In this paper we investigate the completeness of the Stark resonant eigenstates for a particle in a square-well potential. We find that the resonant state expansions for target functions converge inside the potential well and that the existence of this convergence does not depend on the depth of the potential well. By analyzing the asymptotic form of the terms in these expansions we prove some results on the relation between smoothness of target functions and the rate of convergence of the corresponding resonant state expansion.

In this paper we study pulse propagation in complex refractive index materials, modelled by a dispersive wave equation, using the method of multiple scales (MMS), and perform several numerical tests to investigate its accuracy. We assume a complex valued refracting index in a noncentrosymmetric medium with a Kerr response. The key feature of our MMS solution is the linearity of the amplitude equation and the complex nature of the mode-frequency. The MMS is tested as an initial value problem using three different dispersion models. Depending on the parameters of the problem, the amplitude equation can be both well-or ill-posed. Despite the ill-posedness, the MMS solution remains a valid approximation of the solution to the original nonlinear model.

In this paper we introduce a method for creating a transparent computational boundary for the simulation of unidirectional propagation of optical beams and pulses using leaky modes. The key element of the method is the introduction of an artificial-index material outside a chosen computational domain and utilization of the quasi-normal modes associated with such artificial structure. The method is tested on the free space propagation of TE electromagnetic waves. By choosing the material to have appropriate optical properties one can greatly reduce the reflection at the computational boundary. In contrast to the well-known approach based on a perfectly matched layer, our method is especially well suited for spectral propagators. arXiv:1904.00834v1 [physics.optics]