Normalization, orthogonality, and completeness of quasinormal modes of open systems: the case of electromagnetism [Invited].

The scattering of electromagnetic waves by resonant systems is determined by the excitation of the quasinormal modes (QNMs), i.e. the eigenmodes, of the system. This Review addresses three fundamental concepts in relation to the representation of the scattered field as a superposition of the excited QNMs: normalization, orthogonality, and completeness. Orthogonality and normalization enable a straightforward assessment of the QNM excitation strength for any incident wave. Completeness guarantees that the scattered field can be faithfully expanded into the complete QNM basis. These concepts are not trivial for non-conservative (non-Hermitian) systems and have driven many theoretical developments since initial studies in the 70's. Yet, they are not easy to grasp from the extensive and scattered literature, especially for newcomers in the field. After recalling fundamental results obtained in initial studies on the completeness of the QNM basis for simple resonant systems, we review recent achievements and the debate on the normalization, clarify under which circumstances the QNM basis is complete, and highlight the concept of QNM regularization with complex coordinate transforms.

Quasinormal modes expansions for nanoresonators made of absorbing dielectric materials: study of the role of static modes.

The interaction of light with photonic resonators is determined by the eigenmodes of the system. Modal theories based on quasinormal modes provide a natural tool to calculate and understand light scattering by nanoresonators. We show that, in the case of resonators made of absorbing dielectric materials, eigenmodes with zero eigenfrequency (static modes) play a key role in the modal formalism. The excitation of static modes builds a non-resonant contribution to the modal expansion of the scattered field. This non-resonant term plays a crucial physical role since it largely contributes to the off-resonance signal to which resonances are added in amplitude, possibly leading to interference phenomena and Fano resonances. By considering light scattering by a silicon nanosphere, we quantify the impact of static modes. This study shows that the importance of static modes is not just formal. Static modes are of prime importance in an expansion truncated to only a few modes.

Antenna surface plasmon emission by inelastic tunneling.

Surface plasmons polaritons are mixed electronic and electromagnetic waves. They have become a workhorse of nanophotonics because plasmonic modes can be confined in space at the nanometer scale and in time at the 10 fs scale. However, in practice, plasmonic modes are often excited using diffraction-limited beams. In order to take full advantage of their potential for sensing and information technology, it is necessary to develop a microscale ultrafast electrical source of surface plasmons. Here, we report the design, fabrication and characterization of nanoantennas to emit surface plasmons by inelastic electron tunneling. The antenna controls the emission spectrum, the emission polarization, and enhances the emission efficiency by more than three orders of magnitude. We introduce a theoretical model of the antenna in good agreement with the results.

Nanoantenna for Electrical Generation of Surface Plasmon Polaritons.

Light emission by inelastic tunneling has been known for many years. Recently, this technique has been used to generate surface plasmons using a scanning tunneling microscope tip. The emission process suffers from a very low efficiency lower than a photon in 10^{4} electrons. We introduce a resonant plasmonic nanoantenna that allows both enhancing the power conversion to surface plasmon polaritons by more than 2 orders of magnitude and narrowing the emission spectrum. The physics of the emission process is analyzed in terms of local density of states and the efficiency of the nanoantenna to radiate surface plasmon polaritons.

Enhanced nonlinear interaction in a microcavity under coherent excitation.

The large field enhancement that can be achieved in high quality factor and small mode volume photonic crystal microcavities leads to strengthened nonlinear interactions. However, the frequency shift dynamics of the cavity resonance under a pulsed excitation, which is driven by nonlinear refractive index change, tends to limit the coupling efficiency between the pulse and the cavity. As a consequence, the cavity enhancement effect cannot last for the entire pulse duration, limiting the interaction between the pulse and the intra-cavity material. In order to preserve the benefit of light localization throughout the pulsed excitation, we report the first experimental demonstration of coherent excitation of a nonlinear microcavity, leading to an enhanced intra-cavity nonlinear interaction. We investigate the nonlinear behavior of a Silicon-based microcavity subject to tailored positively chirped pulses, enabling to increase the free carrier density generated by two-photon absorption by up to a factor of 2.5 compared with a Fourier-transform limited pulse excitation of equal energy. It is accompanied by an extended frequency blue-shift of the cavity resonance reaching 19 times the linear cavity bandwidth. This experimental result highlights the interest in using coherent excitation to control intra-cavity light-matter interactions and nonlinear dynamics of microcavity-based optical devices.

Multi-resonant absorption in ultra-thin silicon solar cells with metallic nanowires.

We propose a design to confine light absorption in flat and ultra-thin amorphous silicon solar cells with a one-dimensional silver grating embedded in the front window of the cell. We show numerically that multi-resonant light trapping is achieved in both TE and TM polarizations. Each resonance is analyzed in detail and modeled by Fabry-Perot resonances or guided modes via grating coupling. This approach is generalized to a complete amorphous silicon solar cell, with the additional degrees of freedom provided by the buffer layers. These results could guide the design of resonant structures for optimized ultra-thin solar cells.

Plasmon dispersion diagram and localization effects in a three-cavity commensurate grating.

Commensurate gratings of deep-metallic grooves have highly localized cavity resonances which do not exist for purely periodic gratings. In this paper we present the experimental dispersion diagram of the resonances of a commensurate grating with three sub-wavelength cavities per period. We observe selective light localization within the cavities, transition from a localized to a delocalized mode and modifications of the coupling of modes with the external plane-wave that may lead to the generation of black modes. This unexpected complexity is analyzed via a theoretical study in full agreement with the experiments. These results open a way to the control of wavelength-dependent hot spot predicted in more complex commensurate gratings.

Angle-resolved transmission measurements through anisotropic two-dimensional plasmonic crystals.

We report on high-accuracy angle-resolved optical transmission measurements through anisotropic 2D plasmonic crystals made of gold films with large-area rectangular arrays of nanoscale square holes, deposited on GaAs substrates. The measurements reveal the dispersion relations of air-gold and gold-GaAs surface plasmon polaritons. The crystal anisotropy induces a separation between plasmonic modes propagating in different directions. Their symmetry and dispersion properties are discussed.

Broadband blazing with artificial dielectrics.

The efficiency of conventional diffractive optical elements with échelette-type profiles drops rapidly as the illumination wavelength departs from the blaze wavelength. We use high dispersion of artificial materials to synthesize diffractive optical elements that are blazed over a broad spectral range (approximately 1 octave) or for two different wavelengths.

Photonics: tuning holes in photonic-crystal nanocavities.

One challenge in photonics is strongly to confine light in small volumes in order to increase light-matter interaction. Akahane et al. propose a new concept for increasing the lifetime of this interaction, based on tailoring of the Fourier spectrum of cavity modes, which they believe is demonstrated by the surprising enhancement (roughly tenfold) of the quality factor Q of the cavity as a result of fine-tuning the mirror-hole geometry in a photonic-crystal nanocavity. Here we question the validity of their concept and argue that the improvement in Q is due to an increase in the impedance wave matching at the cavity edges and to a slow-wave effect. This alternative interpretation opens the way to new cavity designs.