Optical resonators are widely used in modern photonics. Their spectral response and temporal dynamics are fundamentally driven by their natural resonances, the so-called quasinormal modes (QNMs), with complex frequencies. For optical resonators made of dispersive materials, the QNM computation requires solving a nonlinear eigenvalue problem. This raises a difficulty that is only scarcely documented in the literature. We review our recent efforts for implementing efficient and accurate QNM solvers for computing and normalizing the QNMs of micro- and nanoresonators made of highly dispersive materials. We benchmark several methods for three geometries, a two-dimensional plasmonic crystal, a two-dimensional metal grating, and a three-dimensional nanopatch antenna on a metal substrate, with the perspective to elaborate standards for the computation of resonance modes.

A refractive index sensor can provide refractive index measurement and continuously monitor a dynamic process. Plasmonic nanostructure based sensors suffer from severe metal losses in the optical range, leading to the performance degradation. We design and numerically analyze a high-performance refractive index sensor based on the Fano resonance generated by a dielectric metasurface. The figure of merit (FOM) and the maximum quality factor (Q-factor) of the sensor are 721 and 5126, respectively. The maximum modulation depth can exceed 99% and the enhancement factor of the electric field amplitude can reach a high value of about 100. The uniqueness of the proposed sensor is polarization insensitivity. The transmittance spectra for various polarization states of the incident light can perfectly coincide, which is a rare phenomenon in Fano resonance based sensors and can facilitate experimental measurement.

A quasinormal mode (QNM) coupling theory is proposed for a system of coupled resonators. The theory is generally applicable to systems with energy loss and arbitrary frequency dispersion of permittivity such as plasmonic nanoresonators. The QNM coupling coefficients in the theory are obtained with first-principle calculations without fitting the full-wave numerical results or experimental data. The theory is built up based on the Green's-function formalism, which shows that the coupling between resonators originates from the mutual excitation of scattered field of each resonator. With the theory, the source-excited scattered field or the source-free QNMs of the coupled system can be obtained as an expansion in terms of QNMs of each individual resonator in the system. The theory provides an intuitive physical picture and also shows superior computational efficiency compared with the full-wave numerical method if the scattered field of each resonator in the system can be expanded with a small set of QNMs. The theory is tested against full-wave numerical method and is used to design metallic nanoantennas with a broadband enhancement of the spontaneous emission rate.

As shown in a recent letter [Nature 452, 728 (2008) ] with a microscopic model, the phenomenon of the extraordinary optical transmission (EOT) is intrinsically due to two distinct surface waves: the surface plasmon polariton and the quasi-cylindrical wave (quasi-CW) that efficiently funnel light into the hole aperture at resonance. Here we present a comprehensive microscopic model of the EOT that takes into account the two surface waves. The model preserves the desirable physical insight of the previous approach, but since it additionally takes into account the quasi-CWs, it provides highly accurate predictions over a much broader spectral range, from visible to microwave radiation. The net outcome is a complete understanding of many aspects of the EOT and especially of the role of the metal conductivity that has largely puzzled the initial interpretations. We believe that the main conclusions of the present analysis may be applied to many Wood-type surface resonances on metallic surfaces.

The radiation of an electric dipole emitter can be drastically enhanced if the emitter is placed in the nano-gap of a metallic dipole antenna. By assuming that only surface plasmon polaritons (SPPs) are excited on the antenna, we build up an intuitive pure-SPP model that is able to comprehensively predict the electromagnetic features of the antenna radiation, such as the total or radiative emission rate and the far-field radiation pattern. With the model we can distinguish the respective contributions from SPPs and from other surface waves to the antenna radiation. It is found that for antennas with long arms that support higher-order resonances, SPPs provide a dominant contribution to the antenna radiation, while for other cases, the contribution of surface waves other than SPPs should be considered. The model reveals an intuitive picture that the enhancement of the antenna radiation is due to surface waves that are resonantly excited on the two antenna arms and that are further coupled into the nano-gap or scattered into free space. From the model we can derive a phase-matching condition that predicts the antenna resonance and the resultant enhanced radiation. The model is helpful for a physical understanding and intuitive design of antenna devices.

We present a simple and intuitive model for analyzing the optical response of metallic surfaces patterned by arbitrary one-dimensional arrays of subwavelength (sub-$\lambda${}) structures. In the present microscopic approach, the near-field response close to the surface is composed of a linear combination of elementary hybrid waves, which are shown to solely depend on the frequency and to be merely independent of the incident illumination and of the scatterer geometry. The model is tested against fully vectorial computational results obtained for simple systems that can be handled numerically with fully vectorial methods and, in contrast to classical models that solely rely on surface plasmon polaritons, the present model is shown to be highly accurate over a broad spectral range below the plasma frequency of the metal.