Some Equations of Non-geometrical Optics

Abstract

Suppose an isotropic, non-conducting, non-dissipative medium and a monochromatic electromagnetic field interact in the absence of electric charges. Let n and v denote the refractive index and the wave number, respectively. Here n is a scalar real-valued field, whose reciprocal is proportional to the relevant velocity of propagation through the medium, and v is a large positive parameter, whose reciprocal is proportional to the length of waves involved. The following Helmholtz equation

is an archetype of those partial differential equations that ensue from the Maxwell system and model the affair mathematically. A distinctive feature of (1) is itsstiffness -the order of magnitude of v is significantly greater than that of the other coefficients involved.