Improved transfer matrix method without numerical instability

TL;DR

This paper introduces an improved transfer matrix method that eliminates numerical instability and enhances scalability, offering faster computation compared to the scattering matrix method without additional computational cost.

Contribution

The paper presents a novel transfer matrix method that overcomes numerical instability and improves scalability without increasing computational time.

Findings

The new TMM is free from numerical instability.

It significantly outperforms the scattering matrix method in speed.

The method maintains computational efficiency for large homogeneous regions.

Abstract

A new improved transfer matrix method (TMM) is presented. It is shown that the method not only overcomes the numerical instability found in the original TMM, but also greatly improves the scalability of computation. The new improved TMM has no extra cost of computing time as the length of homogeneous scattering region becomes large. The comparison between the scattering matrix method(SMM) and our new TMM is given. It clearly shows that our new method is much faster than SMM.