Computation for Maxwell's transmission eigenvalues

The transmission eigenvalue problem has important applications in inverse scattering theory. In this paper, based on the series solutions for the Hemholtz equation, we derived the solutions for the Maxwell's transmission eigenproblem using the spherical Bessel functions on balls. Numerical results are presented for the lowest several transmission eigenvalues. The result provides valuable insight and can be used as a benchmark problem for numerical computation on more general domains.