Reflection and transmission coefficients in plane-parallel layers with refractive-index mismatch

1992 ◽  
Vol 31 (1) ◽  
pp. 106 ◽  
Author(s):  
Leonard I. Grossweiner ◽  
James L. Karagiannes ◽  
Linda Ramball Jones ◽  
Porter W. Johnson
1965 ◽  
Vol 43 (5) ◽  
pp. 921-934 ◽  
Author(s):  
R. Burman ◽  
R. N. Gould

Epstein (1930) and Rawer (1939) studied the reflection of waves in a stratified medium by transforming the hypergeometric equation into the wave equation. A particular case of the Epstein profile is a symmetrical layer. Considerable attention has been given in the literature to this case as well as to symmetrical layers with certain other profiles of the refractive index. In the present paper a generalized Epstein profile is considered and the reflection and transmission coefficients are obtained. The special case in which the refractive index tends to the same constant value on either side of a layer is then discussed. The symmetrical Epstein profile is a special case of this layer which, in general, is asymmetrical. Particular attention is given to a layer differing only slightly from the symmetrical Epstein layer, a simple approximate formula for the reflection coefficient being derived.


2008 ◽  
Vol 130 (3) ◽  
Author(s):  
J. Y. Chen ◽  
H. L. Chen ◽  
E. Pan

Reflection and transmission coefficients of plane waves with oblique incidence to a multilayered system of piezomagnetic and/or piezoelectric materials are investigated in this paper. The general Christoffel equation is derived from the coupled constitutive and balance equations, which is further employed to solve the elastic displacements and electric and magnetic potentials. Based on these solutions, the reflection and transmission coefficients in the corresponding layered structures are subsequently obtained by virtue of the propagator matrix method. Two layered examples are selected to verify and illustrate our solutions. One is the purely elastic layered system composed of aluminum and organic glass materials. The other layered system is composed of the novel magnetoelectroelastic material and the organic glass. Numerical results are presented to demonstrate the variation of the reflection and transmission coefficients with different incident angles, frequencies, and boundary conditions, which could be useful to nondestructive evaluation of this novel material structure based on wave propagations.


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