Comparisonbetweenone-dimensionaltime-dependentSchrodingerequationandLewensteinmodel资源-CSDN文库

首发论文

52 浏览量 2020-02-20 08:47:04 上传评论收藏 472KB PDF 举报

资源推荐

资源详情

资源评论

˖ڍመ᝶஠ڙጲ

http://www.paper.edu.cn

一维含时薛定谔方程和Lewenstein模型的比较

杜洪川，胡碧涛

兰州大学核科学与技术学院，兰州　730000

摘要：本工作分别利用Lewenstein模型或一维数值求解含时薛定谔方程结合麦克斯韦方程研究

了高次谐波和阿秒脉冲的产生。结果表明：对于单体响应，数值求解一维含时薛定谔方程

与Lewenstein模型两种方法得到的高次谐波谱与阿秒脉冲是一致的。然而，在宏观情况下，两

种方法得到的结果存在明显的差异。而且，这种差异随着驱动激光脉冲强度增加而增大。研究

发现这一差异来自于一维数值求解含时薛定谔方程对介质中自由电子密度过高估计导致的驱动

激光电场的严重扭曲。当一维含时薛定谔方程仅计算单体响应的偶极加速度，而气体的电离率

用ADK模型计算时，两种方法得到的结果就会符合的非常好。

关键词：阿秒脉冲，高次谐波，强激光

中图分类号： O437

Comparison between one-dimensional

time-dependent Schrodinger equation and

Lewenstein model

Du Hong-Chuan, Hu Bi-Tao

Scho ol of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000

Abstract: The high-order harmonic and attosecond pulse generation are investigated by

solving the Maxwell’s equation using single-atom induced dipole acceleration calculated from

the Lewenstein mo del (SFA) and the one-dimensional time-dependent Schrodinger equation

(TDSE), respectively. In single-atom case, it is found that the results obtained from the

one-dimensional TDSE are agreement with those obtained from the SFA. However, in

macroscopic case, the results obtained from the one-dimensional TDSE are obviously diﬀerent

with those obtained from the SFA. Moreover, the diﬀerence becomes large as the fundamental

laser ﬁeld becomes intense. The diﬀerence can be attributed to the large distortion of the

fundamental laser ﬁeld due to electron density overestimated by one-dimensional TDSE.

When the microscopic single-atom induced dipole acceleration is calculated by using

one-dimensional TDSE and the ionization probability is calculated by using ADK ionization

probability, the results obtained from the one-dimensional TDSE are well agreement with

those obtained from the SFA.

Key words: attosecond pulse, harmonic, intense laser

基金项目：教育部博士点基金(200807300028)和教育部博士研究生学术新人奖资助

作者简介： Du Hong-Chuan（1984-），male，docter，major research direction：nonlinear optics. Correspondence

author：Hu Bi-Tao（1966-），male，professor，major research direction：Nuclear physics.

- 2 -

˖ڍመ᝶஠ڙጲ

http://www.paper.edu.cn

0 Introduction

In the past decade, high-order harmonic generation have been rapidly developed due to

its potential application as a coherent soft x-rays source [1,2] and the generation of attosec-

ond pulses [3-5]. The mechanism of HHG in a single atom can be well understood using the

three-step model [6]: Firstly, the electron tunnels through the barrier formed by the Coulomb

potential and the laser ﬁeld, then it oscillates quasi-freely driven by the laser ﬁeld and acquires

additional kinetic energy, and ﬁnally it can recombine with the parent ion. During the recom-

bination, a photon is emitted with energy equal to the ionization potential plus the kinetic

energy of a recombining electron. This classical picture suggests that the HHG process can be

manipulated via controlling diﬀerent steps. Experimentally, an IAP as short as 80 attoseconds

has b een generated by synthesizing harmonics beyond the cutoﬀ using carrier-envelope-phase

(CEP) stabilized few-cycle laser pulses [7]. The polarization gating technique in which HHG

emission from the central cycle of the pulse is selected, has also produced an isolated 130-as

pulse [8,9]. Ferrari et al. generated the high-energy isolated sub-160-as pulses with the pulse

energy that reaches nanojoule-level by above-saturation few-cycle ﬁelds [10]. Takahashi et

al. generated a continuum harmonic spectrum around the cutoﬀ region by mixing multicycle

two-color laser ﬁelds without carrier-envelope phase stabilization [11]. Theoretically, many ex-

perimental schemes have been proposed to generate isolated attosecond pulse [12-20]. Pfeifer

et al. proposed a method to generate a single attosecond pulse in multicycle-driver regime by

adding a weak second-harmonic ﬁeld [12]. Cao et al. generated a single attosecond pulse with

an intense multicycle driving pulse using oversaturated ionization gating [13]. Our previous

work also generated a broadband supercontinuum using a few-cycle two-color laser pulse and

a high-order pulse, from which an isolated 24-as pulse can be directly obtained [14]. Corkum

et al. proposed a method to generate a single attosecond pulse using a polarization gating

technique, which is based on the strong dependence of the generation of high harmonic on

the ellipticity of the driving pulse [15]. Very recently, we also proposed a method to obtain

an ultra-broadband supercontinuum combining mid-infrared chirped-pulse modulation and a

generalized polarization gating, which supports the isolated sub-100-as pulse generation with a

tunable wavelength [16].

