On the reference wave vector of paraxial Helmholtz equations

The reference wave vector for both scalar and vectorial formulations of the paraxial Helmholtz equation is determined by using various strategies which aim at the optimization of different features of the approximated solution. It turns out that all optimization schemes yield similar results, i.e., an overall optimization of the paraxial Helmholtz equation. A detailed analysis of a benchmark example shows that the reference wave vector must be adapted continuously during beam propagation. However, the required evaluation is so efficient that the additional numerical effort can be neglected.