# Zero reflection and transmission in graded index media

## TL;DR

This paper explores graded index media satisfying Kramers-Kronig relations that are not only reflectionless but can also have negligible transmission, enabling maximal wave absorption through pole manipulation.

## Contribution

It introduces a method to control and minimize wave transmission in graded index media by tuning complex poles, extending the understanding of wave behavior in such materials.

## Key findings

- Media can be made reflectionless for all angles.
- Transmission can be tuned to be arbitrarily small.
- Numerical simulations confirm the theoretical control of transmission.

## Abstract

Graded index media whose electric susceptibility satisfies the spatial Kramers-Kronig relations are known to be one-way reflectionless to electromagnetic radiation, for all angles of incidence. We demonstrate how a family of these media, in addition to being reflectionless, also have negligible transmission. To this end, we discuss how the transmission coefficient for the propagation of waves through a medium whose permittivity is built from poles in the complex position plane, with residues that sum to infinity, can be controlled by tuning the positions and residues of the poles. In particular, we have shown how to make the transmission arbitrarily small, and hence maximise the absorption of the wave's energy. This behaviour is confirmed by numerical simulations.