Analysis in the instantaneous frequency forms of a chirped laser pulse

Abstract

We analyze two forms of the instantaneous frequency of a linearly chirped laser pulse. Using a 3D test particle simulation, numerical results are presented for electrons accelerated by a chirped laser pulse with these two linearly chirped forms of the instantaneous frequency. We summarize that the linearly chirped frequency, xðtÞ ¼ x 0 1 À aðt À z=cÞ ½ is reasonable, x 0 is laser frequency at z ¼ 0 and t ¼ 0, and a is the frequency chirp parameter.After Shimoda in 1961 had first proposed the use of lasers to accelerate particles was as a clean and simple physical system, 1 vacuum laser acceleration has received much attention in particular. [2][3][4][5][6][7] The key concept in vacuum laser acceleration is breaking the symmetry between acceleration and deceleration so that the former exceeds the latter. 8 Many various schemes have been proposed to achieve just that! Most of these adopt a fixed laser frequency, but what of a time-dependent frequency? Some schemes with chirped laser pulses have been studied in recent years. [9][10][11][12][13][14] The studies that the chirped laser pulses, for which the instantaneous frequency varies with time, could significantly enhance acceleration. Singh introduced the instantaneous frequency xðtÞ ¼ x 0 ð1 À atÞ, where x 0 is the laser frequency at z ¼ 0 and t ¼ 0, and a is the frequency chirp parameter. 10 However, in many other schemes, 11-15 the instantaneous frequency was set as xðtÞ ¼ x 0 1 À aðt À z=cÞ ½ . The question posed is which of the two is reasonable in the end?To begin, we analyze the physical picture of the chirped laser pulses in vacuum for each of these two forms. The latter signifies that the frequency of a fixed point inside a chirped laser pulse will change with time. However, in terms of the moving frame g ¼ t À z=c of the laser pulse, the frequency distribution of a chirped pulse relative to the pulse center will remain unchanged. Thus, the total energy of the chirped laser pulse with the latter form will keep the same, i.e., will not change over time. The former signifies that the frequency in every region inside a chirped laser pulse will uniformly change with time. Then, the total energy of the laser pulse with the former form will change with time. In vacuum, this is unreasonable.We next consider the phase /ðtÞ of the wave which can be written to a Taylor series about the time t,where / 0 is the initial phase and / 1 ¼ x 0 is the instantaneous frequency at t ¼ 0. Thus, the instantaneous frequency isNormally, only the first few terms are typically required to describe well-behaved pulses. If spatial coordinates are considered, a linearly chirped Gaussian pulse of one dimension can be mathematically expressed aswhere g ¼ t À z=c is the retarded time, 5 exp Àðg=sÞ 2 h i the Gaussian profile factor, expðix 0 gÞ the carrier wave, and exp ibg 2 ð Þ the linear chirp part. Normally, the phase term is written aswhere xðtÞ ¼ x 0 þ bg ¼ x 0 ð1 À agÞ, k ¼ xðtÞ=c, and a ¼ Àb=x 0 . Finally, we present some results from our simulations using the above-mentioned two ...

Investigation on a field description of the chirped laser pulse

“…8,9 For a linearly CLP, ω(t, z) = ω 0 (1 − α(t − z/c)), where α is the chirping parameter and ω 0 the central frequency of the laser pulse (the frequency when t − z/c = 0); then k = ω(t, z)/c.…”

“…[25][26][27][28][29][30][31][32][33] In these studies, knowledge of laser's spatiotemporal distribution of all six electromagnetic field components is imperative. A specific study of these field-description functions for CLPs has been investigated before, but in most cases the focus was on a 1D description function, 8,9,[34][35][36] placing all interests on one specific physical property of the CLP, such as its field intensity distribution. 35,37,38 Up until now, obtaining accurate descriptions for all six field components still remains a challenge.…”

“…3 The rapid development of ultra-intense laser technology in recent years has boosted many frontier research areas in both applied and fundamental physics. [4][5][6][7] Among the research into laser-matter interactions, there were studies delving into the intrinsic properties of a chirped laser pulse (CLP) [8][9][10] and the interactions between CLPs and matters, as CLP-based particle acceleration [11][12][13][14][15][16][17][18][19][20][21][22][23][24] and atomic excitations using CLP. [25][26][27][28][29][30][31][32][33] In these studies, knowledge of laser's spatiotemporal distribution of all six electromagnetic field components is imperative.…”