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当两束激光同时聚焦形成等离子体时,会产生三阶非线性光学效应,由洛伦兹力产生的非线性相互作用以及等离子体密度的急剧上升,导致了等离子体在轴方向上的散焦现象,这种现象引起等离子体的折射率和相位发生变化[9]:
$$\Delta \varphi = \Delta {\varphi _{\rm plasma}} - \Delta {\varphi _{\rm air}}$$ (1) $$\Delta {\varphi _{\rm air}} \approx 0$$ (2) 这种引起的折射率的变化导致在等离子体的电子密度逐渐减弱的地方,形成一个对太赫兹吸收的非均匀场,在非均匀场中,电子在有质动力的作用下进行加速运动,在有质动力作用下,等离子体中的带电粒子进行无规则的运动,互相发生碰撞,等离子粒子间相互碰撞形成不规则的简谐运动,使得部分粒子从低能级状态跃迁到高能级状态,此时,为了向跃迁能级提供所需要的能量,等离子体对太赫兹波能量进行吸收,使得太赫兹波辐射强度降低。在能级跃迁中,能级跃迁几率(
${A_{\rm {i - f}}}$ )决定着等离子体对太赫兹波吸收的幅度大小:$${A_{\rm{i - f}}} = \frac{{2\pi }}{{2{ j_{\rm_i}} + 1}}{\sum\limits_{{M{\rm_i}}} {\sum\limits_{{M_{\rm f}}} {({M_{\rm fi}})} } ^2}$$ (3) 式中:
${j_{\rm i}}$ 为激发态能量;${M_{\rm fi}}$ 为 激发态($\rm i$ )向高能级态($\rm f$ )跃迁所需要的能量。等离子体间非线性相互作用是导致太赫兹波幅度降低的主要因素,此时等离子体对太赫兹波的反射和散射作用十分微弱,可以忽略不计,待等离子体密度恢复原有密度时,这种散焦现象迅速消失,太赫兹能量恢复初始状态[10-11]。 -
为进一步探究双束等离子体间的非线性作用,笔者研究了激发等离子体的激光波长对非线性作用影响,将理论和实验相结合研究了长波长下等离子体对太赫兹波的吸收状况,将光学参量放大器(TOPAS)放置在其中一路光束中,改变Prelasma光路的波长,以此研究等离子体在不同波长下太赫兹波的吸收作用。研究中,将Is光路产生的Plasma 1等离子体(800 nm波长)固定泵浦光功率为330 mW。对于Ic光路产生的Plasma 2等离子体波长为1 200~1600 nm的泵浦光,并且改变调制光功率,从200~800 mW,间隔100 mW。用高莱探测器测得了不同调制光功率下的双色场产生的太赫兹强度,并且计算出太赫兹吸收强度。得到了不同泵浦波长下,太赫兹吸收强度随800 nm等离子体功率的变化,如图4(a)所示。之后将Ic光路等离子体功率固定在900 mW。记录了太赫兹波吸收强度,如图4(b)所示。从图中可以看出对于同一激发波长,等离子体功率越大,太赫兹波吸收越大。在相同的激光功率下,等离子体波长越长,太赫兹吸收越大。
图 4 (a)不同等离子体波长,太赫兹波吸收随800 nm等离子体功率的变化;(b)太赫兹波吸收随等离子体波长的变化
Figure 4. (a) THz wave absorption varies with the plasma power at 800 nm for different plasma wavelengths; (b) THz wave absorption varies with the plasma wavelength
笔者认为产生这种现象是由于等离子体波长使等离子体密度发生了改变,从而导致电子碰撞更加激烈,使得部分粒子从低能级状态跃迁到高能级状态时,等离子体对太赫兹波能量吸收更加明显。在双色光场产生太赫兹波辐射中,等离子体波长的相位差导致非线性作用逐渐增强,不同的等离子体波长导致的非线性效应也不同,这种非线性效应下的光电流模型可以表示为:
$$ \dfrac{{\partial {J_x}}}{{\partial t}} + \dfrac{{{J_x}}}{{{\tau _c}}} = \dfrac{{{e^2}}}{{{m_e}}}{N_e}{E_x} - \dfrac{e}{{{m_e}}}\dfrac{{{J_{\textit{z}}}}}{c}{E_x} $$ (4) $$ \dfrac{{\partial {J_x}}}{{\partial t}} + \dfrac{{{J_x}}}{{{\tau _c}}} = \dfrac{{{e^2}}}{{{m_e}}}\frac{{{J_ {\textit{z}}}}}{c}{E_x} $$ (5) 式中:e、me、Ne分别为电子电荷、电子质量和电子密度;τc为 碰撞时间;Ex为双色激光电场强度;Jx和Jy分别为电子电流密在脉冲传播方向上的水平部分和垂直部分。这种模型源于电子的动力学耦合的连续性方程。公式(4)和公式(5)等号右边的两项式包含了洛伦兹力和激光脉冲电场。假设脉冲电场强度E沿着x轴方向是线偏振的,电子的等离子体密度Ne是由光场电离产生的,这个过程涉及由中性原子(A)和分子(M)电离产生的电子密度
${N_{\rm{A,M}}}\left( {{{r}},{{ {\textit{z}}}},{{t}}} \right)$ [12]:$$ \frac{{\partial {N_{\rm{A,M}}}}}{\partial t} = - W\left( {\left| E \right|} \right){N_{\rm{A,M}}} $$ (6) 由电荷守恒定律可知,电子密度
${N_{\rm{A,M}}}( {{r}}, $ $ {{ {\textit{z}}}},{{t}})$ 为:$$ {N_{\rm{A,M}}}\left( {{{r}},{{{\textit{z}}}},{{t}}} \right) = {N_0} - {N_{\rm{A,M}}}\left( {{{r}},{{{\textit{z}}}},{{t}}} \right) $$ (7) 这里,N0表示激光脉冲到来前的中性原子或分子的电子密度。独立场电离率符合Keldysh公式。在这个模型中,有效的多光子隧穿机制包含依赖于多光子电离的波长参数。设z轴方向的二次谐波的偏振态平行于基频波的偏振态,双色光形成的电场可以写为:
