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Spectral expansions of open and dispersive optical systems : Gaussian regularization and convergence

Given the importance of modal methods in wave physics for describing the properties and dynamics of closed systems in terms of eigenmodes and eigenvalues, physicists have quite naturally sought to describe open systems in terms of open system eigenstates (often called Resonant States or Quasi-Normal-Modes) characterized by complex eigenvalues. Our work invokes the interaction of electromagnetic waves with particles to resolve two technical obstacles confronting such an endeavor.

The first problem we address is how one can define resonant state scalar products despite the fact that Resonant State wave-functions diverge exponentially in the far field. The resolution of this problematic is crucial for defining concepts like orthogonality and normalization for resonant states and has consequently received considerable attention, but we present the merits of a Gaussian regularization technique that can produce fully analytical results in certain circumstances (like scattering from a sphere), and partially analytic results in more general situations. With the scalar product issue resolved, we address another problematic that has been appreciated only quite recently, namely that directly truncated resonant state spectral expansions may `converge’ slowly, or not at all. We propose a solution to this problem that consists of constraining truncated spectral expansions to obey the same analytic structure and conservation laws as the complete solutions.

 Watch this Video on New Journal of Physics website: https://iopscience.iop.org/article/10.1088/1367-2630/ac10a6/meta

Spectral expansions of open and dispersive optical systems : Gaussian regularization and convergence, Brian Stout, Rémi Colom, Nicolas Bonod and Ross Mc Phedran. Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft, New Journal of Physics, Volume 23, August 2021.

Partners: This research is collaborative work between Institut Fresnel and Ross McPhedran, Macquarie University, Australian National University (ANU).

Fundings: This research received funding from LIA ALPHha, Associated Laboratory for Photonics between France and Australia

Contact : Brian STOUT, Team CLARTE