1.State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China 2.University of Chinese Academy of Sciences, Beijing 100049, China 3.Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 11874373) and the Strategic Priority Research Program of Chinese Academy of Sciences, China (Grant No. XDB16000000)
Received Date:05 August 2019
Accepted Date:05 November 2019
Available Online:01 January 2020
Published Online:20 January 2020
Abstract:Broadband terahertz (THz) emission generated from laser induced gas plasma provides an effective tool for studying nonlinear spectrum, imaging and remote sensing. Recently, the contribution of plasma oscillation to the THz emission was revealed from the nitrogen molecules pumped by intense two-color laser pulses. Plasma oscillation contributes only to the THz emission at relatively low plasma density due to negligible plasma absorption. More generally, with the THz emission generated from the ionizing gaseous medium, the surrounding plasma is expected to play an important role in the generation process. For the THz radiation from laser filament, the plasma region is extended in the laser propagation direction, and the effect of surrounding plasma on the emitted THz spectrum needs studying. In this work, we investigate the relation between pump power and filament length from THz spectrum emitted by air filament driven by two-color laser pulse. The time domain spectrum of THz field is recorded by an electro-optic (EO) sampling technique. In our experiments, significant frequency shifts are observed as the pump power and the filament length increase, and we find that the center frequency of the THz radiation is shifted towards longer wavelength, which is the so called red-shift of the THz spectrum. This red-shift is independent of THz radiation angle. The observations are explained by the plasma absorption inside the air filament. Our theoretical model is based on three mechanisms: the ionization-induced photocurrent, the plasma current oscillation and the plasma absorption. We coherently add up all the local THz fields inside the air filament, and simultaneously consider the plasma absorption induced correction of the THz spectrum. The simulation well reproduces the experimental observation. The skin depth decreases as the plasma density increases, thus the plasma absorption dominates the red-shift process. If the skin depth is larger than the filament length, the plasma oscillation contributes to the THz spectrum dominantly, and thus leading to the blue-shift of THz spectrum. Our results indicate that for the extended filament length or higher plasma density, the combining effect of photocurrent, plasma oscillation and absorption, results in the observed low-frequency broadband THz spectrum. Our study offers a method of coherently controlling the broadband THz spectrum. Keywords:terahertz radiation/ laser plasma/ plasma frequency/ plasma absorption
3.实验结果与分析实验首先测量了不同的驱动光功率下双色激光场激发空气等离子体产生THz辐射的时域光谱, 如图2(a)和(b)所示. 分别为峰值功率25 GW与75 GW时测量到的时域波形和对应的频谱. 当驱动光功率变化时, THz光谱的中心频率发生明显的移动. 为了进一步观察THz光谱随驱动光功率的变化规律, 我们测量了峰值功率从18 GW增加至62 GW时一系列的THz波形, 并提取出对应的中心频率. 如图2(c)所示, 随着驱动光功率的增强, THz频谱往低频方向移动, 红移量约为0.3 THz. 该实验结果与在较高背压时喷气靶条件下的结果相似[22]. 图 2 当驱动光功率分别为25 GW (红色实线)及75 GW(蓝色点线)时实验测量的(a)时域光谱及(b)归一化频谱; (c) THz光谱的中心频率随着驱动光功率的变化(其中蓝色点图为实验结果图, 红色曲线为模拟结果) Figure2. Measured (a) THz temporal waveforms and (b) normalized THz spectra at different pump power; (c) central frequencies as a function of the pump energy (The blue dots are the experimental results and the red solid line is from the simulation).
