Abstract

A planar waveguide with either or both of its boundaries periodically corrugated can support Floquet–Bloch (F–B) waves, i.e., waves consisting of an infinite number of spatial harmonics. These waves can be either guided or leaky depending on the grating period. When the propagation direction of a F–B wave is collinear to the grating vector (the normal-incidence case), its polarization is either purely TE or purely TM. When the propagation direction is not collinear to the grating vector (the oblique-incidence case), the polarization of the F–B wave is more complicated. In the past, the polarization of the F–B waves and the associated polarization phenomena (mode coupling and radiation) in the oblique-incidence case have been described almost exclusively in terms of the TE (or s) and TM (or p) components and the conversions between these two components. Such a description is incomplete because it ignores the phase difference between the two components that is necessary for the full description of the elliptically polarized wave. While this partial description may suffice in some instances, such as the coupling between two guided waves, it is inadequate in other instances, such as the coupling from a guided mode to a radiation mode. This paper presents a full description of the polarization states of the dominant spatial harmonics of the F–B waves supported by a periodic waveguide. Both the coupling between a guided mode and a radiation mode and the coupling between two guided waves in the vicinity of the stop bands are considered.

© 1992 Optical Society of America