# Transfer matrix method for the analysis of space-time modulated media and systems

## TL;DR

This paper introduces a generalized transfer matrix method for analyzing wave propagation in space-time modulated media, enabling advanced control of wave phenomena like nonreciprocity and gain in various physical systems.

## Contribution

It develops a versatile framework that handles arbitrary space-time modulation profiles and complex system configurations, extending the analysis capabilities for dynamic wave systems.

## Key findings

- Enables analysis of nonreciprocal wave transport
- Supports arbitrary modulation profiles in space-time systems
- Facilitates investigation of high order modes

## Abstract

Space-time modulation adds another powerful degree of freedom to the manipulation of classical wave systems. It opens the door for complex control of wave behavior beyond the reach of stationary systems, such as nonreciprocal wave transport and realization of gain media. Here we generalize the transfer matrix method and use it to create a general framework to solve wave propagation problems in time-varying acoustic, electromagnetic, and electric circuit systems. The proposed method provides a versatile approach for the study of general space-time varying systems, which allows any number of time-modulated elements with arbitrary modulation profile, facilities the investigation of high order modes, and provides an interface between space-time modulated systems and other systems.