Numerical Tool for Analyzing Planar Semiconductor Multilayers Within the Two-Fluid Hydrodynamic Model Framework

We present a numerical tool to study the electromagnetic response of planar semiconductor multilayer structures when nonlocal effects of the materials are considered, where a two-fluid hydrodynamic model is adopted. The electric field is expanded in terms of scalar wave functions, whose governing equations and corresponding boundary conditions are derived. It is found that scattering matrices are well suited to handle the nonlocal response within the hydrodynamic framework, indicating that the proposed method can readily be extended to deal with the nonlocal effects when more than two types of charge carriers are included. We found that the spatial dispersion would lead to a higher transmission for a hyperlens while they may make the lens disfunctional.