Poynting’s theorem for plane waves at an interface: A scattering matrix approach (original) (raw)
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Physical Review A, 2015
We present the total transmission effect of inhomogeneous electromagnetic waves between dissipative media. The total transmission of a p-polarized plane wave at the interface between two lossless dielectrics happens at the Brewster angle. However, when a dielectric-conductor interface is considered, the effect cannot be achieved and there is only a minimum, different from zero, of the reflection coefficient. We prove that, by considering an inhomogeneous plane wave, the total transmission can be obtained both at the interface between two dissipative media and at the dielectric-conductor interface.
Optical Theorems for Electromagnetic Scattering by Inhomogeneities in Layered Dielectric Media
The well-known optical theorem that relates the forward scattering amplitude to the total cross section of a scatterer in free-space, is extended to problems of scattering of an incident transverse electric (TE) plane wave or guided mode by inhomogeneities in lossless, waveguiding, dielectric interfaces or layers. The cases of a compact irregularity on either the interface between two unbounded dielectric media or in the waveguiding layer of a dielectric-slab waveguide are considered. Simple formulas that connect the scattered amplitudes of the different types of waves excited by the incident energy are derived. They can be used as an independent check of numerical codes when benchmark solutions are not available or are hard to obtain. In addition, a relationship between the scattered amplitudes and the spectral power of each excited wave is derived using the method of stationary phase.
A Transverse Electric (TE) mode of propagation having the electric field perpendicular to the interface is considered. Two media are assumed to be lossless. Phase velocities of the waves through the two media and the interface are calculated. These velocities are found to be different from the actual phase velocities in the dielectrics. The phase velocity in one dielectric is modified by the presence of another dielectric medium. The phase velocities in the two media are greater than the phase velocity of the wave along with the interface. Also, the phase velocities in the media in contact are greater than the velocities of the wave in the two media when they are separated. The wave is found to bend away from the interface in both the media. Very low loss dielectric media are practically lossless at very low frequencies. These dielectric media may be useful for Wireless Power Transmission (WPT) system. The bending property of the electromagnetic wave away from the interface and the low loss will help one to locate the receivers away from the transmitter in the WPT system. The use of very low loss dielectric media and Very Low Frequency (VLF) transmitter are suggested for efficient WPT systems.
Total transmission of electromagnetic waves at interfaces associated with an indefinite medium
Journal of The Optical Society of America B-optical Physics, 2006
We investigate the problem of total transmission at the interface separating an isotropic regular material and an indefinite medium [Phys. Rev. Lett. 90, 077405 (2003)] in which not all of the principal elements of the permeability and permittivity tensors have the same sign, for TE-and TM-polarized electromagnetic waves. We make a detailed investigation on the existence conditions of total transmission and the corresponding Brewster's angles when an electromagnetic wave is incident on the interface from an isotropic regular material. We show that the propagation characteristics of electromagnetic waves at such interfaces are quite different from those at regular interfaces. For both TE and TM waves, total transmission is possible at the interfaces containing an indefinite medium; in particular, normally incident total transmission and omnidirectional total transmission are also allowed, provided that suitable physical parameters for the two materials across the interface are chosen.
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Journal of the Optical Society of America, 2012
An overview of the problems involved in the study of electromagnetic power transmission between lossy media is presented. Starting from the well-known problem of the transmission at a dielectric-conductor interface, the different representations of the complex propagation vector of the plane waves are introduced. Analytical expressions to convert from one formulation to the other are obtained. Moreover, the transmission of a plane wave at the interface between two lossy media is taken into account. An explanation of the strange behavior of the transmitted wave is developed by means of power considerations. Finally, the interesting effect of the parallel-attenuated transmitted wave is presented, and its properties as a function of the incident phase vector amplitude are deduced.
Communications in Mathematical Sciences, 2013
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The efficient solution of electromagnetic scattering for inhomogeneous media
Journal of Computational and Applied Mathematics, 2007
We consider an electromagnetic scattering problem for inhomogeneous media. In particular, we focus on the numerical computation of the electromagnetic scattered wave generated by the interaction of an electromagnetic plane wave and an inhomogeneity in the corresponding propagation medium. This problem is studied in the VV polarization case, where some special symmetry requirements for the incident wave and for the inhomogeneity are assumed. This problem is reformulated as a Fredholm integral equation of second kind, which is discretized by a linear system having a special form. This allows to compute efficiently an approximate solution of the scattering problem by using iterative techniques for linear systems. Some numerical examples are reported.
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A new theory for scattering of electromagnetic waves from conducting or dielectric rough surfaces
IEEE Transactions on Antennas and Propagation, 1992
The problem of scattering of electromagnetic waves from a conducting or dielectric rough surface with arbitrary shape is studied. An exact solution, using a differential method, is provided for a plane wave with one-dimensional irregularity of the interface. The proposed formalism involves using the covariant form of Maxwell equations written in nonorthogonal coordinate system. This permits the analytical writing of the exact boundary conditions. The problem is reduced to the resolution of a linear system of partial differential equations with constant coefficients, and to the computation of eigenvalues and eigenvectors of truncated infinite matrix. Numerical application is made to show the angular distribution of energy density in the case of an arbitrary profile of the scattering surface and its evolution when the nonperiodic profile tends to become periodic. The near field is computed on the interface and its enhancement in the illuminated region is well observed. It increases with the height of the irregularity and with the frequency.