# Invisibility on demand based on a generalized Hilbert transform

## TL;DR

This paper introduces a novel method for achieving invisibility on demand by using a generalized Hilbert transform to suppress wave scattering in specific directions and frequency ranges without extreme materials.

## Contribution

It presents a new theoretical approach based on a generalized Hilbert transform to control wave scattering, enabling practical invisibility for arbitrary objects with low-index contrast.

## Key findings

- Near-perfect invisibility for low-index contrast objects
- Extension to high-index objects and practical limits
- Numerical confirmation of the theoretical model

## Abstract

Designing invisible objects without the usage of extreme materials is a long-sought goal for photonic applications. Invisibility techniques demonstrated so far typically require high anisotropy, gain and losses, while also not being flexible. Here we propose an invisibility approach to suppress the scattering of waves from/to given directions and for particular frequency ranges, i.e. invisibility on demand. We derive a Born approximation-based generalized Hilbert transform for a specific invisibility arrangement relating the two quadratures of the complex permittivity of an object. The theoretical proposal is confirmed by numerical calculations, indicating that near-perfect invisibility can be attained for arbitrary objects with low-index contrast. We further demonstrate the cases where the idea can be extended to high-index objects or restricted to within practical limits by avoiding gain areas. The proposed concept opens a new route for the practical implementation of complex-shaped objects with arbitrarily suppressed scatterings determined on demand.

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Source: https://tomesphere.com/paper/1703.09490