Wave propagation in the presence of a dielectric slab: The paraxial approximation (original) (raw)
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Nonlinear waves guided by a dielectric slab
Applied Physics B Photophysics and Laser Chemistry, 1983
We consider dispersion relations and field structure of TE-polarized guided waves travelling along an asymmetric dielectric slab surrounded by two different nonlinear media. For a given configuration there are four types of guided waves. Three of this four types possess at least one field maximum outside the slab region and have no counterpart in linear waveguide optics. The solutions of the dispersion relations depend now on an additional parameter making them more flexible with respect to the linear limit.
Transient electromagnetic fields in a lossy dielectric slab
Applied Scientific Research, 1982
The problem of the determination of transient fields in a lossy dielectric slab, irradiated by an electromagnetic plane wave, is solved by analytical evaluation of the inverse Laplace transform of the step response. The response to a modulated step is also considered. Numerical examples are given having in mind applications to the microwave heating of biological bodies.
Dielectric slab reflection/transmission as a self-consistent radiation phenomenon
arXiv: Classical Physics, 2018
We revisit the electromagnetic problem of wave incidence upon a uniform, dissipative dielectric slab of finite thickness. While this problem is easily solved via interface field continuity, we treat it under the viewpoint of radiative self-consistency, with interior current sources gauged by ohmic/polarization comparisons against those of the exterior medium. Radiative self-consistency yields an integral equation over the slab field giving a fully constructive buildup of the reflected/transmitted contributions, without any need for implicit determination via boundary conditions. Solution steps lead to an exact cancellation of the interior field, and bring in still other contributions of a reference medium variety, required to balance the incoming excitation. Such balancing provides the linear conditions for slab field determination. This two-step solution provides evidence of Ewald-Oseen extinction, even though the analytic framework here differs from the proofs available. We solve ...
Electromagnetic field in an active slab: conditions for spontaneous oscillation
Journal of Physics: Conference Series, 2015
In this work we analyze the conditions for the propagation of plane waves emitted spontaneously within an active slab of width d and complex relative permittivity ߝ̃. The slab is immersed in transparent, semi-infinite media of relative permittivities ε a and ε c , respectively, without external field sourcesexcept, of course, the power source used for pumping the active medium in the slab. It is well known that, if there is enough gain in the active medium, it may sustain the so-called spontaneous electromagnetic field. For many applications it is important to avoid this condition.
EM Pulse Transit across a Uniform Dielectric Slab
2007 Workshop on Computational Electromagnetics in Time-Domain, 2007
A fully time dependent electromagnetic field solution describing the transit of a flat pulse of width c T across a uniform dielectric sandwich is obtained herein by use of a Green's function technique in the Laplace transform domain. Once the ensuing integral equation has been solved self-consistently within the dielectric sheet, the remainder of field evolution on its exterior follows constructively without any need to cope with boundary conditions or any sort of temporal sequencing on internal pulse bounces. Transform inversion into the temporal plane, relying on a simple development into geometric series at the appropriate steps of analysis, reveals transmitted/reflected pulse trains composed of whole retinues of secondary echo pulses suitably arranged in time and diminished by ascending powers of in/out reflection coefficients. A transcription into computer code verifies that electromagnetic energy content in the transmitted/reflected pulse trains properly sums into that of the impinging pulse, and yields a graphical depiction of the individual, fore/aft pulse trains. Additional work, elsewhere reported, goes on finally to generalize the uniform pulse solution so as to embrace a slab excitation that is profiled [read "carrier modulated by an amplitude/phase signal"] in response to a magnetic amplitude h( τ ) extended across a temporal support of width τ = T past the point of first contact.
IEEE Transactions on Antennas and Propagation, 2000
The problem of diffraction at the edge of a semi-infinite grounded dielectric slab excited by a line source is investigated. This canonical problem may be used as a reference solution in the high-frequency regime for patch antennas radiating from a finite grounded slab. Both physical optics (PO) and integral equation (IE) approaches are used and compared. The PO formulation is cast in a convenient asymptotic form that neatly describes the diffraction processes associated with the various wave species. The IE, solved by the method of moments, is formulated by enforcing the continuity of the electric field on an infinite aperture orthogonal to the slab. This allows a drastic reduction of unknowns, provided that appropriate entire domain basis functions are used that are shaped to match the asymptotic behavior of the aperture field. Comparison between the PO and IE solutions is presented to determine the range of validity of PO.
Electromagnetic wave propagation through inhomogeneous material layers
2013
We use Maxwell's equations in a sourceless, inhomogeneous medium with continuous permeability μ (r) and permittivity (r) to study the wave propagation. The general form of the wave equation is derived and by virtue of some physical assumptions, including μ and ϵ as functions of z, the equation has been simplified. Finally by introducing a smooth step dielectric variable we solve the wave equation in the corresponding medium which is in conform with the well known results. Exact double-layer solution in analytic form has been given in terms of the Heun functions.
Electromagnetic waves dynamics in a nonlinear dielectric slab by the method of characteristics
Electrical Engineering, 1997
Contents Electromagnetic shock waves are a relatively unexplored field. This paper considers their propagation in the case of a dielectric slab. At first we examine the mathematical problem relating to the physical interpretation of the uniqueness of the solution. A link between uniqueness and irreversibility is pointed out as in the case of shock waves in gasdynamics. Then we illustrate an algorithm, based on the concept of characteristics curves, which gives a very interesting performance.
The wave hierarchy for propagation in relaxing dielectrics
We consider the propagation of arbitrary electromagnetic pulses in anomalously dispersive dielectrics characterized by M relaxation processes. A partial differential equation for the electric field in the dielectric is derived and analyzed. This single equation describes a hierarchy of M + 1 wave types, each type characterized by an attenuation coefficient and a wave speed. Our analysis identifies a "skin-depth" where the pulse response is described by a telegrapher's equation with smoothing terms, travels with the wavefront speed, and decays exponentially. Past this shallow depth we show that the pulse response is described by a weakly dispersive advection-diffusion equation, travels with the sub-characteristic advection speed equal to the zero-frequency phase velocity in the dielectric, and decays algebraically. The analysis is verified with a numerical simulation. The relevance of our results to the development of numerical methods for such problems is discussed.