The specificity of modal-expansion formalisms is their capabilities to model the physical properties in the natural resonance-state basis of the system in question, leading to a transparent interpretation of the numerical results. In electromagnetism, modal-expansion formalisms are routinely used for optical waveguides. In contrast, they are much less mature for analyzing open non-Hermitian systems, such as micro and nanoresonators. Here, by accounting for material dispersion with auxiliary fields, we considerably extend the capabilities of these formalisms, in terms of computational effectiveness, number of states handled and range of validity. We implement an efficient finite element solver to compute the resonance states, and derive new closed-form expressions of the modal excitation coefficients for reconstructing the scattered fields. Together, these two achievements allow us to perform rigorous modal analysis of complicated plasmonic resonators, being not limited to a few resonance states, with straightforward physical interpretations and remarkable computation speeds. We particularly show that, when the number of states retained in the expansion increases, convergence towards accurate predictions is achieved, offering a solid theoretical foundation for analyzing important issues, e.g. Fano interference, quenching, coupling with the continuum, which are critical in nanophotonic research.

By placing a quantum emitter in the mouths of nanogaps consisting of two metal nanoparticles nearly into contact, significant increases in emission rate are obtained. This mechanism is central in the design of modern plasmonic nanoantennas. However, due to the lack of general knowledge on the balance between the different decay rates in nanogaps (emission, quenching, and metal absorption), the design of light-emitting devices based on nanogaps is performed in a rather hazardous fashion; general intuitive recipes do not presently exist. With accurate and simple closed-form expressions for the quenching rate and the decay rate into gap plasmons, we provide a comprehensive analysis of nanogap light emitting devices in the limit of small gap thickness. We disclose that the total decay rate in gap plasmons can largely overcome quenching for specifically selected metallic and insulator materials, regardless of the gap size. To confront these theoretical predictions, we provide a comprehensive numerical analysis of nanocube-type antennas in the limit of small gap thickness and further provide upper bounds for the photon-radiation efficiency.

Light localization due to random imperfections in periodic media is paramount in photonics research. The group index is known to be a key parameter for localization near photonic band edges, since small group velocities reinforce light interaction with imperfections. Here, we show that the size of the smallest localized mode that is formed at the band edge of a one-dimensional periodic medium is driven instead by the effective photon mass, i.e. the flatness of the dispersion curve. Our theoretical prediction is supported by numerical simulations, which reveal that photonic-crystal waveguides can exhibit surprisingly small localized modes, much smaller than those observed in Bragg stacks thanks to their larger effective photon mass. This possibility is demonstrated experimentally with a photonic-crystal waveguide fabricated without any intentional disorder, for which near-field measurements allow us to distinctly observe a wavelength-scale localized mode despite the smallness (~1/1000 of a wavelength) of the fabrication imperfections.

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We propose a semianalytical formalism based on a time-domain resonant-mode-expansion theory to analyze the ultrafast temporal dynamics of optical nanoresonators. We compare the theoretical predictions with numerical data obtained with the FDTD method, which is commonly used to analyze experiments in the field. The comparison reveals that the present formalism (i) provides deeper physical insight onto the temporal response and (ii) is much more computationally efficient. Since its numerical implementation is easy, the formalism, albeit approximate, can be advantageously used to both analyze and design ultrafast nano-optics experiments.

Very large spontaneous-emission-rate enhancements (∼1000) are obtained for quantum emitters coupled with tiny plasmonic resonance, especially when emitters are placed in the mouth of nanogaps formed by metal nanoparticles that are nearly in contact. This fundamental effect of light emission at subwavelength scales is well documented and understood as resulting from the smallness of nanogap modes. In contrasts, it is much less obvious to figure out whether the radiation efficiency is high in these gaps, or if the emission is quenched by metal absorption especially for tiny gaps a few nanometers wide; the whole literature only contains scattered electromagnetic calculations on the subject, which suggest that absorption and quenching can be kept at a small level despite the emitter proximity to metal. Thus through analytical derivations in the limit of small gap thickness, it is our objective to clarify why quantum emitters in nanogap antennas offer good efficiencies, what are the circumstances in which high efficiency is obtained, and whether there exists an upper bound for the maximum efficiency achievable.Spontaneous emission remains at the core of the performance of many optoelectronic devices, including not only lighting components and displays, but also lasers, optical amplifiers, single photon sources and non-classical light sources in general. Metal nanogaps formed by a thin insulator layer sandwiched between two metals films have very rich physical properties and many established applications ranging from electron tunneling microscopy, nanocatalysis, Raman spectroscopy to disruptive electronics, but they are also likely to profoundly impact spontaneous emission [1]. Owing to the strong localization in the gap, metal nanogaps strongly modify the electromagnetic density of modes. It follows that the spontaneous emission of dye molecules or quantum dots which are placed in the gap can be enhanced considerably. This fundamental phenomenon of light emission, known as the Purcell effect [2], has been first demonstrated in optics by coupling quantum emitters with resonant dielectric microcavities [3] with very high quality factors and mode volumes of the order of the wavelength cube. The use of deep-subwavelength confinements with plasmonic nanostructures has created a totally new framework with mode volumes 10,000 times smaller and broadband responses [4,5], and thus have opened promising route toward new applications in optical spectroscopy [6][7][8], spaser or low-threshold nanolasers [9-10], or broadband non-classical light sources [5].

One--dimensional (1D) infinite periodic systems exhibit vanishing group velocity and diverging density of states (DOS) near band edges. However, in practice, systems have finite sizes and inevitably this prompts the question of whether helpful physical quantities related to infinite systems, such as the group velocity that is deduced from the band structure, remain relevant in finite systems. For instance, one may wonder how the DOS divergence can be approached with finite systems. Intuitively, one may expect that the implementation of larger and larger DOS, or equivalently smaller and smaller group velocities, would critically increase the system length. Based on general 1D--wave--physics arguments, we demonstrate that the large slow--light DOS enhancement of periodic systems can be observed with very short systems, whose lengths scale with the logarithm of the inverse of the group velocities. The understanding obtained for 1D systems leads us to propose a novel sort of microstructure to enhance light-matter interaction, a sort of photonic speed bump that abruptly changes the speed of light by a few orders of magnitude without any reflection. We show that the DOS enhancements of speed bumps result from a classical electromagnetic resonance characterized by a single resonance mode and also that the nature and the properties of the resonance are markedly different from those of classical defect--mode photonic--crystal cavities.

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