Shape Deformation of Nanoresonator: A Quasinormal-Mode Perturbation Theory

Manipulating the quasi-normal modes of radially symmetric resonators

The frequency response of a resonator is governed by the locations of its quasi-normal modes in the complex frequency plane. The real part of the quasi-normal mode determines the resonance frequency and the imaginary part determines the width of the resonance. For applications such as energy harvesting and sensing, the ability to manipulate the frequency, linewidth and multipolar nature of resonances is key. Here, we derive two methods for simultaneously controlling the resonance frequency, linewidth and multipolar nature of the resonances of radially symmetric structures. Firstly, we formulate an eigenvalue problem for a global shift in the permittivity of the structure to place a resonance at a particular complex frequency. Next, we employ quasi-normal mode perturbation theory to design radially graded structures with resonances at desired frequencies.

Q-Factor Optimization of Modes in Ordered and Disordered Photonic Systems Using Non-Hermitian Perturbation Theory

The quality factor, Q, of photonic resonators permeates most figures of merit in applications that rely on cavity-enhanced light-matter interaction such as all-optical information processing, high-resolution sensing, or ultralow-threshold lasing. As a consequence, large-scale efforts have been devoted to understanding and efficiently computing and optimizing the Q of optical resonators in the design stage. This has generated large know-how on the relation between physical quantities of the cavity, e.g., Q, and controllable parameters, e.g., hole positions, for engineered cavities in gaped photonic crystals. However, such a correspondence is much less intuitive in the case of modes in disordered photonic media, e.g., Anderson-localized modes. Here, we demonstrate that the theoretical framework of quasinormal modes (QNMs), a non-Hermitian perturbation theory for shifting material boundaries, and a finite-element complex eigensolver provide an ideal toolbox for the automated shape optimization of Q of a single photonic mode in both ordered and disordered environments. We benchmark the non-Hermitian perturbation formula and employ it to optimize the Q-factor of a photonic mode relative to the position of vertically etched holes in a dielectric slab for two different settings: first, for the fundamental mode of L3 cavities with various footprints, demonstrating that the approach simultaneously takes in-plane and out-of-plane losses into account and leads to minor modal structure modifications; and second, for an Anderson-localized mode with an initial Q of 200, which evolves into a completely different mode, displaying a threefold reduction in the mode volume, a different overall spatial location, and, notably, a 3 order of magnitude increase in Q.

Superscattering emerging from the physics of bound states in the continuum

We study the Mie-like scattering from an open subwavelength resonator made of a high-index dielectric material, when its parameters are tuned to the regime of interfering resonances. We uncover a novel mechanism of superscattering, closely linked to strong coupling of the resonant modes and described by the physics of bound states in the continuum (BICs). We demonstrate that the enhanced scattering occurs due to constructive interference described by the Friedrich-Wintgen mechanism of interfering resonances, allowing to push the scattering cross section of a multipole resonance beyond the currently established limit. We develop a general non-Hermitian model to describe interfering resonances of the quasi-normal modes, and study subwavelength dielectric nonspherical resonators exhibiting avoided crossing resonances associated with quasi-BIC states. We confirm our theoretical findings by a scattering experiment conducted in the microwave frequency range. Our results reveal a new strategy to boost scattering from non-Hermitian systems, suggesting important implications for metadevices.

Material- and shape-dependent optical modes of hyperbolic spheroidal nano-resonators

Hyperbolic nanoresonators, composed of anisotropic materials with opposite signs of permittivity, have unique optical properties due to a large degree of freedom that hyperbolic dispersion provides in designing their response. Here, we focus on uniaxial hyperbolic nanoresonators composed of a model silver-silica multilayer in the form of spheroids with a broad aspect ratio encompassing both prolate and oblate particles. The origin and evolution of the optical response and mode coupling are investigated using both numerical (T-matrix and FDTD) and theoretical methods. We show the tunability of the optical resonances and the interplay of the shape and material anisotropy in determining the spectral response. Depending on the illumination conditions as well as shape and material anisotropy, a single hyperbolic spheroid can show a dominant electric resonance, behaving as a pure metallic nanoparticle, or a strong dipolar magnetic resonance even in the quasistatic regime. The quasistatic magnetic response of indicates a material-dependent origin of the mode, which is obtained due to coupling of the magnetic and electric multipoles. Such coupling characteristics can be employed in various modern applications based on metasurfaces.

Optomechanical Hot-Spots in Metallic Nanorod-Polymer Nanocomposites

Plasmonic coupling between adjacent metallic nanoparticles can be exploited for acousto-plasmonics, single-molecule sensing, and photochemistry. Light absorption or electron probes can be used to study plasmons and their interactions, but their use is challenging for disordered systems and colloids dispersed in insulating matrices. Here, we investigate the effect of plasmonic coupling on optomechanics with Brillouin light spectroscopy (BLS) in a prototypical metal-polymer nanocomposite, gold nanorods (Au NRs) in polyvinyl alcohol. The intensity of the light inelastically scattered on thermal phonons captured by BLS is strongly affected by the wavelength of the probing light. When light is resonant with the transverse plasmons, BLS reveals mostly the normal vibrational modes of single NRs. For lower energy off-resonant light, BLS is dominated by coupled bending modes of NR dimers. The experimental results, supported by optomechanical calculations, document plasmonically enhanced BLS and reveal energy-dependent confinement of coupled plasmons close to the tips of NR dimers, generating BLS hot-spots. Our work establishes BLS as an optomechanical probe of plasmons and promotes nanorod-soft matter nanocomposites for acousto-plasmonic applications.

