A Diffractive Study of Parametric Process in Nonlinear Photonic Crystals

TL;DR

This paper extends X-ray diffraction theory to describe phase-matched parametric processes in nonlinear photonic crystals, revealing diffraction mechanisms and structural factors influencing these processes in 1D and 2D NLPC.

Contribution

It introduces a modified Ewald construction for NLPC, analyzing virtual wave diffraction and phase-matching in 1D and 2D structures with new rules for multiple resonances.

Findings

1D NLPC favors single parametric processes over 2D NLPC.

Structural parameters and atom size influence virtual wave diffraction.

A general rule for multiple phase-matching resonances in 1D NLPC is established.

Abstract

We report a general description of quasi-phase-matched parametric process in nonlinear photonic crystals (NLPC) by extending the conventional X-ray diffraction theory in solids. Under the virtual wave approximation, phase-matching resonance is equivalent to the diffraction of the scattered virtual wave. Hence a modified NLPC Ewald construction can be built up, which illustrates the nature of the accident for the diffraction of the virtual wave in NLPC and further reveals the complete set of diffractions of the virtual wave for both of the air-dielectric and dielectric-dielectric contacts. We show the two basic linear sequences, the anti-stacking and para-stacking linear sequences, in one-dimension (1D) NLPC and present a general rule for multiple phase-matching resonances in 1D NLPC. The parameters affecting the NLPC structure factor are investigated, which indicate that not only the Ewald construction but also the relative NLPC atom size together determine whether a diffraction of the virtual wave can occur in 2D NLPC. The results also show that 1D NLPC is a better choice than 2D NLPC for a single parametric process.