Magnetic field effects on the localization of electromagnetic waves in random 1D systems which are almost periodic

The effects of an externally applied magnetic field on the Anderson localization of electromagnetic waves in an alternating layered system of vacuum and semiconducting slabs are studied. Specifically, a waveguide formed from perfectly conducting parallel plates which contain between them an array of vacuum and n-type semiconductor slabs is examined in the presence of an external static magnetic field applied parallel to both the plates and the slab surfaces. The widths of the slabs in the array are random but with a randomness such that the array of slabs is almost periodic, and we study only electromagnetic modes which propagate perpendicular to the slab surfaces. The localization length is obtained by studying the reflection and transmission properties of a finite array of slabs in the limit that it becomes semi-infinite. Two types of system are treated: (i) a reciprocal system which exhibits a localization length that does not depend on the sign of the applied magnetic field, and (ii) a non-reciprocal system which exhibits a localization length that depends on the sign of the applied magnetic field.     

Magnetic field effects on the localization of electromagnetic waves in random 1D systems which are almost periodic

Abstract

The effects of an externally applied magnetic field on the Anderson localization of electromagnetic waves in an alternating layered system of vacuum and semiconducting slabs are studied. Specifically, a waveguide formed from perfectly conducting parallel plates which contain between them an array of vacuum and n-type semiconductor slabs is examined in the presence of an external static magnetic field applied parallel to both the plates and the slab surfaces. The widths of the slabs in the array are random but with a randomness such that the array of slabs is almost periodic, and we study only electromagnetic modes which propagate perpendicular to the slab surfaces. The localization length is obtained by studying the reflection and transmission properties of a finite array of slabs in the limit that it becomes semi-infinite. Two types of system are treated: (i) a reciprocal system which exhibits a localization length that does not depend on the sign of the applied magnetic field, and (ii) a non-reciprocal system which exhibits a localization length that depends on the sign of the applied magnetic field.     

On Reflection and Transmission of Electromagnetic Waves Obliquely Incident on Relativistically Moving Uniaxial and Isotropic Plasma Slabs

The oscillations in the power reflection coefficient as a function of the normalized slab velocity are shown for electromagnetic waves obliquely incident on a relativistically moving uniaxial plasma slab with an infinitely strong magneto-static field parallel to the slab boundaries. This paper also summarizes and concludes the sequence on the reflection and transmission of electromagnetic waves obliquely incident on relativistically moving uniaxial and isotropic plasma slabs.     

Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: Random phase approximation

We consider the propagation of p-polarized electromagnetic waves obliquely incident on stratified random dielectric media. Using the invariant imbedding method generalized to random media and applying the random phase approximation, we derive a simple analytical expression of the localization length and calculate the disorder-averaged reflectance and transmittance and the fluctuations of the localization length and the reflectance as functions of the incident angle. We also calculate the disorder-averaged intensity profile of the magnetic field inside the random medium. We find that within the random phase approximation, the p wave can be delocalized and transmitted completely at a certain critical incident angle, which is bigger than the Brewster angle in the uniform case.     

On the dielectric theory of a crystalline slab of point molecules

We discuss the dielectric response of a crystalline slab of point molecules to an incident plane electromagnetic wave. The slab is assumed to be made up of non-polar, polarizable molecules (a) lying at points of a simple cubic lattice and (b) interacting only via the electromagnetic field. Expressions for the dispersion relations, polarisation and electric fields and the transmission coefficient are derived. Conditions under which a point dielectric equation of state holds are obtained. This simple system exhibits three resonances near the transverse optic frequency.     

On Multiple Scattering of Radiation by an Infinite Grating of Dielectric Circular Cylinders at Oblique Incidence

A rigorous analytical representation for the multiple scattering coefficients of the fields radiated by an infinite grating of dielectric circular cylinders excited by an obliquely incident plane electromagnetic wave is derived in terms of the “well-known scattering coefficients of an isolated dielectric cylinder at oblique incidence” and “Schl?milch series”. In addition, a generalized sum-integral grating equation is acquired for the multiple scattered amplitude of a cylinder at oblique incidence in the grating in terms of the scattering coefficients of the insulating dielectric circular cylinder at oblique incidence.      