Quasinormal Mode Expansion Theory for Mesoscale Plasmonic Nanoresonators: An Analytical Treatment of Nonclassical Electromagnetic Boundary Condition

Nonclassical quantum effects will significantly affect the optical response of plasmonic nanoresonators with mesoscale feature sizes between about 2 and 20 nm, and can be fully described by the nonclassical electromagnetic boundary condition (NEBC) expressed with the surface-response Feibelman d parameters. In this Letter, a quasinormal mode (QNM) expansion theory under the NEBC is proposed. By adopting the easily solved classical QNMs under the classical electromagnetic boundary condition as a complete set of basis functions, rigorous expansions of the nonclassical source-free QNMs and source-excited electromagnetic field under the nonperturbative NEBC are provided. With the obtained nonclassical QNMs as basis functions, expansions of the nonclassical source-excited field and Green's function tensor are further obtained. These expansions have a fully analytical dependence on the NEBC and classical QNMs, thus transparently unveiling their impact on the nonclassical QNMs and source-excited electromagnetic field. For instance, a new expression of mode volume is proposed for analyzing the nonclassically corrected Purcell factor. The proposed theory is physically intuitive and computationally efficient which is enabled by the dominance of a small set of classical QNMs, thus providing an efficient tool for understanding and designing mesoscale plasmonic nanoresonators.

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.

Revealing topology with transformation optics

Symmetry deepens our insight into a physical system and its interplay with topology enables the discovery of topological phases. Symmetry analysis is conventionally performed either in the physical space of interest, or in the corresponding reciprocal space. Here we borrow the concept of virtual space from transformation optics to demonstrate how a certain class of symmetries can be visualised in a transformed, spectrally related coordinate space, illuminating the underlying topological transitions. By projecting a plasmonic system in a higher-dimensional virtual space onto a lower-dimensional system in real space, we show how transformation optics allows us to construct a topologically non-trivial system by inspecting its modes in the virtual space. Interestingly, we find that the topological invariant can be controlled via the singularities in the conformal mapping, enabling the intuitive engineering of edge states. The confluence of transformation optics and topology here can be generalized to other wave realms beyond photonics.

Efficient hybrid method for the modal analysis of optical microcavities and nanoresonators

We propose a novel hybrid method for accurately and efficiently analyzing microcavities and nanoresonators. The method combines the marked spirit of quasinormal mode expansion approaches, e.g., analyticity and physical insight, with the renowned strengths of real-frequency simulations, e.g., accuracy and flexibility. Real- and complex-frequency simulations offer a complementarity between accuracy and computation speed, opening new perspectives for challenging inverse design of nanoresonators.

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.

Quasinormal-Mode Perturbation Theory for Dissipative and Dispersive Optomechanics

Despite the several novel features arising from the dissipative optomechanical coupling, such effect remains vastly unexplored due to the lack of a simple formalism that captures non-Hermiticity in the engineering of optomechanical systems. In this Letter, we show that quasinormal-mode-based perturbation theory is capable of correctly predicting both dispersive and dissipative optomechanical couplings. We validate our model through simulations and also by comparison with experimental results reported in the literature. Finally, we apply this formalism to plasmonic systems, used for molecular optomechanics, where strong dissipative coupling signatures in the amplification of vibrational modes could be observed.

Perturbation theory for Kerr nonlinear leaky cavities

In emerging open photonic resonators that support quasinormal eigenmodes, fundamental physical quantities and methods have to be carefully redefined. Here, we develop a perturbation theory framework for nonlinear material perturbations in leaky optical cavities. The ambiguity in specifying the stored energy due to the exponential growth of the quasinormal mode field profile is lifted by implicitly specifying it via the accompanying resistive loss. The capabilities of the framework are demonstrated by considering a third-order nonlinear ring resonator and verified by comparing against full-wave nonlinear finite element simulations. The developed theory allows for efficiently modeling nonlinear phenomena in contemporary photonic resonators with radiation and resistive loss.

Dispersive optomechanics of supercavity modes in high-index disks

In this work, we study the dispersive coupling between optical quasi-bound states in the continuum at telecom wavelengths and GHz-mechanical modes in high-index wavelength-sized disks. We show that such cavities can display values of the optomechanical coupling rate on par with optomechanical crystal cavities (g₀/2π≃800kHz). Interestingly, optomechanical coupling of optical resonances with mechanical modes at frequencies well above 10 GHz seems attainable. We also show that mechanical leakage in the substrate can be extremely reduced by placing the disk over a thin silica pedestal. Our results suggest a new route for ultra-compact optomechanical cavities that can potentially be arranged in massive arrays forming optomechanical metasurfaces for application in signal processing or sensing.