Optimisation approach to the time-domain electromagnetic inverse problem for a bi-isotropic slab

A one-dimensional time-domain electromagnetic inverse problem for a bi-isotropic slab is solved using an optimisation approach. The bi-isotropy and dispersion result in time convolutions of four susceptibility kernels in the time-domain constitutive relations. To make the computation simpler, dual functions are introduced to derive an explicit expression for the gradient. A matrix formalism is introduced to derive the system of equations for the dual functions. After the gradient has been computed, a conjugate gradient method is used to reconstruct all the four susceptibility kernels simultaneously. Numerical results for the reconstruction are presented, and the algorithm is tested with both the clean and noisy data