# Perfect Broadband Invisibility in Isotropic Media with Gain and Loss

## TL;DR

This paper presents a method to design isotropic optical media that are perfectly invisible for a range of wavelengths, using a specific Fourier transform condition on the scattering potential, enabling broadband invisibility.

## Contribution

It introduces a novel approach to achieve perfect broadband invisibility in isotropic media by controlling the Fourier transform of the scattering potential.

## Key findings

- Constructed a permittivity profile for an optical slab with perfect invisibility in a specific wavenumber range.
- Established a Fourier transform condition that guarantees omnidirectional invisibility.
- Demonstrated the feasibility of designing broadband invisible media with gain and loss.

## Abstract

We outline a method for constructing effectively two-dimensional isotropic optical media that are perfectly and omnidirectionally invisible for both TE and TM waves provided that their wavenumber does not exceed a preassigned value $\alpha$. This relies on the observation that a complex scattering potential $v(x,y)$ displays perfect invisibility for wavenumbers $k\leq\alpha$ provided that its Fourier transform with respect to $y$, which we denote by $\tilde v(x,\mathfrak{K}_y)$, vanishes for $\mathfrak{K}_y\leq 2\alpha$. We use this result to construct the permittivity profile for a realistic optical slab that is perfectly invisible in the wavenumber window $[0,\alpha]$.