Towards numerical vector Helmholtz solutions in integrated photonics

Much present day simulation and design for optoelectronics involves approximations due to the limitations of today´s computer resources. For example, finite difference beam propagation (FD-BPM) methods assume that the propagation takes the form of an envelope function multiplied by a propagation factor. These approximations can limit the utility of present methods. The next generation of software must aim to eliminate these limitations, ideally correctly solving the vector Helmholtz equation subject to open boundary conditions. In this paper we will address how advances in our understanding, novel approaches and computer power are moving us towards this goal.