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Register a new userQuasinormal mode solvers for resonators with dispersive materials
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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 rises 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 nano-resonators 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, in the perspective to elaborate standards for the computation of resonance modes.
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We present a quantized quasinormal approach to rigorously describe coupled lossy resonators, and quantify the quantum coupling parameters as a function of distance between the resonators. We also make a direct connection between classical and quantum quasinormal modes parameters and theories, offering new and unique insights into coupled open cavity resonators. We present detailed calculations for coupled microdisk resonators and show striking interference effects that depend on the phase of the quasinormal modes, an effect that is also significant for high quality factor modes. Our results demonstrate that commonly adopted master equations for such systems are generally not applicable and we discuss the new physics that is captured using the quantized quasinormal mode coupling parameters and show how these relate to the classical mode parameters. Using these new insights, we also present several models to fix the failures of the dissipative Jaynes-Cummings type models for coupled cavity resonators. Additionally, we show how to improve the classical and quantum lossless mode models (i.e., using normal modes) by employing a non-diagonal mode expansion based on the knowledge of the quasinormal mode eigenfrequencies, and analytical coupled mode theory, to accurately capture the mode interference effects for high quality factors.
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 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 are observed.
Perturbation theory is a kind of estimation method based on theorem of Taylor expansion, and is useful to investigate electromagnetic solutions of small changes. By considering a sharp boundary as a limit of smoothed systems, previous study has solved the problem when applying standard perturbation theory to Maxwells equations for small shifts in isotropic dielectric interfaces. However, when dealing with anisotropic materials, an approximation is conducted and leads to an unsatisfactory error. Here we develop a modified perturbation theory for small shifts in anisotropically dielectric interfaces. By using optimized smoothing function for each component of permittivity, we obtain a method to calculate the intrinsic frequency shifts of anisotropic permittivity field when boundaries shift, without approximation. Our method shows accurate results when calculating eigenfrequencys shifts in strong-anisotropy materials, and can be widely used for small shifts in anisotropically dielectric interfaces.
We demonstrate that yttrium iron garnet microspheres support optical whispering gallery modes similar to those in non-magnetic dielectric materials. The direction of the ferromagnetic moment tunes both the resonant frequency via the Voigt effect as well as the degree of polarization rotation via the Faraday effect. An understanding of the magneto-optical coupling in whispering gallery modes, where the propagation direction rotates with respect to the magnetization, is fundamental to the emerging field of cavity optomagnonics.
Quantum emitters coupled to plasmonic resonators are known to allow enhanced broadband Purcell factors, and such systems have been recently suggested as possible candidates for on-demand single photon sources, with fast operation speeds. However, a true single photon source has strict requirements of high efficiency (brightness) and quantum indistinguishability of the emitted photons, which can be quantified through two-photon interference experiments. To help address this problem, we employ and extend a recently developed quantized quasinormal mode approach, which rigorously quantizes arbitrarily lossy open system modes, to compute the key parameters that accurately quantify the figures of merit for plasmon-based single photon sources. We also present a quantized input-output theory to quantify the radiative and nonradiative quantum efficiencies. We exemplify the theory using a nanoplasmonic dimer resonator made up of two gold nanorods, which yields large Purcell factors and good radiative output beta factors. Considering an optically pulsed excitation scheme, we explore the key roles of pulse duration and pure dephasing on the single photon properties, and show that ultrashort pulses (sub-ps) are generally required for such structures, even for low temperature operation. We also quantify the role of the nonradiative beta factor both for single photon and two-photon emission processes. Our general approach can be applied to a wide variety of plasmon systems, including metal-dielectrics, and cavity-waveguide systems, without recourse to phenomenological quantization schemes.
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