A Photonic Crystal Slab Laplace Differentiator

Abstract

We introduce an implementation of a Laplace differentiator based on a photonic crystal slab that operates at transmission mode. We show that the Laplace differentiator can be implemented provided that the guided resonances near the Γ point exhibit an isotropic band structure. Such a device may facilitate nanophotonics-based optical analog computing for image processing.This document provides supplementary information to "A Photonic Crystal Slab Laplace Differentiator". This supplementary document consists of four sections. In Section 1, we derive the effective Hamiltonian near the Γ point, when the states are two-fold degenerate at the Γ point. In Section 2 we provide numerical validation of the effective Hamiltonian. In Section 3, we calculate the transmission for an arbitrary polarized state from the transmission response for S and P polarized light. In Section 4, we plot the transmittance |t| in a larger wavevector region for the device configuration that operates as a differentiator. Such information on transmittance is used in demonstrating the performance of the differentiator.