Three-dimensional structures in diffractive and dispersive nonlinear ring cavities

Three-dimensional structures in nonlinear cavities containing left-handed materials.

We study the coupling between negative diffraction and direct dispersion in a nonlinear ring cavity containing slabs of Kerr nonlinear right-handed and left-handed materials. Within the mean field approximation, we show that a portion of the homogeneous response curve is affected by a three-dimensional modulational instability. We show numerically that the light distribution evolves through a s...

Design of optimized dispersive resonant cavities for nonlinear wave mixing.

Dispersive mirrors can be designed to create cavities that resonate at set multiple frequencies while simultaneously meeting the conditions for efficient nonlinear wave mixing. We analyze the conditions that such a cavity design must meet and the free parameters that can be used for optimization. Using numerical methods, we show the benefit in conversion efficiency attained with multiple resona...

Dynamic Analysis of Three Dimensional Asymmetric Isolated Structures

Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions.

We discuss the linear dispersive properties of finite one-dimensional photonic band-gap structures. We introduce the concept of a complex effective index for structures of finite length, derived from a generalized dispersion equation that identically satisfies the Kramers-Kronig relations. We then address the conditions necessary for optimal, phase-matched, resonant second harmonic generation. ...

Embedded cavities and waveguides in three-dimensional silicon photonic crystals