Nonlinear optics in novel periodic media.

Abstract

The major focus of the work in this thesis is on the solution of the electromagnetic wave equations in novel structures that exhibit nonlinearity in their response to the incident field. These structures are further characterized by the presence of a spatial periodicity in their dielectric permittivity. The presence of spatial periodicity results in a number of coherent scattering phenomena when the light wavelength is comparable to the period of this spatial perturbation. Here we use a combination of analytical and numerical methods to gain insight into these phenomena. Two problems each involving a different nonlinear phenomenon have been considered. First, we take the classical problem of hysteretic switching response exhibited by a nonlinear periodic structure. This problem is reexamined in the context of the presence of a negative refractive index (left-handed electromagnetic structure). We theoretically predict an exotic behavior that involves an omnidirectional response quite distinct from the well known behavior. We examine the field distribution in detail and propose the existence of a spatial soliton called the zero-n gap soliton. Next, we investigate the practical problem of output power scaling in fiber lasers. Self scattering nonlinearities currently set the limit on power scalability. In particular, for narrow linewidth systems, Stimulated Brillouin scattering (SBS) is known to be the limiting nonlinearity. This scattering phenomenon is a result of Bragg reflection from a periodic index modulation induced by an acoustic wave. Several novel schemes are proposed and analyzed in terms of their ability to suppress SBS and enhance power scalability.