# Efficient Analysis of Confined Guided Modes in Phoxonic Crystal Slabs

## TL;DR

This paper introduces an improved plane wave expansion method for analyzing confined guided modes in phoxonic crystal slabs, overcoming convergence issues of standard methods and enabling efficient, accurate mode calculations for practical photonic and phononic devices.

## Contribution

The authors propose a modified PWE method that uses eigenmodes of an unstructured slab for better convergence and accuracy in analyzing phoxonic crystal slabs.

## Key findings

- The new method is faster and more accurate than conventional PWE.
- It effectively estimates confined propagating modes in phoxonic slabs.
- Application to a non-reciprocal photonic device demonstrates practical utility.

## Abstract

Today's standard fabrication processes are just capable of manufacturing slab of photonic and phononic crystals, so an efficient method for analysis of these crystals is indispensable. Plane wave expansion (PWE) as a widely used method in studying photonic and phononic (phoxonic) crystals in full three dimensions is not suitable for slab analysis in its standard form, because of convergence and stability issues. Here, we propose a modification to this method which overcomes these limitations. This improved method can be utilized for calculation of both photonic and phononic modes in phoxonic slabs. While in the standard three-dimensional PWE, Fourier series are used to estimate the field dependence across the normal component of the slab, we expand the fields across the third dimension using eigenmodes of a plain unstructured slab. Despite its approximate nature, this approach is observed to be both much faster and more accurate than the conventional PWE method and can give a very accurate estimation of confined propagating modes. As an application example of the proposed method we investigate a non-reciprocal photonic device. This device is a phoxonic slab waveguide which changes modes of optical waves by elastic waves and can be used as an optical insulator or mode converter.