Numerical Methods in Photonics

3.2.2  NUMERICAL STABILITY CRITERIA

It is clear that the choice of time and coordinate grid spacings influences the accurateness and robustness of a numerical scheme a lot. We are especially interested in any constrains on time step δt, because it defines the scenery and dynamical resolution of fields evolution in time-domain methods. A δt too small will make the total computation routine extensive; a δt too big will reasonably violate the causal connection between fields updates in different grid points. To estimate the restrains on the acceptable time step range, we need a numerical scheme stability analysis.

Assuming that the frequency can be extended to complex values ω = ω′ × iω″, Equation (3.41) can be solved in a very formal way. We introduce ...