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Register a new userAn efficient solver for the generalized normal modes of non-uniform open optical resonators
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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.
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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.
In [Z. Hu, R. Li, and Z. Qiao. Acceleration for microflow simulations of high-order moment models by using lower-order model correction. J. Comput. Phys., 327:225-244, 2016], it has been successfully demonstrated that using lower-order moment model correction is a promising idea to accelerate the steady-state computation of high-order moment models of the Boltzmann equation. To develop the existing solver, the following aspects are studied in this paper. First, the finite volume method with linear reconstruction is employed for high-resolution spatial discretization so that the degrees of freedom in spatial space could be reduced remarkably without loss of accuracy. Second, by introducing an appropriate parameter $tau$ in the correction step, it is found that the performance of the solver can be improved significantly, i.e., more levels would be involved in the solver, which further accelerates the convergence of the method. Third, Heuns method is employed as the smoother in each level to enhance the robustness of the solver. Numerical experiments in microflows are carried out to demonstrate the efficiency and to investigate the behavior of the new solver. In addition, several order reduction strategies for the choice of the order sequence of the solver are tested, and the strategy $m_{l-1} = lceil m_{l} / 2 rceil$ is found to be most efficient.
We study the cross-sectional profiles and spatial distributions of the fields in guided normal modes of two coupled parallel optical nanofibers. We show that the distributions of the components of the field in a guided normal mode of two identical nanofibers are either symmetric or antisymmetric with respect to the radial principal axis and the tangential principal axis in the cross-sectional plane of the fibers. The symmetry of the magnetic field components with respect to the principal axes is opposite to that of the electric field components. We show that, in the case of even $mathcal{E}_z$-cosine modes, the electric intensity distribution is dominant in the area between the fibers, with a saddle point at the two-fiber center. Meanwhile, in the case of odd $mathcal{E}_z$-sine modes, the electric intensity distribution at the two-fiber center attains a local minimum of exactly zero. We find that the differences between the results of the coupled mode theory and the exact mode theory are large when the fiber separation distance is small and either the fiber radius is small or the light wavelength is large. We show that, in the case where the two nanofibers are not identical, the intensity distribution is symmetric about the radial principal axis and asymmetric about the tangential principal axis.
We generalize normal mode expansion of Greens tensor $bar{bar{G}}(bf{r},bf{r})$ to lossy resonators in open systems, resolving a longstanding open challenge. We obtain a simple yet robust formulation, whereby radiation of energy to infinity is captured by a complete, discrete set of modes, rather than a continuum. This enables rapid simulations by providing the spatial variation of $bar{bar{G}}(bf{r},bf{r})$ over both $bf{r}$ and $bf{r}$ in one simulation. Few eigenmodes are often necessary for nanostructures, facilitating both analytic calculations and unified insight into computationally intensive phenomena such as Purcell enhancement, radiative heat transfer, van der Waals forces, and F{o}rster resonance energy transfer. We bypass all implementation and completeness issues associated with the alternative quasinormal eigenmode methods, by defining modes with permittivity rather than frequency as the eigenvalue. We obtain true stationary modes that decay rather than diverge at infinity, and are trivially normalized. Completeness is achieved both for sources located within the inclusion and the background through use of the Lippmann-Schwinger equation. Modes are defined by a linear eigenvalue problem, readily implemented using any numerical method. We demonstrate its simple implementation on COMSOL Multiphysics, using the default inbuilt tools. Results were validated against direct scattering simulations, including analytical Mie theory, attaining arbitrarily accurate agreement regardless of source location or detuning from resonance.
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equation for neutral and ionic solutions, respectively. In the present work solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented to the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of a ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency, and allow for the treatment of different boundary conditions, as for example surface systems. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
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