Operator Formulation for Lossy Materials about mpb HOT 2 CLOSED

This is the paper that describes MPB in detail:

http://www.opticsinfobase.org/abstract.cfm?URI=oe-8-3-173

This is linked in the manual from https://mpb.readthedocs.io/en/latest/Developer_Information/#the-mathematics-of-mpb

In principle, similar techniques can be used for lossy media, with the caveats that:

• Lossy media make the operator non-Hermitian, requiring completely different eigensolver techniques and a different way of describing the eigenvalues you want. ("Lowest bands" is not applicable any more.)

• Realistic lossy media are often dispersive, transforming it into a nonlinear eigenproblem. (Of course, if the frequency dependence is a rational function, you can transform it into a polynomial eigenproblem and from there back into a linear eigenproblem, but it is still messier).

• Weakly lossy materials can often be handled via perturbation theory (with MPB computing the lossless solutions). Strongly lossly materials like metals really call for a different discretization scheme that can employ nonuniform grids, like FEM or BEM.

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Thank you for your comprehensive response. Sorry, I should have picked up on some of those links from the docs.

Using perturbation theory in conjunction with MPB is an interesting idea. Has anyone done this before?

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