Propagation phenomena in a multilayer waveguide

摘要

Periodic structures play an important role in integrated optics. The main purpose of this paper is to study electromagnetie radiation propagating in a one-dimensional periodic dielectric waveguide; or equivalently, in a simple multilayer waveguide. Since periodic dielectrics are photonic crystals, it is beneficial to study their symmetry and periodicity first: inversion, translation, rotation, mirror reflection and time-reversal symmetries; dispersion relations and their behaviour of band-pass filters. These principles help us in understanding the propagation of light modes in a periodic layered medium. This simple system exhibits interesting phenomena: photonic band-gaps, localized modes at defects, surface states and omnidirectional reflection, that appear in many optical components, such as diffraction gratings, distributed-feedback lasers, optical waveguides and optical filters, When the periodic dielectric medium is bounded, it becomes a waveguide and light modes that propagate within become guided modes. Some general and fundamental properties of dielectric waveguide modes are briefly described. Then, by treating the periodic dielectric waveguide as a dielectric perturbed waveguide, propagation of electromagnetic radiation within may be described using the method of variation of constants approach, which formu-lates the coupled-mode theory. For significant mode coupling, the Bragg reflection type is studied. Finally, more complicated multilayer waveguide structures are briefly mentioned.