Quantized media with absorptive scatterers and modified atomic emission rates

Modifications in the spontaneous emission rate of an excited atom that are caused by extinction effects in a nearby dielectric medium are analyzed in a quantummechanical model, in which the medium consists of spherical scatterers with absorptive properties. Use of the dyadic Green function of the electromagnetic field near a dielectric sphere leads to an expression for the change in the emission rate as a series of multipole contributions for which analytical formulas are obtained. The results for the modified emission rate as a function of the distance between the excited atom and the dielectric medium show the influence of both absorption and scattering processes.     

规范不变系统量子水平的变换性质及应用

按Faddeev-Popov路径积分量子化方法,给出规范不变系统在位形空间中的生成泛函,导出了系统位形空间中量子水平的变换性质.讨论了该系统量子水平的守恒律问题,且给出了Poincar群变换下电磁场在介质分界面附近量子水平的变换性质,在量子水平上说明了电磁波反射和折射时能量中心的“横移”现象. 关键词： 规范理论 位形空间 路径积分 “横移”效应     

A representation of Kerr-like nonlinearity for the analytical TM surface polariton solution

The TM-polarized waves propagating along the interface between a nonlinear Kerr-like material and linear cladding are investigated. We analyse the nonlinear dielectric permittivity as a function of the electromagnetic field. It is shown that an exact analytical solution of Maxwell's equations corresponding to the TM surface polariton in the form described by sech function do exist in a Kerr-like nonlinear medium with the permittivity profile given by a hypergeometric function. We compare our analytical solution and analogous exact numerical solution in a Kerr medium. The power flow down the interface between two media is also discussed.     

Exact solutions for a mode of the electromagnetic field in a resonator with time-dependent characteristics of the internal medium

The problem of quantization of the electromagnetic field inside a resonator filled with a dielectric medium with time-dependent characteristics in the presence of the external alternating current is studied. The exact propagator and the coherent and Fock's states are obtained for a quantum oscillator with time-dependent frequency linearly coupled via momentum with external current. Delta-pulse excitation of the medium is considered as an example.     

电磁波在等离子体中的非线性吸收衰减

研究平面电磁波在等离子体中的非线性吸收衰减.首先应用电磁波在等离子体中传播的极化理论得到非线性介电函数,进而求出了考虑非线性情况下的波矢.采用垂直入射具有金属衬底的均匀等离子体模型,对不同入射频率的电磁波的衰减以及总出入射功率比进行了数值模拟.与只考虑线性情况的结果作了比较,结果显示非线性项在研究过程中所起的作用是不可忽视的.     

Sum-Frequency Generation from a Thin Cylindrical Layer

In the Rayleigh–Gans–Debye approximation, we have solved the problem of the sum-frequency generation by two plane elliptically polarized electromagnetic waves from the surface of a dielectric particle of a cylindrical shape that is coated by a thin layer possessing nonlinear optical properties. The formulas that describe the sum-frequency field have been presented in the tensor and vector forms for the second-order nonlinear dielectric susceptibility tensor, which was chosen in the general form, containing chiral components. Expressions describing the sum-frequency field from the cylindrical particle ends have been obtained for the case of a nonlinear layer possessing chiral properties. Three-dimensional directivity patterns of the sum-frequency radiation have been analyzed for different combinations of parameters (angles of incidence, degrees of ellipticity, orientations of polarization ellipses, cylindrical particle dimensions). The mathematical properties of the spatial distribution functions of the sum-frequency field, which characterize the symmetry of directivity patterns, have been revealed.     

