Optical resonators play an essential role in many areas of modern photonics, from quantum plasmonics, optical metamaterials, integrated photonic circuits, to optical sensors. This predominant role is the outcome of the recent progress of bottom-up and top-down technologies that have allowed a proliferation of totally new resonator constructs with very distinct properties and dimensions, such as high-Q dielectric microcavities, plasmonic nanoantennas or associations of them. Comparatively, the resonator modelling has seen much less progress, and we enter an era where optical resonator technologies are limited by the lack of effective design tools rather than by creativity and fabrication.

Here we elaborate a theoretical and numerical formalism that has the potential to bring a real difference in resonator design. Developed for the most general case of 3D plasmonic resonators in inhomogeneous backgrounds, the formalism differs markedly from classical methods. It is the equivalent of waveguide-mode-theory for resonators, and offers similar strengths: an intuitive modelling that sticks to the physics of the resonance and a high-performance with computational speeds that are much faster than those presently available with classical methods.

Related recent publications by the group:

1. Yang, H. Giessen, P. Lalanne, Nano Lett. 15, 3439 (2015)

"Simple Analytical Expression for the Peak-Frequency Shifts of Plasmonic Resonances for Sensing"

1. Yang, M. Perrin, P. Lalanne, Phys. Rev. X 5, 021008 (2015)

"Analytical formalism for the interaction of 2-level quantum systems with metal nanoresonators"

1. Faggiani, A. Losquin, J. Yang, E. Mårsell, A. Mikkelsen, P. Lalanne, ACS Photonics (submitted).

"Modal analysis of the ultrafast dynamics of optical nanoresonators"

1. Fauché, S.G. Kosionis and P. Lalanne, (submitted)

"Collective scattering in hybrid nanostructures with many atomic oscillators coupled to an electromagnetic resonance"