Invited Paper
Modal Approach for Absorptive and Dispersive Resonators

Micro-nanoresonators play an important role in the conversion of energy from localized fields to radiating waves and have many applications, especially in sensing, nonlinear nano-optics, or quantum optics. An interesting question is how to recover a diffracted field with the modes as building blocks. This can be done by expanding any diffracted field on the complete (?) basis of the eigenmodes.

Normal-mode theories rely on the fact that energy dissipation in the system remains small enough. This key assumption may remain approximately valid for dielectric microresonators, but completely breaks down for metallic nanoresonators that confine light at a deep-subwavelength scale, for which absorption and thus dispersion losses are large. Studying such systems with usual normal-mode theories does not give satisfying predictions.

Recently, our group has made a significant step forward [1], by deriving analytical expressions for the coupling coefficients. The mathematical derivation that relies on reciprocity arguments is fully rigorous, the only hypothesis being on the completeness of resonance-mode basis used to expand the scattered field. Except for this hypothesis that is at least valid if the dispersion is weak, the derivation is mathematically sound. The same year, we have also proposed a simple and general numerical method [1] that allows us to compute and normalize the resonance modes with any Maxwell solver.

The talk will review some consequences of the formalism including

• LDOS modal theory (Purcell factor) [1]
• Modal theory of the spatial coherence in complex systems [2]
• Quantum formalism for the analysis of hybrid systems made of quantum emitters and plasmonic resonators, which provides closed-form expressions for the optical response [3]
• An analytical treatment for complex-valued resonance shifts for plasmonic sensing [4]

[1] C. Sauvan, et al., Phys. Rev. Lett. 110, 237401 (2013). Q. Bai, et. al., Opt. Exp. 21, 27371 (2013).

[2] C. Sauvan, et al., Modal Representation of Spatial Coherence in Dissipative and Resonant Photonic Systems. Phys. Rev. A. 89, 043825 (2014).

[3] J. Yang et al., Analytical formalism for the interaction of two-level quantum systems with metal nanoresonators (submitted).

[4] J. Yang, H. Giessen and P. Lalanne, Closed-form expression for the frequency shifts of perturbed localized plasmon resonances (submitted).

Philippe.Lalanne@institutoptique.fr