Kerr nonlinear layered photonic crystal coatings

Abstract

Theoretical studies are presented of the electromagnetic fields in one dimensional photonic crystal coatings deposited on interfaces and mirrors. The coatings are finite photonic crystal arrays of a Kerr nonlinear dielectric medium alternating with a linear dielectric medium and exhibit a series of electromagnetic transmission pass and stop frequency bands. The pass and stop bands are related to the underlying photonic crystal structure of the coatings. Within the coatings high field intensities occur in the pass bands and low field intensities occur in the stop bands. In addition, certain high field intensity excitations arising solely from the Kerr nonlinearity occur at certain stop band frequencies. The origins and nature of these stop band excitations are discussed and the enhanced fields associated with them are studied with regards to the Kerr nonlinearity. A mapping is presented of the nature of the excitations generated in the coating within the parameter space of the linear and nonlinear components of the Kerr media dielectric. The field enhancements of the stop band excitations are studied and the optimum conditions for field enhancement within a coating determined. The nature of the wave functions of the modes excited within the stop bands is studied as a function of the stop band frequency intervals in which they occur. Discussions are made of the significance of these results to field enhancement due to nonlinearity, surface enhanced Raman spectroscopy, and in the generation of second harmonics at mirror surfaces and interfaces.