柱面非线性麦克斯韦方程组的行波解

柱面电磁波在各种非均匀非线性介质中的传播问题具有非常重要的研究价值.对描述该问题的柱面非线性麦克斯韦方程组进行精确求解,则是最近几年新兴的研究热点.但由于非线性偏微分方程组的极端复杂性,针对任意初边值条件的精确求解在客观上具有极高的难度,已有工作仅解决了柱面电磁波在指数非线性因子的非色散介质中的传播情况.因此,针对更为确定的物理场景,寻求能够精确描述其中更为广泛的物理性质的解,是一种更为有效的处理方法.本文讨论了具有任意非线性因子与幂律非均匀因子的非色散介质中柱面麦克斯韦方程组的行波精确解,理论分析表明这种情况下柱面电磁波的电场分量E已不存在通常形如E=g(r-kt)的平面行波解;继而通过适当的变量替换与求解相应的非线性常微分方程,给出电场分量E=g(lnr-kt)形式的广义行波解,并以例子展示所得到的解中蕴含的类似于自陡效应的物理现象.     

Modeling of the electromagnetic wavefront sharpening in a nonlinear dielectric

The results of physical and numerical modeling of electromagnetic wavefront sharpening in a nonlinear dielectric are given. A technique of mathematical modeling of wave propagation is described in terms of a modified vector magnetic potential. It is shown how the level of the applied field strength and the degree of nonlinearity of the dielectric affect the electromagnetic wavefront sharpening.     

Casimir Effect for Dielectric Plates

We generalize Kupisewska method to the three-dimensional system and another derivation of the Casimir effect between two dielectric plates is presented based on the explicit quantization of the electromagnetic field in the presence of dielectrics, where the physical meaning of “evanescent mode” is discussed. The Lifshitz's formula is rederived using all the vacuum mode functions, which include the contribution of the ‘evanescent modes’. Only in the case of the perfect metallic plates will the evanescent modes become unimportant.     

Pulse propagation in a nonlinear dielectric slab waveguide

The evolution of an optical pulse in a single-mode, step index dielectric slab waveguide which is characterized by an intensity dependent dielectric function in the core and cladding regions is treated by means of differential equation techniques. A cubic order non-linearity is considered. The electromagnetic field distribution in the slab waveguide region satisfies a non-linear wave equation. This field can be represented in terms of even TE guided modes with a slowly varying envelope amplitude function.Then using the well known approximation, based on the slowly varying character of the amplitude function, a non linear partial differential equation is obtained for the amplitude function. As the coefficients of this equation depend on the distance across the transverse direction X, an averaging technique over x is applied to reduce the nonlinear partial differential equation into a form that is easily transformed to the so-called non-linear Scroedinger differential equation.This equation is then attacked by means of the well known Inverse Scattering method in the case of reflection less potentials. The single and double soliton solutions are obtained explicitly for a single-mode slab waveguide. Finally numerical results are presented in the time domain.     

Canonical Quantization of Electromagnetic Field in the Presence of Nonlinear Anisotropic Magnetodielectric Medium with Spatial-Temporal Dispersion

Modeling a nonlinear anisotropic magnetodielectric medium with spatial-temporal dispersion by two continuum collections of three dimensional harmonic oscillators, a fully canonical quantization of the electromagnetic field is demonstrated in the presence of such a medium. Some coupling tensors of various ranks are introduced that couple the magnetodielectric medium with the electromagnetic field. The polarization and magnetization fields of the medium are defined in terms of the coupling tensors and the oscillators modeling the medium. The electric and magnetic susceptibility tensors of the medium are obtained in terms of the coupling tensors. It is shown that the electric field satisfy an integral equation in frequency domain. The integral equation is solved by an iteration method and the electric field is found up to an arbitrary accuracy.     

Solitary Surface Waves in Plasmas Interacting with a High-Frequency Electric Field

We show that a solitary surface wave can exist at the boundary between a plasma and a dielectric, due to a balance between the nonlinear surface charge terms and the dispersive terms which here are caused by the presence of a high-frequency incident electromagnetic wave. The solitary wave propagation velocity, which depends on the intensity of the incident field, is also calculated.     

