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. The combination of enhanced density of modes, field localization, and exact phase matching near the band edge conspire to yield conversion efficiencies orders of magnitude higher than quasi-phase-matched structures of similar lengths. We also discuss an unusual and interesting effect: counterpropagating waves can simultaneously travel with different phase velocities, pointing to the existence of two dispersion relations for structures of finite length.
The anomalous transmission properties of zero-permittivity ultranarrow channels are used to boost Kerr nonlinearities and achieve switching and bistable response for moderate optical intensities. Strong field enhancement, uniform all along the channel, is a typical feature of ε-near-zero supercoupling and is shown to be particularly suited to enhance nonlinear effects. This is obtained by designing narrow apertures at cutoff in a plasmonic screen. We show that this nonlinear mechanism can significantly outperform nonlinearities in traditional Fabry-Pérot resonant gratings.
Extraordinary optical transmission through metallic gratings is a well established effect based on the collective resonance of corrugated screens. Being based on plasmonic resonances, its bandwidth is inherently narrow, in particular, for thick screens and narrow apertures. We introduce here a different mechanism to achieve total transmission through an otherwise opaque screen, based on an ultrabroadband tunneling that can span from dc to the visible range at a given incidence angle. This phenomenon effectively represents the equivalent of Brewster transmission for plasmonic and opaque screens.
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