Solving dielectric and plasmonic waveguide dispersion relations with a pocket calculator

TL;DR

This paper introduces a simple, robust iterative method for solving complex dispersion equations in integrated optics, suitable for multilayer dielectric and plasmonic waveguides, and easily implementable on a pocket calculator.

Contribution

The authors develop a new iterative algorithm that simplifies solving complex dispersion relations, reducing sensitivity to initial guesses and enabling easy implementation on basic devices.

Findings

Effective for multilayer dielectric and plasmonic waveguides

Handles complex and leaky structures without extra complexity

Can be implemented on a pocket calculator

Abstract

We present a robust iterative technique for solving complex transcendental dispersion equations routinely encountered in integrated optics. Our method especially befits the multilayer dielectric and plasmonic waveguides forming the basis structures for a host of contemporary nanophotonic devices. The solution algorithm ports seamlessly from the real to the complex domain--i.e., no extra complexity results when dealing with leaky structures or those with material/metal loss. Unlike several existing numerical approaches, our algorithm exhibits markedly-reduced sensitivity to the initial guess and allows for straightforward implementation on a pocket calculator.