$$ {E_x} = {E_\omega } + {E_{2\omega }} $$ (8) 那么,泵浦光电流密度可以表示为:
$$ {J_x} \propto \frac{{{e^2}}}{{\omega {m_e}}}{N_e}{E_x} $$ (9) 在隧穿电离中,横向电流正比于泵浦光波长。所以随着等离子体波长的增加,等离子体密度增加,导致电子碰撞更加激烈,太赫兹波的降低更加明显。
基于上述理论分析,图5(a)给出了在不同等离子体波长下,太赫兹吸收强度随800 nm等离子体功率的变化模拟结果。图5(b)中的红线为计算得出的太赫兹波吸收强度随泵浦激光波长的变化结果,蓝点为实验数据。基频波与二次谐波之间固定的π/2相位差,330 mW的泵浦光功率,5%的二次谐波倍频转换效率和900 mW的等离子体脉冲功率。从图中可以看出,计算出的太赫兹波吸收强度随等离子体功率的增加而增加,太赫兹波的吸收强度随激光波长的增加而增加,模拟结果与实验结果拟合良好。从图5(a)还可以看出:随着调制光功率的逐渐增加,太赫兹波调制深度增加的速度变慢,趋于饱和。这种饱和可以理解为在双色脉冲到达之前,空气中等离子体被800 nm的光脉冲完全电离。
图 5 (a)计算得出的太赫兹吸收强度与800 nm等离子体功率的函数关系;(b)太赫兹波吸收强度随等离子体波长变化的模拟结果与实验结果对比
Figure 5. (a) Calculated terahertz absorption intensity as a function of the 800 nm plasma power; (b) Comparison between the simulated and experimental results of the terahertz absorption intensity as a function of plasma wavelength
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在双束等离子体间的非线性过程中,当两束等离子体光丝处于分离—重合—分离的过程中,周围不同气体环境会对等离子体的非线性作用产生影响,从而使得等离子体对太赫兹波能量的吸收发生变化。Jayashis Das的研究团队在氮气N2的实验环境下进行了相关研究认为,在双束等离子体重合时,含有
$\rm N_2^ +$ 的离子首先和氮气N2发生结合形成$\rm N_4^ +$ 粒子,然后再和电子e在氮气环境下快速地重组产生新的氮气N2,进而导致了等离子体电离的电子数量急剧下降,以此导致产生的太赫兹波辐射能量发生明显的降低[13]:$$ \rm N_2^ + + {\rm N_2} =\rm N_4^ + $$ (10) $$ {\rm{N}}_{\rm{4}}^{\rm{ + }}{\rm{ + e = }}{{\rm{N}}_{\rm{2}}}\left( {{C^3}{\Pi _u}} \right){\rm{ + }}{{\rm{N}}_{\rm{2}}} $$ (11) 这里
$ {C^3}{\Pi _u} $ 表示氮气状态,其弛豫时间影响电子e与$\rm N_4^ +$ 相结合的概率。但是通过研究发现,笔者认为等离子体吸收和周围气体中N离子的关系不大,为了验证分析,在双束等离子体产生太赫兹波辐射系统中将双色等离子体放置进一个气室,通过气阀和真空泵改变气室内的气体(Ar和氮气N2)环境,结果表明,在氮气和氩气环境下,当两束等离子体丝重合时,太赫兹波辐射能量分别降低了2.72倍和2.82倍。在氮气和氩气环境下均可以观察到太赫兹波辐射能量的降低,表明Jayashis Das等人认为的电子e与
$\rm N_4^ +$ 快速重组的过程并不是太赫兹波辐射能量降低的真正原因。为了进一步研究该现象,测量了4种气体环境下双束等离子体产生的太赫兹波辐射的强度。图6为在氦气(He)、氖气(Ne)、氮气(N2)和氩气(Ar)下所测量的太赫兹波能量降低的幅值。结果表明,在氩气环境下太赫兹波降低的辐值最大,在氦气环境下太赫兹波降低的辐值最小。这是由于分子动力学理论中:
图 6 不同气体环境下得到的太赫兹波辐射强度变化(黑色实线为在氩气环境得到的结果,红色实线为在氮气环境下得到的实验结果)
Figure 6. THz wave radiation intensity changes obtained in different gas environments (the black solid line is the result obtained in an argon atmosphere, and the red solid line is the experimental result obtained in a nitrogen environment)
$$ \frac{{{\rm d}\vec v({{t}})}}{{{\rm d}t}} + \frac{{\vec v({{t}})}}{\tau } = - \frac{e}{m}{\vec E_{Loc}}({{t}}) $$ (12) 式中:
$v\left( {{t}} \right)$ 为分子速度;m为分子质量。从公式可以看出,气体分子质量决定着飞秒激光聚焦空气电离出的等离子体所形成的电场强度,分子质量越高,所形成的电场强度越强,双束等离子体重合时对太赫兹波降低的辐值越大。图7为不同气体环境下太赫兹波降低的辐值。
Influence of nonlinear interaction between femtosecond plasmas on ultra-high frequency electromagnetic waves
