Classical treatment of evanescent electromagnetic fields interacting with an amplifying or attenuating medium upon total internal reflection

The present study deals with total internal reflection of a plane electromagnetic wave at an infinite plane boundary between a transparent medium and an amplifying or attenuating lower-index medium. Solutions of Maxwell’s equations are sought with the effect of gain or loss taken into account by means of the effective indices of refraction and extinction associated with the real angles representing the directions of propagation and amplitude change. Analytical expressions are found for the reflection coefficients and the refracted electric and magnetic fields, which describe the amplification or attenuation of the evanescent field resulting from the interaction with the totally reflecting medium