# Spatial Integration by a Dielectric Slab Waveguide and its Planar Graphene-based Counterpart

## TL;DR

This paper introduces a novel spatial integrator using dielectric slab waveguides and their graphene-based counterparts, enabling reconfigurable, miniaturized, and ultrafast analog computing applications.

## Contribution

It presents the first implementation of spatial integration using dielectric slab waveguides and extends it to a graphene-based, reconfigurable, and compact design.

## Key findings

- Dielectric slab waveguide transmission coefficient matches Green's function for first order integration.
- Graphene-based integrator is reconfigurable and highly miniaturized.
- Potential for ultrafast analog computation and signal processing.

## Abstract

Motivated by the recent progress in analog computing [Science 343, 160 (2014)], a new approach to perform spatial integration is presented using a dielectric slab waveguide. Our approach is indeed based on the fact that the transmission coefficient of a simple dielectric slab waveguide at its mode excitation angle matches the Green's function of first order integration. Inspired by the mentioned dielectric-based integrator, we further demonstrate its graphene-based counterpart. The latter is not only reconfigurable but also highly miniaturized in contrast to the previously reported designs [Opt. Commun. 338, 457 (2015)]. Such integrators have the potential to be used in ultrafast analog computation and signal processing.