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摘要: 主要研究了飞秒等离子间相互的非线性作用对超高频电磁波——太赫兹波产生的影响。国内外许多研究机构已经证实,在太赫兹波产生的过程中,等离子体间的相互非线性作用会对太赫兹波产生影响。笔者结合理论分析设计并搭建一种了双束等离子体重合产生太赫兹波的测试系统,研究发现等离子体间相互非线性作用时,会产生三阶非线性光学效应,等离子体的折射率和相位发生变化形成非均匀场导致了太赫兹波辐射能量的降低,并在实验测量研究中发现随着等离子体波长双束等离子波长的增加,等离子体密度增加,导致太赫兹波的辐射能量的降低现象更加明显,另外,等离子体功率越大,太赫兹波吸收越大。同时,研究发现等离子体周围惰性气体分子质量影响太赫兹降低程度,气体分子质量决定着飞秒激光聚焦空气电离出的等离子体所形成的电场强度,分子质量越高,所形成的电场强度越强,双束等离子体重合时对太赫兹波降低的辐值越大。这些为研究等离子体间非线性作用对太赫兹波的影响提供了更加全面的理论支撑,有助于推动太赫兹波技术在军事及民用领域的快速发展。Abstract: The influence of the nonlinear interaction between femtosecond plasmas on the ultra-high frequency electromagnetic wave—terahertz (THz) wave was mainly studied in this paper. Many research institutions had confirmed that in the process of generating THz wave, the interaction between plasmas would affect THz wave. Combined theoretical analysis, a test system for generating THz wave due to the coincidence of two-beam plasmas was designed by the author. The study found that the nonlinear interaction between plasmas will produce a third-order nonlinear optical effect. The refractive index and phase of the plasma changed to form a non-uniform field, which led to a decrease in the radiant energy of the THz wave. In the experimental measurement research, it was found that with the increase of the plasma wavelength of the double beam plasma wavelength, the plasma density increased, resulting in a more obvious decrease in the radiation energy of the THz wave. In addition, the greater the plasma power, the greater the absorption of THz wave. At the same time, it was found that the mass of inert gas molecules around the plasma affected terahertz reduction degree. The mass of gas molecules determined the intensity of the electric field formed by the plasma ionized by the femtosecond laser focusing on the air. The higher the molecular mass, the stronger the intensity of the electric field formed, and the greater the magnitude of the THz wave reduced when the two-beam plasma overlapped. The study provides more comprehensive theoretical support for influence of the nonlinear interaction between plasmas on the THz wave, which helps to promote the rapid development of THz wave technology in the military and civilian fields.
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Key words:
- terahertz /
- plasma /
- nonlinear effect
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图 5 (a)计算得出的太赫兹吸收强度与800 nm等离子体功率的函数关系;(b)太赫兹波吸收强度随等离子体波长变化的模拟结果与实验结果对比
Figure 5. (a) Calculated terahertz absorption intensity as a function of the 800 nm plasma power; (b) Comparison between the simulated and experimental results of the terahertz absorption intensity as a function of plasma wavelength
图 6 不同气体环境下得到的太赫兹波辐射强度变化(黑色实线为在氩气环境得到的结果,红色实线为在氮气环境下得到的实验结果)
Figure 6. THz wave radiation intensity changes obtained in different gas environments (the black solid line is the result obtained in an argon atmosphere, and the red solid line is the experimental result obtained in a nitrogen environment)
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