# Approximate cloaking for time-dependent Maxwell equations via transformation optics

## TL;DR

This paper develops an approximate cloaking method for time-dependent Maxwell equations using transformation optics, analyzing visibility across all frequencies with novel techniques in low and high frequency regimes.

## Contribution

It introduces a new approach combining variational, multiplier, and duality techniques for electromagnetic cloaking in the time domain, extending previous wave equation methods.

## Key findings

- Effective cloaking estimates across frequency spectrum
- Novel variational and multiplier techniques applied
- Enhanced understanding of cloaking in low and high frequency regimes

## Abstract

We study approximate cloaking using transformation optics for electromagnetic waves in the time domain. Our approach is based on estimates of the degree of visibility in the frequency domain for all frequencies in which the frequency dependence is explicit. The difficulty and the novelty analysis parts are in the low and high frequency regimes. To this end, we implement a variational technique in the low frequency domain, and multiplier and duality techniques in the high frequency domain. Our approach is inspired by the work of Nguyen and Vogelius on the wave equation.