An Electromagnetic Formulation for Treating Optical Reflections From Graded-Material Surfaces (Classic Reprint) - Tapa blanda

Sinopsis

Excerpt from An Electromagnetic Formulation for Treating Optical Reflections From Graded-Material Surfaces

Exact solutions of Maxwell's equations, in terms of well-known functions, are available for only a few simple depth-dependent material geometries. In those cases the complex reflection coefficient is deter mined by solving Maxwell's equations for the fields within the inhomogeneous region, applying boundary conditions to match the interior fields with the exterior plane wave fields, and finally forming the ratio of the appropriate components of the incident and reflected plane wave fields. This procedure may not be easy or practicable to perform. Fortunately, the theory can be reformulated to provide the reflection coefficient directly as the solution of an ordinary differential equation, and thereby completely circumvent the field solutions. This approach is particularly convenient when the material properties are numerically specified.

In the present formulation the entire space -00 z co) is filled with a medium whose properties are permitted to vany with coordinate 2 (fig. L). For sufficiently negative 2 the (exterior) medium is homogeneous and supports the incident and reflected plane waves. In the vicinity of z O the medium undergoes a transition which eventually develops, for sufficiently positive 2, into a second homogeneous region. The latter, representing the uniform interior of the medium, supports the transmitted plane wave. For the sake of generality both the permittivity (e) and the permeability (u) are treated as arbitrary, independent functions which for large positive and negative values of z approach constant values. Losses are included by treating the permittivity and permeability functions as complex entities in the frequency domain.

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