Spatial differentiation and integration of optical beams in a slab waveguide by a single dielectric ridge

TL;DR

This paper demonstrates that a simple dielectric ridge on a slab waveguide can perform optical beam differentiation and integration in transmission and reflection, respectively, enabling ultrafast all-optical signal processing.

Contribution

The study introduces a novel, simple dielectric ridge structure that achieves spatial differentiation and integration of optical beams without parasitic effects, confirmed by rigorous numerical simulations.

Findings

High-quality differentiation and integration achieved

Resonant excitation of cross-polarized eigenmode is key

Tradeoff between resonance quality factor and operation quality

Abstract

We show that a very simple structure consisting of a single subwavelength dielectric ridge on the surface of a slab waveguide enables spatial differentiation and integration of the profile of optical beams propagating in the waveguide. The differentiation and integration operations are performed in transmission and in reflection, respectively, at oblique incidence of the beam impinging on the ridge. The implementation of these operations is associated with the resonant excitation of a cross-polarized eigenmode of the ridge. At the considered parameters of the structure and incidence geometry, neither "parasitic" out-of-plane scattering nor polarization conversion occurs. The presented rigorous numerical simulation results confirm high-quality differentiation and integration. We demonstrate that by choosing the quality factor of the resonance, one can achieve the required tradeoff between the differentiation (or integration) quality and the amplitude of the resulting beam. The proposed integrated structure may find application in ultrafast all-optical analog computing and signal processing systems.