# Confirmation of Cylindrical Perfect Invisibility Cloak Using Fourier-Bessel Analysis

## TL;DR

This paper develops a Fourier-Bessel analysis method to confirm that an ideal cylindrical invisibility cloak achieves perfect invisibility, while highlighting the sensitivity of the cloak to small perturbations affecting its scattering properties.

## Contribution

The paper introduces a cylindrical wave expansion approach to analyze and confirm the perfect invisibility of an ideal cylindrical cloak, addressing boundary conditions and scattering coefficients.

## Key findings

- Ideal cloak achieves perfect invisibility with zero scattering.
- Small perturbations cause noticeable scattering and field penetration.
- Zero-th order scattering coefficient convergence is slow, affecting robustness.

## Abstract

A cylindrical wave expansion method is developed to obtain the scattering field for an ideal two-dimensional cylindrical invisibility cloak. A near-ideal model of the invisibility cloak is set up to solve the boundary problem at the inner boundary of the cloak shell. We confirm that a cloak with the ideal material parameters is a perfect invisibility cloak by systematically studying the change of the scattering coefficients from the near-ideal case to the ideal one. However, due to the slow convergence of the zero$^{th}$ order scattering coefficients, a tiny perturbation on the cloak would induce a noticeable field scattering and penetration.