include sinusoidal phase modulation as , where parameters* a* and* n* correspond to the modulation amplitude and spatial frequency, respectively. The angular spectrum distributions of the signal beam and idler beam are displayed in Figure 1 under small-signal conditions. The insets in the top right corner are the local enlarged figure. As shown in Figure 1, the angular spectrum of the signal beam remain basically unchanged as the walk-off effect is not considered (the dotted line in Figure 1(a)). The phase modulation of the pump beam leads to angular spectrum aberration of the idler beam (the dotted line in Figure 1(b)). However, the angular spectrum of the signal beam become aberrated as the spatial walk-off effect is taken into account (the solid and dashed lines in Figure 1(a)). Additionally, the greater parameter* a*, the worse the angular spectrum aberration in the output signal beam, and the aberration of the idler beam is weakened accordingly. With regard to saturation amplification, the spatial characteristics of OPA are similar to those of the small signal.