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Register a new userEfficient near-field to far-field transformations for quasinormal modes of optical cavities and plasmonic resonators
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We describe an efficient near-field to far-field transformation for optical quasinormal modes, which are the dissipative modes of open cavities and plasmonic resonators with complex eigenfrequencies. As an application of the theory, we show how one can compute the reservoir modes (or regularized quasinormal modes) outside the resonator, which are essential to use in both classical and quantum optics. We subsequently demonstrate how to efficiently compute the quantum optical parameters necessary in the theory of quantized quasinormal modes [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)]. To confirm the accuracy of our technique, we directly compare with a Dyson equation approach currently used in the literature (in regimes where this is possible), and demonstrate several order of magnitude improvement for the calculation run times. We also introduce an efficient pole approximation for computing the quantized quasinormal mode parameters, since they require an integration over a range of frequencies. Using this approach, we show how to compute regularized quasinormal modes and quantum optical parameters for a full 3D metal dimer in under one minute on a standard desktop computer. Our technique is exemplified by studying the quasinormal modes of metal dimers and a hybrid structure consisting of a gold dimer on top of a photonic crystal beam. In the latter example, we show how to compute the quantum optical parameters that describe a pronounced Fano resonance, using structural geometries that cannot practically be solved using a Dyson equation approach. All calculations for the spontaneous emission rates are confirmed with full-dipole calculations in Maxwells equations and are shown to be in excellent agreement.
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In the past decade, advances in nanotechnology have led to the development of plasmonic nanocavities which facilitate light-matter strong coupling in ambient conditions. The most robust example is the nanoparticle-on-mirror (NPoM) structure whose geometry is controlled with subnanometer precision. The excited plasmons in such nanocavities are extremely sensitive to the exact morphology of the nanocavity, giving rise to unexpected optical behaviors. So far, most theoretical and experimental studies on such nanocavities have been based solely on their scattering and absorption properties. However, these methods do not provide a complete optical description of a NPoM. Here, the NPoM is treated as an open non-conservative system supporting a set of photonic quasinormal modes (QNMs). By investigating the morphology-dependent optical properties of nanocavities, we propose a simple yet comprehensive nomenclature based on spherical harmonics and report spectrally overlapping bright and dark nanogap eigenmodes. The near-field and far-field optical properties of NPoMs are explored and reveal intricate multi-modal interactions.
Modal expansion is an attractive technique for solving electromagnetic scattering problems. With the one set of resonator modes, calculated once and for all, any configuration of near-field or far-field sources can be obtained almost instantaneously. Traditionally applied to closed systems, a simple and rigorous generalization of modal expansion to open systems using eigenpermittivity states is also available. These open modes are suitable for typical nanophotonic systems, for example. However, the numerical generation of modes is usually the most difficult and time-consuming step of modal expansion techniques. Here, we demonstrate efficient and reliable mode generation, expanding the target modes into the modes of a simpler open system that are known. Such a re-expansion technique is implemented for resonators with non-uniform permittivity profiles, demonstrating its rapid convergence. Key to the methods success is the inclusion of a set of longitudinal basis modes.
We introduce a second quantization scheme based on quasinormal modes, which are the dissipative modes of leaky optical cavities and plasmonic resonators with complex eigenfrequencies. The theory enables the construction of multi-plasmon/photon Fock states for arbitrary three-dimensional dissipative resonators and gives a solid understanding to the limits of phenomenological dissipative Jaynes-Cummings models. In the general case, we show how different quasinormal modes interfere through an off-diagonal mode coupling and demonstrate how these results affect cavity-modified spontaneous emission. To illustrate the practical application of the theory, we show examples using a gold nanorod dimer and a hybrid dielectric-metal cavity structure.
We present a bi-orthogonal approach for modeling the response of localized electromagnetic resonators using quasinormal modes, which represent the natural, dissipative eigenmodes of the system with complex frequencies. For many problems of interest in optics and nanophotonics, the quasinormal modes constitute a powerful modeling tool, and the bi-orthogonal approach provides a coherent, precise, and accessible derivation of the associated theory, enabling an illustrative connection between different modeling approaches that exist in the literature.
We first present a quasinormal mode (QNM) theory for coupled loss-gain resonators working near an exceptional point. Assuming linear media, which can be fully quantified using the complex pole properties of the QNMs, we show how the QNMs yield a quantitatively good model to a full dipole spontaneous emission response in Maxwells equations at various spatial positions and frequencies (linear response). We also develop a highly accurate and intuitive QNM coupled-mode theory, which can be used to rigorously model such systems using only the QNMs of the bare resonators, where the hybrid QNMs of the complete system are automatically obtained. Near a lossy exceptional point, we analytically show how the QNMs yield a Lorentzian-like and a Lorentzian-squared-like response for the spontaneous emission lineshape, consistent with other works. However, using rigorous analytical and numerical solutions for microdisk resonators, we demonstrate that the general lineshapes are far richer than what has been previously predicted. Indeed, the classical picture of spontaneous emission can take on a wide range of positive and negative Purcell factors from the hybrid modes of the coupled loss-gain system. These negative Purcell factors are unphysical and signal a clear breakdown of the classical dipole picture of spontaneous emission in such media, though the negative local density of states is correct. We also show the rich spectral features of the Green function propagators, which can be used to model various physical observables. Second, we present a QNM approach to model index modulated ring resonators working near an exceptional point and show unusual chiral power flow from linearly polarized emitters, in agreement with recent experiments, which is quantitatively explained without invoking the interpretation of a missing dimension (the Jordan vector) and a decoupling from the cavity eigenmodes.
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