Because the laser ﬁeld interacts with a macroscopic number of atoms, the full description

of this process requires solving not only the strong-ﬁeld laser-atom interaction at the micro-

scopic level, but also the Maxwell wave equation which describes, at the macroscopic level, the

propagation of the driving pulse and the radiation through the nonlinear medium [21]. Altucci

et al. investigated macroscopic eﬀects of attosecond pulse generation in a few-cycle [22] and

multicycle [23] polarization gating regime. Schiessl et al. investigated the high-order harmonic

generation with the two-color ﬁeld considering the inﬂuence of propagation eﬀects [24]. Gaarde

et al. investigated the large enhancement of macroscopic yield in attosecond pulse train-assisted

- 3 -

˖ڍመ᝶஠ڙጲ

http://www.paper.edu.cn

harmonic generation [25]. Hong et al. generated a broadband water window supercontinuum

using a phase-stabilized few-cycle mid-IR pulse tailored by a much weaker 800nm pulse [26].

Lan et al. also found that the two-color ﬁeld can restrict the ionization peak within one half

cycle and also enhance its amplitude, which is dubbed ”ionization gating”, then the high-

eﬃciency harmonics in the plateau merge to a broadband supercontinuum [27]. Very recently,

we investigated propagation eﬀects of isolated attosecond pulse generation with a multicycle

chirped and chirped-free two-color ﬁeld [28]. In order to obtain the macroscopic harmonic spec-

trum, the induced dipole acceleration on each atom is inserted as a source term. This induced

dipole acceleration can be calculated by solving the time-dependent Schrodinger equation or

using the strong ﬁeld approximation (SFA) [29]. Since three-dimensional TDSE calculation for

single-atom response for feeding the macroscopic propagation equations is very time consuming,

one-dimensional TDSE is used to calculate the dipole acceleration of single-atom response. It

has been well known that the single-atom harmonic spectrum obtained from one-dimensional

TDSE is well agreement with that obtained from the SFA except for the intensity of harmonic

spectrum. However, the high-density free electrons due to the overestimated ionization proba-

bility by the one-dimensional TDSE can lead to the large distortion of the driving laser electric

ﬁeld in the propagation. Therefore, the macroscopic harmonic spectrum and attosecond pulse

obtained from the one-dimensional TDSE may be disagreement with them that obtained from

the SFA. To the best of our knowledge, the comparison of the macroscopic harmonic spec-

trum and attosecond pulse obtained from the one-dimensional TDSE and SFA has never been

reported.

In this work, we compare the high-order harmonic spectrum and attosecond pulse gener-

ation by combining the Maxwell’s equation and the SFA or one-dimensional TDSE. In single-

atom case, we found that the results obtained from the one-dimensional TDSE are agreement

with those obtained from the SFA. However, in macroscopic case, the results obtained from

the one-dimensional TDSE are obviously diﬀerent with those obtained from the SFA. More-

over, the diﬀerence becomes large as the fundamental laser pulse becomes intense. We show

that the large distortion of the fundamental laser ﬁeld is responsible for the diﬀerence due to

electron density overestimated by the one-dimensional TDSE. The results obtained from the

one-dimensional TDSE are well agreement with those obtained from the SFA by only calcu-

lating the microscopic single-atom induced dipole acceleration using one-dimensional TDSE

and calculating the ionization probability using ADK ionization probability. Hence, we expect

that the ionization probability obtained from one-dimensional TDSE should be replaced by the

ADK ionization probability when the single-atom induced dipole acceleration is calculated by

one-dimensional TDSE.

- 4 -

剩余14页未读，继续阅读

评论收藏

内容反馈

weixin_38627769

粉丝: 4
资源: 920

Comparison between one-dimensional time-dependent Schrodinger eq...

最新资源

Comparison between one-dimensional time-dependent Schrodinger eq...

数值求解含时薛定谔方程的方法

System Infra architecture between On-premise and Cloud

Comparison-of-OFDMA-and-NOMA

Comparison Theorems of the multi-dimensional BDSDEs and Applications

Comparison-of-Disparity-Estimation-Algorithms:实现简单的块匹配、动态规划的块匹配和使用置信传播算法的立体匹配-matlab开发

Theoretical Comparison of Direct-Sampling Versus Heterodyne RF Receivers

Comparison-of-PID.zip

Performance Comparison Between Full-Duplex and Half-Duplex CSMA/CD EPON

Time-dependent nonlinear theory and numerical simulation of folded waveguide traveling wave tubes

A Survey and Comparison of Time-Delay Estimation Methods in Linear Systems

Comparison Between Segregation Model and Maximum Mixedness Model.ppt

Comprehensive Comparison of Region-Based Image Similarity Models

An Experimental Comparison of Min-Cut/Max-Flow Algorithms

Arm Cortex-M Comparison Table_v3.pdf

Attribute Weighting for Averaged One-Dependence Estimators

comparison_dc-acconverter_

A comparison of first-year, fifth-year, and former teachers on efficacy, ego development, and problem solving

atlassian-visual-comparison-2.5.4-jira20.jar

On the comparison theorem for $1$-dimensional generalized anticipated BSDEs

Comparison-of-Statis-and-Dynamic-Cerebral.pdf

comparison-1.2.10-pl_modxmodmore_

Two-data-comparison-error-correction.rar_对比纠错

Python库 | string_comparison-1.0.2-py3-none-any.whl

A comparison of single-cell trajectory inference methods.pdf

A comparison of GPS-TEC with IRI-TEC at low latitudes in China in 2006

2008-CHOI-Comparison-of-envelope-extraction-algor_extraction

Performance-Comparison-of-VSC-Based-Shunt-and-SER_CONVERTER VSC_

最新资源