The reflectivity of a single-channel waveguide mode upon resonantly coupling to a Kerr-active nonlinear resonant cavity is calculated analytically, including the effects of two-photon absorption. The resonant reflectivity takes the form of a Fano resonance because the solution includes linear reflections from perturbations downstream of the localized cavity. Instead of using a Hamiltonian formulation of the scattering problem, an intuitive set of basis states is used to expand the Green's function of the electric field wave equation. All resulting overlap functions describing the linear coupling between guided and localized states, and the nonlinear renormalization of the material's refractive index, are in terms of well-defined physical quantities. Although derived in the context of photonic crystal-based waveguides and cavities, the treatment is valid for any low-loss waveguide-resonator geometry that satisfies specific weak coupling criteria. For a cavity consisting of Al0.18Ga0.82As, hosting a localized mode at 1.55 microm with a Q of 4000 and a mode volume of 0.055 microm(3), we predict the onset of bistable reflection at incident powers of approximately 40 mW. The downstream reflections lead to hysteresis loops in the reflectivity that are topologically distinct from conventional Lorentzian-derived loops characteristic of isolated Fabry-Perot cavities. We provide a stability argument that reveals the unstable branches of these unique hysteresis loops, and we illustrate some of the rich bistable behaviors that can be engineered with such downstream sources.

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The real and imaginary photonic band structure of modes attached to two-dimensionally textured semiconductor membranes is determined experimentally and theoretically. These porous waveguides exhibit large ͑1000 cm Ϫ1 at 9500 cm Ϫ1 ) second-order optical gaps, highly dispersive lifetimes, and bands with well-defined polarization along directions of high symmetry.

Strongly enhanced second-harmonic generation is observed from a two-dimensional square lattice GaAs/AlGaAs photonic crystal waveguide when the fundamental beam, the second-harmonic beam, or both beams resonantly couple to a leaky eigenmode. P-polarized second-harmonic spectra are obtained for s-polarized, 150-fs pump pulses that are tuned from 5000 to 5600 cm(-1) and directed along the gamma-chi direction of the crystal for various angles of incidence. Compared with off-resonant conditions, enhancements of >1200x in the second-harmonic conversion are observed for resonant coupling of both the fundamental and the second-harmonic fields to leaky eigenmnodes. The angular and spectral positions of the peaks are in good agreement with simulations.

An 80 MHz pulse train of ~ 100 fs optical pulses centred at ~ 1.5 microm is propagated through a variety of high-index-contrast silicon-on-insulator waveguide structures less than 1 mm long. All-optical power limiting and negative differential transmission, based only on the intrinsic nonlinear response of the untextured waveguides near 1.5 microm, are demonstrated for average in-guide power levels of ~ 1 mW. Superlinear transmission is observed in a textured silicon waveguide for power levels less than 20 microW.