On the theory of TE-polarized waves guided by a nonlinear three-layer structure

TE-polarized electromagnetic waves guided by a three-layer structure consisting of a film surrounded by semi-infinite media (all media are characterized by a Kerrlike dielectric function) are investigated by expressing the solution of the field equations in terms of Weierstrass' elliptic functions. Evaluation leads to a universal dispersion relation and its solutions and a universal expression for the power flow. Numerical results are presented for the effective wave number as a function of the intensity of the electric field at the lower surface of the nonlinear film, for various profiles of the field intensity, and for the power flow as a function of the effective wave number.     

Investigation of 2-D electromagnetic transients in a circular cylinder with time discontinuity in permittivity via the resolvent method

The resolvent method approach is proposed for analytically solving the time domain Volterra integral equation (TDVIE) which describes the electromagnetic fields in 2-D cylindrical structures with time changes in the permittivity. It is shown that the approach allows investigation of the electromagnetic field transformation due to an abrupt time change in dielectric permittivity inside a circular cylinder as well as the construction of the Green’s function for an initial-boundary value problem. Key mechanisms of electromagnetic field transformation are investigated and a qualitative distinction of the processes is shown that depends on an initial field configuration.     

Wave chaotic behaviour generated by linear systems

It is shown that regimes with dynamical chaos are inherent not only to nonlinear system but they can be generated by initially linear systems and the requirements for chaotic dynamics and characteristics need further elaboration. Three simplest physical models are considered as examples. In the first, dynamic chaos in the interaction of three linear oscillators is investigated. Analogous process is shown in the second model of electromagnetic wave scattering in a double periodical inhomogeneous medium occupying half-space. The third model is a linear parametric problem for the electromagnetic field in homogeneous dielectric medium which permittivity is modulated in time.     

Controlled hysteresis in optical systems surrounded by two feedback loops

The absorptive bistability in a nonlinear optical system surrounded by two feedback loops is studied. The role of the nonlinear element is played by a cell with Λ-type atom vapors placed in a unidirectional ring cavity. The feedback includes two electromagnetic fields interacting with two atomic transitions. A two-dimensional domain of stability was found in the coordinates of field intensities at the input. The dependence of its shape on the values of different parameters of the optical system is studied. The input-output curves corresponding to different trajectories in the domain of stability are obtained.     

非线性平板光波导中TM波的网络分析

用横向等效网络方法分析了非线性平板波导中TM的色散关系和场分布.这种方法基于传输线理论,把非线性介质波导中复杂的电磁场问题等效于电路网络问题,用横向谐振技术得到色散方程.用数值方法计算了不同非线性机制下三层平板非线性波导中的TM波传输特性.     

Quantum features of electromagnetic field

The quantum theory of electromagnetic field, developed by Fermi and Dirac, revealed some difficulties in quantizing this field. Although these difficulties have been considered in numerous publications, the situation was far from clear. Currently, this problem is even more urgent, because quantum properties of electromagnetic field are proposed to use in a number of devices. In this paper we consider the quantization problems anew. Some features of scalar potential quantization are revealed. A basis system of stationary states, which is conventionally normalized, is constructed. This construction made it possible to reject an unnecessary design: the so-called indefinite metric. The requirements to the field state with respect to the Lorentz condition are formulated. A state satisfying the Lorentz condition and describing the state of the Coulomb field is constructed. It is shown that the component of the four-potential of electromagnetic field (the difference component), which describes the Coulomb field, has zero quantum-mechanical uncertainty. The other (sum) component of the four-potential of electromagnetic field has an infinite quantum dispersion or, in other words, infinite quantum-mechanical uncertainty. Apparently, specifically this circumstance served a basis for numerous statements about unobservability of these potentials. However, it is only the aforementioned sum component of the four-potential of electromagnetic field that is in fact unobservable.     

有损耗介质中非线性光导波的数值模拟

发展了一种以有限元法为基础的数值方法，用它分析由损耗任意大小材料构成的平面非线性波导结构所传导的非线性有损耗光波。在这种方法中，从给出的非线性有损耗波导直接得到ＴＥ和ＴＭ波与功率有关的复传播常数和局域电磁场分布。