非线性各向异性介质中辐射场的量子化
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摘要
自从激光器出现以来,激光与物质相互作用就逐渐成为物理学研究的前沿和热点问题。特别是,在这些相互作用过程中可以产生各个频段的辐射,使得对其作用过程的研究不仅具有极其重要的学术意义,而且具有广泛的应用前景。同时,这些辐射产生的过程在本质上是量子问题,只有采用量子力学描述才能更加深入地认识辐射过程的物理实质。本论文通过修正和推广Langevin噪音理论,对非均匀吸收介质和各向异性吸收介质中电磁场的量子化进行了系统的理论研究,并利用这些量子化的电磁场分别建立了各向异性吸收介质中Cherenkov辐射的全量子理论和激光-等离子体中辐射的全量子理论,获得了一系列有意义的结果。
以下为本论文的主要研究结果：
1.利用Langevin噪音理论对具有二次连续变化形式介电函数的吸收介质中电磁场进行了量子化,用所得量子化电磁场计算了电场在真空态中波动的功率谱,所得结果可以在讨论无限均匀吸收介质时给出与前人相同的结论。
2.提出了一种在任意非均匀吸收介质中求解格林函数的新方法,该方法把满足亥姆霍兹方程的格林函数设成一个积分表达式,从而将姆霍兹方程转变为一个可利用Feyman路径积分法求解的复势薛定谔方程。利用这个方法可以得到任意非均匀吸收介质中的格林函数,进而可以实现任意非均匀吸收介质中的电磁场量子化。
3.通过将Langevin噪音理论中定义的修正因子从标量形式推广的矢量形式,使Langevin噪音理论的适用范围从各向同性吸收介质拓展到各向异性吸收介质,从而实现三维各向异性吸收介质中电磁场的量子化。
4.发现了各向异性吸收介质中修正因子所必须满足的积分方程,利用这个积分方程可得到任意各向异性吸收介质相对应的修正因子,进而通过Langevin噪音理论实现任意各向异性吸收介质中电磁场的量子化。
5.建立了各向异性吸收介质中Cherenkov辐射的全量子理论,发现利用全量子理论得到的Cherenkov辐射角比经典定义的要小。吸收介质的各向异性性质对Cherenkov辐射角没有影响,但会改变Cherenkov辐射功率的大小,这样通过调节吸收介质的各向异性性质可以来控制Cherenkov辐射功率。
6.建立了激光-等离子体中辐射的全量子理论,从理论上说明,强度在1010W／cm2到1012W／cm2之间的激光与等离子相互作用中产生的辐射,主要是来自于等离子体共振。并且,出射光子率与非束缚自由电子和辐射场之间的夹角有关。此外,低碰撞率的等离子体内部更容易产生光子。
Since the advent of laser, the interactions between laser and matter have become a hotspot and frontier of research in physics. Especially, mechanism of various radiations generated during interactive process is of considerable importance not only in the basis interest in academy but also in application. Simultaneously, the radiation is a quantum problem from its microcosmic mechanism. To understand the physical essence of radiation process in depth, imaginably, the development of a fully quantum mechanical description is necessary. In this thesis, quantizations of electromagnetic field in inhomogeneous and anisotropic absorptive dielectrics are theoretically investigated, using Langevin noise scheme. Subsequently, full quantum theory of Cherenkov radiation in an anisotropic absorbing media and radiation in laser plasma are explored by means of these quantization fields, and some worthful results are presented.
The important results obtained are summed up as following:
1. According to Langevin noise scheme, the wave equation with regard to Green function is analytically solved by direct integral method for a quadratic continuous nonlinear absorptive dielectric medium. The quantization of electromagnetic field in such a nonlinear absorptive dielectric is carried out for which the material dielectric function is assumed as separable variable about the frequency and the space coordinate. The vacuum field fluctuations for different spatial continuous variations of dielectric function are numerically calculated, which shows that the present result is self-consistent.
2. A new approach is developed to solve the Green's function that satisfies the Hehmholtz equation with complex refractive index. Especially, the Green's function for the Helmholtz equation can be expressed in terms of a one-dimensional integral, which can convert Helmholtz equation into a Schrodinger equation with complex potential. And Schrodinger equation can be solved by Feynman path integral. Using this approach, the Green's function in arbitrary inhomogeneous absorptive dielectrics can be solved, which is useful for realizing electromagnetic field quantization in arbitrary inhomogeneous absorptive dielectrics.
3. Based on Langevin noise scheme, we suggest a general approach to realize the quantization of radiation field in an anisotropic dispersive dielectric medium by defining a modified new coefficient of Langevin force operator. The transformation relation between the quantization methods for isotropic and anisotropic dispersive media is presented.
4. The integral equation of modified coefficient satisfying in anisotropic absorptive dielectrics is discovered, which can realize electromagnetic field quantization in arbitrary anisotropic absorptive dielectrics.
5. A fully quantum mechanical treatment is presented for the Cherenkov radiation stimulated by a uniformly moving charge particle in both isotopic medium and anisotropic medium. The relation between Cherenkov radiation intensity and dielectric tensor is analyzed. The results showed that, the medium dielectric tensor changes the density of the Cherenkov radiation but does not change the emitting angle of the radiation, which is of advantage for the collection of radiation wave with expectant wavelengths.