Localization of Classical Waves II: Electromagnetic Waves

We consider electromagnetic waves in a medium described by a position dependent dielectric constant . We assume that is a random perturbation of a periodic function and that the periodic Maxwell operator has a gap in the spectrum, where . We prove the existence of localized waves, i.e., finite energy solutions of Maxwell's equations with the property that almost all of the wave's energy remains in a fixed bounded region of space at all times. Localization of electromagnetic waves is a consequence of Anderson localization for the self-adjoint operators . We prove that, in the random medium described by , the random operator exhibits Anderson localization inside the gap in the spectrum of . This is shown even in situations when the gap is totally filled by the spectrum of the random operator; we can prescribe random environments that ensure localization in almost the whole gap. Received: 1 July 1996 / Accepted: 15 August 1996     

On the refractive index for a nonmagnetic two-component medium: Resolution of a controversy

The refractive index of a dielectric medium comprising both passive and inverted components in its permittivity was determined using two methods: (i) in the time-domain, a finite-difference algorithm to compute the frequency-domain reflectance from reflection data for a pulsed plane wave that is normally incident on a dielectric half-space and (ii) in the frequency-domain, the deflection of an obliquely incident Gaussian beam on transmission through a dielectric slab. The dielectric medium was found to be an active medium with a negative real part for its refractive index. Thereby, a recent controversy in the scientific literature was resolved.     

Structure for localizing electromagnetic waves with a left-handed-medium slab and a conducting plane

A new structure is proposed for localizing electromagnetic waves and energies with a left-handed-medium (LHM) slab and a perfectly electrically conducting (PEC) plane. When a current source is placed in front of a perfectly matched LHM slab with negative permittivity -epsilon0 and negative permeability -mu0 and a PEC plane is placed at the image point, we show rigorously that all the electromagnetic waves are confined in a region between the source and the PEC plane, and the fields outside the region are completely zero. Such an energy-localization system would be useful in medical treatments that use concentrated optical and microwave energies. However, a perfectly matched LHM is unphysical and does not exist in nature. Hence we further study the loss and retardation effects of LHM on the energy localization. Numerical results are presented for the lossy LHM structure to demonstrate the energy localization.     

Optimal dispersion relations for enhanced electromagnetic power deposition in dissipative slabs

Broadband analysis of a prototype model associated with electromagnetic waves absorption in a lossy dielectric slab renders a closed-form theoretical prediction of an infinite number of optimal absorption paths in the complex refractive index domain. While for thin slabs (in terms of incident wavelength range) each path corresponds to a lossy Fabry-Perot-type resonance modes of order m=0,1,2,... and provides at least 50% absorption of the incident wave power even for ultrathin slabs, for optimal thick slabs, the fraction of absorbed power, asymptotically estimated via Lambert W function, increases up to 100% for consecutive continuation of the m=1 normal mode only.     

Confinement of infrared radiation to nanometer scales through metallic slit arrays

One-dimensional metallic slit array has been intensively studied in the spectral range from ultraviolet to near-infrared due to its enhanced transmission for transverse magnetic waves. However, the transmission enhancement is sensitive to the wavelength of incident radiation because of resonance characteristics. In this paper, we theoretically demonstrate that confining mid-infrared radiation to nanometer scales with a large transmission enhancement can be achieved from an aluminum slit array in a wavelength-insensitive manner, for potential applications in localized heating and nanothermal patterning. The Poynting vector and energy density calculated from the rigorous coupled-wave analysis (RCWA) are used to explain the strong localization of electromagnetic energy in the near-field regime. Furthermore, the localization of energy is also studied when a dielectric substrate is used to support the slit array in practical applications.     

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分析了电磁波以任意角度入射到有限磁场中的激光等离子体通道天线(LPCA)时的电磁散射特性。根据LPCA的工作原理建立了其电磁分析模型,推导出广义柱坐标系下各向异性磁化等离子体中纵向分量所满足的波动方程和纵向场与横向场的关系,得到LPCA和周围媒质中的电磁场,利用边界切向电磁场连续,得出了散射系数方程。通过计算实例,将结果与文献结果比较,吻合较好。该研究结果预期可应用于高功率微波武器系统的研究。     

Three-dimensional step discontinuities in planar waveguides: Angular-spectrum representation of guided wavefields and generalized matrix-operator formalism

For obliquely incident guided modes the light propagation in slab waveguides with step discontinuities can be described by means of an angular-spectrum representation of the electromagnetic fields together with a generalized matrix-operator formalism. By means of a discretization of the radiation and evanescent modes, the computation of the reflection and transmission coefficients can be reduced to the numerical solution of algebraic equations. The TE-TM coupling, which takes place for oblique incidence, and the different evanescent field effects are discussed in detail.     

