not yet discussed is the effect of the discretization of space on the accuracy of the numerical results. Both conditional Yee-type algorithms and unconditionally stable algorithms $U_1(\tau)$, $U_2(\tau)$ and $U_4(\tau)$ suffer from numerical dispersion (see Ref.[@Taflove], chapter 4 for an in-depth discussion). Simple methods to reduce numerical dispersion are taking a finer mesh or employing more accurate finite-difference approximations for the spatial derivates [@Taflove]. The former obviously can be used here too (for the simulations discussed below we used a mesh size that yields sufficiently accurate results for the present purposes). There are no fundamental nor practical problems to incorporate the latter method in the Suzuki-product-formula approach [@DeRaedt87; @DeRaedt94]. However as the emphasis of the present paper is on the construction of unconditionally stable algorithms we relegate a presentation of these technical but for applications important extensions to future publications.

Data analysis {#sec5}
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Time-domain algorithms obviously yield the time development of the EM fields. The scattering (transmission) of the EM fields from (through) objects is one of the main applications of this technique [@Taflove]. One approach is to prepare an initial state $\Psi(0)$ of the EM fields, propagate the fields in time for a number of time-steps and analyse 