Omar R. Asfar

The Application of the Method of Multiple Scales to Wave Propagation in Periodic Structures

A brief review of recent advances in the field of wave propagation in periodic structures is made. The review focuses on the application of, the method of multiple scales to a class of problems in closed- and open-acoustic and electromagnetic. waveguides. The examples considered are concerned with simple periodic perturbations with one example on multiperiodic perturbations. The treatment is confined to first-order perturbation theory in order to simplify the algebra.

Parallel-plate waveguide with sinusoidally perturbed boundaries

The method of multiple scales is used to obtain a uniformly valid asymptotic expansion for the propagation of TM modes on a parallel‐plate waveguide with perfectly conducting boundary surfaces that are sinusoidally perturbed in the direction of propagation. The analysis shows that resonance occurs whenever the wave number of the wall distortion function is equal to the difference between the wave numbers of two propagating modes. It is further shown that the generated mode is the same order of magnitude as the excited mode due to resonance and that energy is continuously exchanged between the two modes as they propagate down the guide.

Circular Waveguide with Sinusoidally Perturbed Walls

Uniform second-order asymptotic expansions are obtained for the propagation of TM waves in a perfectly conducting circular waveguide with sinusoidally perturbed walls using the method of multiple scales. The analysis concerns the interaction of two propagating modes satisfying the resonance condition imposed by the periodicity of the waveguide walls. Two cases of resonance are treated as well as the case of decoupled modes. In the first case resonance occurs whenever the difference between the wavenumbers of the two interacting modes is nearly equal to the wall wavenumber, while in the second case the difference is nearly equal to twice the wall wavenumber. The results of the theory are then applied to the design of a mode coupler.

A method for calculating the stability of boundary layers

Abstract A variable-step method is developed for the calculation of the two- and three-dimensional stability of compressible and incompressible two-dimensional boundary layers. The proposed method is compared with the computer code SUPORT and a finite-difference method. It is more efficient and requires less computer storage than both of these methods.

Mechanical-wave filtering in a periodically corrugated elastic plate

The method of multiple scales is employed to analyze the interaction of SH modes in an elastic plate having periodically corrugated outerfaces. Two types of resonant conditions leading to two-mode as well as four-mode interactions are considered. The results of the analysis are utilized to develop ultrasonic mechanical wave filters operating on frequency bands centered at the resonant frequency. The stop-band filter frequency response is presented in terms of the power reflection coefficient. The characteristics of reflection of these filters are enhanced by imposing amplitude taper on the periodic corrugations.

Riemann-Green function solution of transient electromagnetic plane waves in lossy media

B. Riemanns (1953) solution of the Cauchy problem for the linear wave equation is used to find a closed-form solution for the problem of transient nonsinusoidal waves is lossy media. A method for finding the required Riemann-Green function is discussed. The evolution of a wavefront propagating in a semi-infinite lossy medium is studied, and a series solution for the corresponding electric field is obtained. >

Calculation of Filter Response of a Dielectric Slab Waveguide Having Multiperiodic Interface Corrugations via the Fundamental Matrix Method

The coupled-mode equations of six interacting modes in a dielectric slab waveguide having weak spatially-modulated multiperiodic interface corrugations are derived via the perturbation method of multiple scales and then solved numerically by means of a novel numerical method for two-point boundary-value problems. This numerical method is particularly useful for stiff systems of differential equations which is characteristic of mode coupling in a multiperiodic guide. The power reflection coefficient of a filter section is calculated for the cases of constant amplitude, tapered and chirped corrugations when conditions of simultaneous resonance are nearly satisfied. The method is also applied to a thin film having aperiodic refractive index perturbations and shown to be more efficient when compared with other numerical methods.

Coupled-mode analysis of Love waves in a filter film with periodically corrugated surfaces

Mode coupling of Love waves in an orthotropic thin film having periodically corrugated surfaces over an isotropic elastic half space is considered. Six modes are coupled by both surfaces by means of three simultaneous resonant conditions. On the basis of the weakness of the corrugations, the method of multiple scales is used to derive the coupled-mode equations. These equations together with relevant boundary conditions form a two-point boundary-value problem, which is solved numerically. The filter frequency response of a corrugated film designed as a stop-band filter is calculated. Enhanced filter characteristics are achieved when tapered corrugations are imposed. A narrow pass-band filter is also designed. Its high quality factor presents the fascinating features that might be realized by including the periodic corrugations in the design of SAW devices.<<ETX>>

Torsional mode coupling and filtering in a composite waveguide with multiperiodic interface corrugations

This study is concerned with the interaction of six torsional modes in a composite axisymmetric waveguide whose interfaces are sinusoidally corrugated in the axial direction. The modes are interacting when two resonant conditions on the codirectional modes and a Bragg condition occur simultaneously. In light of the weakness of the interface corrugations, the perturbation method of multiple scales is used to derive the mode coupling equations. A novel numerical scheme for two‐point boundary‐value problems is used to solve the coupled amplitude equations. The power reflection coefficient of a filter section is then calculated for the cases of uniform, tapered, and chirped corrugations. An optimal filter is realized by combining both taper and chirp thus producing a nearly ideal characteristics.

An analytical solution of the nonlinear eddy-current losses in ferromagnetic materials

The present analysis is concerned with the determination of the electromagnetic field and losses in a cylinder of ferromagnetic material. The method consists of finding a linear solution for the diffusion equation governing the H field and then applying the method of variation of parameters to take the nonlinearity into account. The application of the method of averaging reduces the problem to the solution of two first-order ordinary differential equations governing the amplitude and phase variations with depth. The equation governing the averaged phase is readily integrable, while that governing the averaged amplitude is integrated numerically. The results are in excellent agreement with experimental data and with finite-difference numerical solutions.