Coherent backscattering of light by a layer of discrete random medium

We consider the problem of backscattering of light by a layer of discrete random medium illuminated by an obliquely incident plane electromagnetic wave. The multiply scattered reflected radiation is assumed to consist of incoherent and coherent parts, the coherent part being caused by the interference of multiply scattered waves. Formulas describing the characteristics of the reflected radiation are derived assuming that the scattering particles are spherical. The formula for the incoherent contribution reproduces the standard vector radiative transfer equation. The interference contribution is expressed in terms of a system of Fredholm integral equations with kernels containing Bessel functions. The special case of the backscattering direction is considered in detail. It is shown that the angular width of the backscattering interference peak depends on the polar angle of the incident wave and on the azimuth angle of the reflection direction.     

Simulated Output Images of Near-Field Optics by Volume Integral Equation: Object Placed on the Dielectric Substrate

We investigated near-field optical (NFO) imaging characteristics of a small object placed on a dielectric slab by a computer-code using a three-dimensional volume integral equation with an effective iteration technique called the generalized minimal residual method. A simplified three-dimensional NFO microscope that consists of a small dielectric object placed on the dielectric substrate and a small dielectric sphere as a scanning probe-tip was considered. Calculating two-dimensional output images obtained from scattered far fields, we studied the effect of the substrate on NFO output images, the comparison of NFO output images with electrostatic field around the small object, the dependence of output image characteristics on the wavelength and the difference of imaging characteristics between incident plane waves and incident evanescent waves.     

Anomalous reflection and excitation of surface waves in metamaterials

We consider reflection of electromagnetic waves from layered structures with various dielectric and magnetic properties, including metamaterials. Assuming periodic variations in the permittivity, we find that the reflection is in general anomalous. In particular, we note that the specular reflection vanishes and that the incident energy is totally reflected in the backward direction, when the conditions for resonant excitation of leaking surface waves are fulfilled.     

Electromagnetic modelling of 3D periodic structure containing magnetized or polarized ellipsoids

Coupling matrix and coupling coefficient concepts are applied to the interaction of an incident plane wave with a regular array of small magnetized or polarized ellipsoids, placed in a homogeneous surrounding medium. In general case, the angle of incidence and polarization of the plane wave upon an array of ellipsoids can be arbitrary. In this model, it is assumed that all the ellipsoids are the same, and the direction of their magnetization is also the same. The direction of magnetization is arbitrary with respect to the direction of the propagation of the incident wave and to the boundary plane between the first medium, where the incident wave comes from, and the array material under study. Any magnetized or polarized ellipsoid is represented as a system of three orthogonal elementary magnetic radiators (EMR) and/or three orthogonal elementary electric radiators (EER). Mutual interactions of individual radiators in the array through the incident plane wave and corresponding scattered electromagnetic fields are taken into account. The electrodynamic characteristics — reflection from the surface of the semi-infinite array (in particular, containing uniaxial hexagonal ferrite resonators), transmission through the array, and absorption are analyzed.     

A General Framework for Localization of Classical Waves: II. Random Media

We study localization of classical waves in random media in the general framework introduced in Part I of this work. This framework allows for two random coefficients, encompasses acoustic waves with random position dependent compressibility and mass density, elastic waves with random position dependent Lamé moduli and mass density, electromagnetic waves with random position dependent magnetic permeability and dielectric constant, and allows for anisotropy. We show exponential localization (Anderson localization) and strong Hilbert–Schmidt dynamical localization for random perturbations of periodic media with a spectral gap. This revised version was published online in July 2006 with corrections to the Cover Date.     

Controlled switching of surface waves in 1D photonic crystals by a thin nonlinear cap layer

In this paper, we investigate the electromagnetic surface waves localized at the interface of the homogeneous dielectric medium and a semi-infinite one-dimensional photonic crystal (1D PC), theoretically. The semi-infinite 1D PC is made of alternative layers of left-handed (LH) and right-handed (RH) materials in the presence of a thin nonlinear cap layer. We consider magnetic permeability and electric permittivity of LH layers being dispersive and non-dispersive. We used an analytical direct matching procedure within the Kronig-Penny model to analyze the dispersion behavior of surface waves with controllable localization. It is shown that the thin nonlinear cap layer acts as a tool to change the backward surface waves to forward ones and vice versa and it plays an important role on the localization of them. Also we show that when the LH layers are chosen dispersive, negative dispersion of surface waves are obtained in a wide range of radiation angle and frequency, and we propose an approach to calculate the applied electric field intensity that leads to switching of surface waves from backward to forward and creating a surface mode with maximum localization.