Eigen-energy effects and non-orthogonality in the quasi-normal mode expansion of Maxwell equations

We derive a quasi-normal mode theory for three-dimensional scatterers, taking care to remove an hypothesis of weakly dispersive materials implicitely used in previous works. In our approach, the normalized modes remain unchanged, but the analytic expansion coefficients onto the set of QNM are modified. In particular, we take into account in a simple way the non-orthogonality of the modes, and we set up a rigourous frame, to treat the case where several QNMs are excited. Eventally, the complex concept of PML integration, previously introduced, becomes unnecessary, even to compute the QNM mode volume. Besides, crossover integrals of QNM fields over the whole space can now be written rigourously, as integrals on the finite volume of the scatterer, without surface terms.