Numerical analysis of photonic resonances

Finite Element modal  analysis of open electromagnetic resonators

I have developed a modal approach based on the finite element method (FEM) adapted to diffractive structures (periodic or not) of arbitrary geometry and material properties, possibly embedded in a multilayer stack. Through a complex valued coordinate stretch, the free space is truncated by Perfectly Matched Layers (PML) which provide the suitable non Hermitian extension of Maxwell’s operator, allowing to compute its quasimodes associated with complex eigenvalues.

modes
Top: TE quasimodes of a 2D dielectric rod in free space (surrounded by PMLs). Bottom: quasimode of a 3D periodic photonic crystal slab.

Quasimodal expansion method: a new computational tool

In addition, I showed that it is possible to expand the solution of the problem with sources on a reduced eigenvectors basis. This quasimodal expansion method (QMEM) allows rapid computation of the coupling coefficient of any source with a particular mode, giving valuable information on the conditions of excitation of resonances of the system. The sources can be in particular a plane wave of arbitrary frequency, incidence and polarization, allowing one to obtain the modal expansion of the diffracted field. When considering a point source, we can obtain straightforwardly the Green function and local density of states (LDOS) by the QMEM in a highly time efficient computation. These methods, developed firstly in the 2D scalar case, were generalized to the 3D vector case.

QMEM
Top: scattered electric field calculated with direct FEM simulation (left) and the QMEM (right). Bottom: electric LDOS calculated with direct FEM simulations (left) and the QMEM (right).

Related paper

B. Vial, A. Nicolet, F. Zolla, and M. Commandré. Quasimodal expansion of electromagnetic fields in open two-dimensionnal structures. Phys. Rev. A 89, p. 023829, Feb. 2014. DOI | download