Absorbing Boundary Condition for FDTD Modeling of Waveguides with Lossy Medium

In order to solve diffraction problems with infinite structures (like waveguides) using FDTD needs some method to bound the numerical solution region with absorbing boundary condition imitating semi-infinite waveguide. In several such techniques are described that use either local conditions (ABC) or absorbing layer (PML), but most of these methods result in unacceptable reflection errors in vicinity of cutoff frequencies that may lead to significant errors in analysis of waveguide diffraction problems. In this work we are going to generalize the method onto the case of waveguide filled with lossy medium, provide numerical implementation, and analyze its performance.