Visible light Laue diffraction from woodpile photonic crystals

Abstract

Bragg diffraction is often used as a tool to assess the structural quality of two-dimensional and three-dimensional (3D) photonic crystals. However, direct conclusions from the Laue diagrams to the underlying crystals structure cannot be drawn, as multiple scattering due to the high index contrast takes place. Here we systematically study the scattering of visible light by 3D woodpile photonic crystals with varying internal refractive index contrast Δn, to determine the limits of the single (kinematic) scattering approach. We aim to describe the intensity distribution of diffracting Bragg peaks with analytic expressions similarly to x-ray scattering at electronic crystals. Measured scattering curves of selected Bragg reflections are classified in terms of Δn. We find that the kinematic approach describes the shape and intensity distribution of experimental scattering curves in acceptable accuracy as long as Δn<0.15. The transition between single and multiple scattering is observed for Δn≈0.16-0.25 before multiple scattering dominates for larger Δn. The classification of the scattering regimes is confirmed by simulations in terms of numerical solution of Maxwell's equations.