AMaSiS 2018 Workshop: Abstracts

Poster Numerical methods based on Riesz projections for the investigation of light-matter interaction

Felix Binkowski(1), Lin Zschiedrich(2), and Sven Burger(1,2)

(1) Zuse Institute Berlin

(2) JCMwave GmbH

Resonating structures are omnipresent in physics and especially also in the field of nanooptics. Combining semiconductor quantum dots and nanoresonators represents a promising approach to explore new regimes of light-matter interaction [1, 2]. For the investigation of such devices, theoretical models and numerical simulation of the emitter-resonator coupling are essential. A common and instructive approach is a resonance expansion of the electromagnetic field [3, 4, 5].

In this contribution, we review an expansion approach [6], which is based on Riesz projections [7]. In the Riesz projection expansion, contour integration is applied in the complex frequency plane to precisely quantify the coupling of an emitter to the eigenmodes and to the background continuum of modes of a nanoresonator. The approach is in particular also applicable in the case of material dispersion [6]. A nontrivial dispersion relation is ubiquitous in optical materials and leads to nonlinear eigenproblems.

Furthermore, we comment on how the presented numerical methods are related to eigensolvers based on spectral projectors, e.g., to the FEAST eigensolver [8] and to approaches of [9, 10]. We show details on numerical realizations and convergence studies for topical nanooptical applications.

We acknowledge support by the Einstein Foundation Berlin through ECMath within subproject OT9.

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