# Application of transfer matrix and transfer function analysis to grating-type dielectric laser accelerators: ponderomotive focusing of electrons

## TL;DR

This paper evaluates the applicability of transfer matrix methods to dielectric laser accelerators and introduces a transfer function approach for better modeling of electron dynamics, including a phase-independent focusing structure.

## Contribution

It demonstrates the limitations of transfer matrices for DLA and proposes a transfer function framework, along with a novel phase-independent focusing design.

## Key findings

- Transfer matrices are insufficient for describing DLA electron dynamics.
- Transfer functions provide a more general and effective modeling tool.
- A new focusing structure works for all electron phases.

## Abstract

The question of suitability of transfer matrix description of electrons traversing grating-type dielectric laser acceleration (DLA) structures is addressed. It is shown that although matrix considerations lead to interesting insights, the basic transfer properties of DLA cells cannot be described by a matrix. A more general notion of a transfer function is shown to be a simple and useful tool for formulating problems of particle dynamics in DLA. As an example, a focusing structure is proposed which works simultaneously for all electron phases.