A new look at evanescent waves

A new theory has recently been developed whereby local inhomogeneous plane wave fields of the form A(r) exp[ikS(r)], with A and S complex, are tracked in a manner analogous to that employed for local homogeneous plane wave (geometric optical) fields with real A and S. After a review of the theory, the present discussion involves application to evanescent fields exterior to curved dielectric layers supporting trapped modes. By this method, the propagating mode fields inside the layer are used to furnish fields at the layer boundaries, which serve as initial values for the tracking of weakly evanescent fields in the exterior region. The tracking proceeds by first determining the « phase paths » and phase fronts of the evanescent field and therefrom, by suitable integration along such paths, the complex phase S and the complex amplitude A. The degree of evanescence of the field is intimately connected with the configuration of phase paths and phase fronts which thus provide physical insights similar to those gained from ray diagrams for non-evanescent waves. Because the fields are tracked locally, the method has considerable versatility in dealing with perturbations, scattering, etc., of evanescent waves.