Three-dimensional integral equation approach to light scattering, extinction cross sections, local density of states, and quasi-normal modes

Lasson, Jakob Rosenkrantz de; Mørk, Jesper; Kristensen, Philip Trøst

doi:10.1364/josab.30.001996

Cited by 24 publications

(38 citation statements)

References 49 publications

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“…A numerical variant of this approach is QNM calculations via a Fourier Modal Method framework [18,46,47,48,50]. Another option is to calculate the QNMs via an integral equation formulation [17,42,44,45]. In such approaches, the radiation condition is built in via analytical continuation of the Green tensor, which manifestly fulfills the correct radiation condition.…”

Section: Qnm Calculation Methodsmentioning

confidence: 99%

“…For treating QNMs in general structures, a variety of numerical methods have been employed and are still under active development for both QNM calculation and normalization. These include the use of volume [17,42] or surface [43,44,45] integral equation formulations, as well as the Fourier Modal Method (FMM) -also known as rigorous coupled wave analysis -for periodic structures [46,47], or for single resonators by use of so-called Perfectly Matched Layers (PMLs) [18,48]. In two-dimensional coupled cavity-waveguide structures, the QNMs have been calculated by a Dirichlet-to-Neumann technique in Ref.…”

Section: Theoretical Developmentsmentioning

confidence: 99%

“…2 were calculated with the volume integral equation (VIE) method described in Ref. [42]. This method is specialized to the problem of collections of spherical scatterers, for which it provides relatively precise results.…”

Section: Qnms Of the Plasmonic Dimermentioning

confidence: 99%

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Modeling electromagnetic resonators using quasinormal modes

et al. 2020

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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.

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Section: Qnm Calculation Methodsmentioning

confidence: 99%

Section: Theoretical Developmentsmentioning

confidence: 99%

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Modeling electromagnetic resonators using quasinormal modes

et al. 2020

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“…For example, if we consider a dipole emitter at position r a with a dipole moment = d d n a (n a is a unit vector), the relative SE emission rate is [29] [29]. The Green functions may be computed in a number of ways [6,17,22], but in general they are rather expensive to calculate.…”

Section: Green Function Expansion In Terms Of Normalized Qnmsmentioning

confidence: 99%

Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics

et al. 2014

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We describe a powerful and intuitive theoretical technique for modeling light-matter interactions in classical and quantum nanoplasmonics. Our approach uses a quasinormal mode (QNM) expansion of the photon Green function within a metal nanoresonator of arbitrary shape, together with a Dyson equation, to derive an expression for the spontaneous decay rate and far field propagator from dipole oscillators outside resonators. For a single QNM, at field positions outside the quasi-static coupling regime, we give a closed form solution for the Purcell factor and generalized effective mode volume. We augment this with an analytic expression for the divergent local density of optical states very near the metal surface, which allows us to derive a simple and highly accurate expression for the electric field outside the metal resonator at distances from a few nanometers to infinity. This intuitive formalism provides an enormous simplification over full numerical calculations and fixes several pending problems in QNM theory.

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“…However, this scattered field is not the same field as the QNM and it cannot be properly normalized for use in quantum optics, e.g., for obtaining the Purcell factor and effective mode volume [12]-two well known quantities that help describe the underlying physics of cavity light-matter interactions. While some frequency-domain techniques exist for computing the QNMs of MNRs [18,19], it is highly desirable to be able to compute the QNMs using the commonly employed and general FDTD technique.The FDTD method is already widely used by the plasmonics community, and its accuracy for obtaining the enhanced field has been verified against other numerical techniques such as the multipole expansion technique [20]. In addition, the LDOS can be calculated by employing a dipole excitation source [21][22][23], which can also model local field effects, e.g., associated with finite-size photon emitters inside a MNR [21].…”

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confidence: 99%

Design of an efficient single photon source from a metallic nanorod dimer: a quasi-normal mode finite-difference time-domain approach

Hughes

2014

Opt. Lett.

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We describe how the finite-difference time-domain (FDTD) technique can be used to compute the quasinormal mode (QNM) for metallic nano-resonators, which is important for describing and understanding light-matter interactions in nanoplasmonics. We use the QNM to model the enhanced spontaneous emission rate for dipole emitters near a gold nanorod dimer structure using a newly developed QNM expansion technique. Significant enhanced photon emission factors of around 1500 are obtained with large output β-factors of about 60%. [7]. While the optical properties of MNRs are being actively pursued, numerically modelling of the basic cavity physics is extremely demanding, and analytical solutions of the modes only exists for very simple structures such as spheres. For resonant cavity structures, the natural modes of the system are called quasinormal modes (QNMs) [8,9], defined as the frequency domain solutions to the wave equation with open boundary conditions (the Silver-Müller radiation condition). Kristensen et al. [10] first used the QNMs to introduce a rigorous definition of the "generalized effective mode volume" and Purcell factor [11], and applied these results to photonic cavity structures. For MNRs, the QNMs also form the natural starting point for developing analytical theories of lightmatter interactions in nanoplasmonics [12][13][14].One of the most common numerical techniques for obtaining the cavity mode for dielectric cavities is the finite-difference time-domain (FDTD) technique [15]. The FDTD technique allows one to simulate open boundary conditions with "perfectly matched layers" (PMLs) located at the leaky mode region outside the cavity. For dielectric cavities, this open-boundary FDTD approach has been shown to yield excellent agreement with direct integral equation methods [10]. Other timedomain techniques such as the discontinuous Galerkin time-domain approach can also use PMLs [16]. For metals, a major problem occurs when using the usual mode calculation approach with a dipole excitation source, since the extracted mode depends sensitively on the dipole position [17], and is therefore incorrect. Thus it has been common practice to excite the MNR with a plane wave source and obtain the scattered field. However, this scattered field is not the same field as the QNM and it cannot be properly normalized for use in quantum optics, e.g., for obtaining the Purcell factor and effective mode volume [12]-two well known quantities that help describe the underlying physics of cavity light-matter interactions. While some frequency-domain techniques exist for computing the QNMs of MNRs [18,19], it is highly desirable to be able to compute the QNMs using the commonly employed and general FDTD technique.The FDTD method is already widely used by the plasmonics community, and its accuracy for obtaining the enhanced field has been verified against other numerical techniques such as the multipole expansion technique [20]. In addition, the LDOS can be calculated by employing a dipole excitation source [21][22][23], wh...

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Three-dimensional integral equation approach to light scattering, extinction cross sections, local density of states, and quasi-normal modes

Cited by 24 publications

References 49 publications

Modeling electromagnetic resonators using quasinormal modes

Modeling electromagnetic resonators using quasinormal modes

Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics

Design of an efficient single photon source from a metallic nanorod dimer: a quasi-normal mode finite-difference time-domain approach

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