已有研究表明, 相位匹配条件下不同频率的THz辐射具有不同前向角分布特征[23]. 为了检测这一角度分布, 将光阑置于两个抛物面反射镜之间, 如图1所示. 通过改变光阑大小来控制测量收集角度. 实验上测量了在驱动光功率为45 GW时, THz频率分别为1 THz与3 THz时的角度分布, 如图3(a)所示, 可以看出, 频率越高, 辐射角则越小. 我们还测量当辐射收集角度分别为4°, 5°时, THz光谱的中心频率随驱动光功率的变化, 实验结果如图3(b)所示, 可以看出, 驱动光功率越高, THz辐射整体的锥形辐射角越小, 即随着驱动光功率增加, THz辐射反而越集中. 表明等离子体密度变化会对THz辐射角分布产生的影响, 并且THz辐射中心频率均往低频方向移动, 这与文献报道一致[23,24]. 理论模拟与实验观测吻合, 如图3(b)所示. 由于上述测量角度小于探测系统最大的辐射收集角度(~14°), THz辐射角分布的变化不会对光谱红移造成影响. 因此推断THz光谱红移只可能源自产生过程中. 图 3 (a) 驱动光功率为45 GW时, 频率为1 THz与3 THz的辐射角分布; (b)不同锥形辐射角下, THz光谱的中心频率随着驱动光功率的变化 (虚线连接的实心点为实验结果, 实线为计算结果) Figure3. (a) Far-field THz profiles at different frequencies at the pump power of 45 GW; (b) THz central frequencies as a function of the pump energy at various emission angles (Dashed line with solid dots is the experimental results and the solid line is the simulation results)
为了简化模型, 模拟计算时将等离子体设为圆柱形, 基频光与倍频光均为高斯光束. 图4(a)和图4(b)分别为当功率为25 GW时等离子体沿激光传输方向中点处径向及传输方向的等离子体频率及趋肤深度, 其中, 等离子体频率为fpe = ωpe/(2π), 等离子体角频率为ωpe = [nefe2/(mε0)]1/2. 从图中可以看出, 在等离子体中点处光轴上等离子体频率约为1.84 THz, 趋肤深度为0.31 mm, 而在r等于0.028 mm处, 趋肤深度为4.5 mm, 与THz在等离子体光丝中的传输距离(约5 mm)接近; 越往等离子体径向及传输方向的中心, 等离子体趋肤深度越小, 于是在等离子体中心处辐射的THz波被吸收, 而等离子体外围处由于较低的电离率及较小的等离子体频率对远场辐射的THz波起主要贡献. 上述的机制对THz光谱的蓝移起到压制的作用. 图 4 驱动光功率为25 GW 时 (a)沿激光传输方向中点处径向和(b)沿驱动光传输方向z的等离子体频率(蓝色实线)及趋肤深度(红色点线) Figure4. Plasma frequency (blue solid line) and skin depth (red dot line) as a function of the (a) radial axis and (b) pro-pagation direction at the pump power of 25 GW.
基于以上模型, 分别模拟计算了驱动光功率为25 GW与75 GW时的THz频谱, 如图5所示, 相较于驱动光功率为25 GW时的THz频谱, 75 GW时频谱发生显著红移, 该模拟结果与实验结果相符, 如图2(b)所示. 图 5 当驱动光功率分别为25 GW和75 GW时模拟计算的归一化频谱 Figure5. The simulated THz spectra at 25 and 75 GW pump power.
随着驱动光功率的增加, 等离子体光丝的长度变长, 而趋肤深度随着等离子体密度的增强而变短. 在空气等离子体光丝条件下, THz在等离子体光丝中的传输距离要远大于等离子体的趋肤深度, 因此等离子体吸收的贡献大于等离子体振荡对THz辐射的贡献, 导致频谱的红移. 本文计算了驱动光功率的连续变化与THz频谱的移动的关系, 所得的结果与实验相符, 如图2(c)所示. 为了进一步验证等离子体吸收与等离子体振荡对THz辐射的相对贡献, 还测量了在驱动光功率为45 GW时, 等离子体光丝长度的变化对THz频谱的影响. 如图1所示, 将5 mm的聚四氟乙烯(PTFE)置于平移台上, 移动PTFE来改变挡住等离子体光丝的位置, 以此来控制等离子体光丝长度. 以激光传输方向为z轴正方向, 等离子体光丝开始产生的位置设为0, 使PTFE从等离子体光丝的前端沿着z轴向后移动, 每隔一段距离采一组数据, 为避免PTEE被等离子体破坏, 每采一组数据就将PTEE沿x方向移动1 mm, 实验结果如图6所示. 图 6 THz光谱的中心频率随着等离子体光丝长度的变化(蓝色点图为实验结果图, 红色曲线为模拟结果) Figure6. THz central frequencies as a function of the plasma length (The blue dots are the experimental results and the red solid line is the simulation results).
图 1 实验示意图
图 2 当驱动光功率分别为25 GW (红色实线)及75 GW(蓝色点线)时实验测量的(a)时域光谱及(b)归一化频谱; (c) THz光谱的中心频率随着驱动光功率的变化(其中蓝色点图为实验结果图, 红色曲线为模拟结果)
图 3 (a) 驱动光功率为45 GW时, 频率为1 THz与3 THz的辐射角分布; (b)不同锥形辐射角下, THz光谱的中心频率随着驱动光功率的变化 (虚线连接的实心点为实验结果, 实线为计算结果)
图 4 驱动光功率为25 GW 时 (a)沿激光传输方向中点处径向和(b)沿驱动光传输方向z的等离子体频率(蓝色实线)及趋肤深度(红色点线)
图 5 当驱动光功率分别为25 GW和75 GW时模拟计算的归一化频谱
图 6 THz光谱的中心频率随着等离子体光丝长度的变化(蓝色点图为实验结果图, 红色曲线为模拟结果)