6. Based on the Langevin noise approach, a full quantum theory of radiation in laser plasma is explored, where the laser power is limited to the range from 1010 W/cm2 to 1012 W/cm2 and the plasma is considered as a homogeneous dielectric background. By numerical calculation, the results show that the radiation is generated from resonance of the plasma and the emitted rate of photon depends on the angular relation of the directions of radiation fields as well as the motion of the unbounded free electrons. In addition, the photons are more easily created under the lower collision frequency.
以下为本论文的主要研究结果：
1.利用Langevin噪音理论对具有二次连续变化形式介电函数的吸收介质中电磁场进行了量子化,用所得量子化电磁场计算了电场在真空态中波动的功率谱,所得结果可以在讨论无限均匀吸收介质时给出与前人相同的结论。
2.提出了一种在任意非均匀吸收介质中求解格林函数的新方法,该方法把满足亥姆霍兹方程的格林函数设成一个积分表达式,从而将姆霍兹方程转变为一个可利用Feyman路径积分法求解的复势薛定谔方程。利用这个方法可以得到任意非均匀吸收介质中的格林函数,进而可以实现任意非均匀吸收介质中的电磁场量子化。
3.通过将Langevin噪音理论中定义的修正因子从标量形式推广的矢量形式,使Langevin噪音理论的适用范围从各向同性吸收介质拓展到各向异性吸收介质,从而实现三维各向异性吸收介质中电磁场的量子化。
4.发现了各向异性吸收介质中修正因子所必须满足的积分方程,利用这个积分方程可得到任意各向异性吸收介质相对应的修正因子,进而通过Langevin噪音理论实现任意各向异性吸收介质中电磁场的量子化。
5.建立了各向异性吸收介质中Cherenkov辐射的全量子理论,发现利用全量子理论得到的Cherenkov辐射角比经典定义的要小。吸收介质的各向异性性质对Cherenkov辐射角没有影响,但会改变Cherenkov辐射功率的大小,这样通过调节吸收介质的各向异性性质可以来控制Cherenkov辐射功率。
6.建立了激光-等离子体中辐射的全量子理论,从理论上说明,强度在1010W／cm2到1012W／cm2之间的激光与等离子相互作用中产生的辐射,主要是来自于等离子体共振。并且,出射光子率与非束缚自由电子和辐射场之间的夹角有关。此外,低碰撞率的等离子体内部更容易产生光子。
Since the advent of laser, the interactions between laser and matter have become a hotspot and frontier of research in physics. Especially, mechanism of various radiations generated during interactive process is of considerable importance not only in the basis interest in academy but also in application. Simultaneously, the radiation is a quantum problem from its microcosmic mechanism. To understand the physical essence of radiation process in depth, imaginably, the development of a fully quantum mechanical description is necessary. In this thesis, quantizations of electromagnetic field in inhomogeneous and anisotropic absorptive dielectrics are theoretically investigated, using Langevin noise scheme. Subsequently, full quantum theory of Cherenkov radiation in an anisotropic absorbing media and radiation in laser plasma are explored by means of these quantization fields, and some worthful results are presented.
The important results obtained are summed up as following:
1. According to Langevin noise scheme, the wave equation with regard to Green function is analytically solved by direct integral method for a quadratic continuous nonlinear absorptive dielectric medium. The quantization of electromagnetic field in such a nonlinear absorptive dielectric is carried out for which the material dielectric function is assumed as separable variable about the frequency and the space coordinate. The vacuum field fluctuations for different spatial continuous variations of dielectric function are numerically calculated, which shows that the present result is self-consistent.
2. A new approach is developed to solve the Green's function that satisfies the Hehmholtz equation with complex refractive index. Especially, the Green's function for the Helmholtz equation can be expressed in terms of a one-dimensional integral, which can convert Helmholtz equation into a Schrodinger equation with complex potential. And Schrodinger equation can be solved by Feynman path integral. Using this approach, the Green's function in arbitrary inhomogeneous absorptive dielectrics can be solved, which is useful for realizing electromagnetic field quantization in arbitrary inhomogeneous absorptive dielectrics.
3. Based on Langevin noise scheme, we suggest a general approach to realize the quantization of radiation field in an anisotropic dispersive dielectric medium by defining a modified new coefficient of Langevin force operator. The transformation relation between the quantization methods for isotropic and anisotropic dispersive media is presented.
4. The integral equation of modified coefficient satisfying in anisotropic absorptive dielectrics is discovered, which can realize electromagnetic field quantization in arbitrary anisotropic absorptive dielectrics.
5. A fully quantum mechanical treatment is presented for the Cherenkov radiation stimulated by a uniformly moving charge particle in both isotopic medium and anisotropic medium. The relation between Cherenkov radiation intensity and dielectric tensor is analyzed. The results showed that, the medium dielectric tensor changes the density of the Cherenkov radiation but does not change the emitting angle of the radiation, which is of advantage for the collection of radiation wave with expectant wavelengths.
6. Based on the Langevin noise approach, a full quantum theory of radiation in laser plasma is explored, where the laser power is limited to the range from 1010 W/cm2 to 1012 W/cm2 and the plasma is considered as a homogeneous dielectric background. By numerical calculation, the results show that the radiation is generated from resonance of the plasma and the emitted rate of photon depends on the angular relation of the directions of radiation fields as well as the motion of the unbounded free electrons. In addition, the photons are more easily created under the lower collision frequency.
引文
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