Quasi-normal mode theory of the scattering matrix, enforcing fundamental constraints for truncated expansions

Benzaouia, Mohammed; Joannopoulos, John D.; Johnson, Steven G.; Karalis, Aristeidis

doi:10.1103/physrevresearch.3.033228

Cited by 27 publications

(18 citation statements)

References 29 publications

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“…On the other hand, the current coupled-mode formalism does not work well for resonance modes that are not well isolated. To accurately include the effects of all resonance modes supported by a resonator, it is necessary to introduce quasi-normal modes to the coupled-mode formalism. , Meanwhile, plane-wave channels do not describe the near field around the metasurface. More complex basis for the channels in the coupled-mode formalism are required to achieve inverse design of near field …”

Section: Discussionmentioning

confidence: 99%

Inverse Design of Metasurfaces Based on Coupled-Mode Theory and Adjoint Optimization

et al. 2021

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Metasurfaces typically have sizes much larger than the wavelength yet contain a large number of subwavelength features. Thus, it is difficult to design entire metasurfaces using full-wave simulations. However, without full-wave simulations, most existing design approaches cannot accurately model the interactions between the individual elements comprising the metasurface. Here, we demonstrate an approach for the design of resonant metasurfaces based on coupled-mode theory. Our approach fully describes wave dynamics and coupling in metasurfaces and is much more computationally efficient than full-wave simulations. As an example, we show that the combination of coupled-mode theory and adjoint optimization can be used for the inverse design of high-numerical-aperture (0.9) metalenses with sizes as large as 10000 wavelengths. The computation efficiency of our approach is orders of magnitude faster than full-wave simulations. Complex functionalities such as angle-multiplexed metasurface holograms can also be realized. With its accuracy and efficiency, the proposed framework can be a powerful design tool for large-scale resonant flat-optics devices.

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Section: Discussionmentioning

confidence: 99%

Inverse Design of Metasurfaces Based on Coupled-Mode Theory and Adjoint Optimization

et al. 2021

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“…This is because the largest contributions come from terms where β 0;m,k (z) is smallest due to the integral over the phase in Eq. (36). In this case, β 0;m,k (z) may be smallest when k = −1, 0, or 1 depending on the propagation directions of the incident wave and guided mode (if both propagate in the same direction, it is when k = 0).…”

Section: Validationmentioning

confidence: 98%

“…II C, for a particular instantaneous waveguide, we compute the guided mode and LPA solutions, then use these to compute the overlap integrals and phase terms in Eq. (36). While Eq.…”

Section: Validationmentioning

confidence: 99%

“…However, LPA and LUA cannot be applied to the "nonlocal" problem of radiation coupling to and from guided modes since in a periodic surface guided modes do * sefisher@mit.edu not radiate by definition [35]. This is in contrast to previous nonlocal metasurfaces employing leaky resonances [36][37][38][39][40][41][42][43] which radiate even for purely periodic surfaces [44]. On the other hand, guided-wave propagation can be treated by spatial coupled-wave theories (CWTs)-eigenmode-expansion methods resulting in a set of coupled ordinary differential equations in the mode coefficients, which can be solved perturbatively for slowly varying media [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

“…Other methods of domain decomposition besides LUA and LPA have been proposed to handle strong near-field intercell coupling, such as overlapping domains that model the overlapping regions from neighboring unit cells [61], combined with absorbing-wall domains that model each unit cell with perfectly matched layer boundary conditions [62]; however, these methods explicitly discard long-range interactions and hence omit guided-mode propagation. We also note that many techniques have been developed to design large-scale metasurface antennas, filters, and other devices at optical and microwave frequencies, but these make use of leaky waves rather than completely guided waves and thus solve a fundamentally different problem [36][37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient perturbative framework for coupling of radiative and guided modes in nearly periodic surfaces

2022

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We present a semianalytical framework for computing the coupling of radiative and guided waves in slowly varying (nearly uniform or nearly periodic) surfaces, which is especially relevant to the exploitation of nonlocal effects in large-area metasurfaces. Our framework bridges a gap in the theory of slowly varying surfaces: aside from brute-force numerical simulations, current approximate methods can model either guided or radiative waves but cannot easily model their coupling. We solve this problem by combining two methods: the locally periodic approximation, which approximates radiative scattering by composing a set of periodic scattering problems, and spatial coupled-wave theory, which allows the perturbative modeling of guided waves using an eigenmode expansion. We derive our framework for both nearly uniform and nearly periodic surfaces, and we validate each case against brute-force finite-difference time-domain simulations, which show increasing agreement as the surface varies more slowly.

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A Framework to Compute Resonances Arising from Multiple Scattering

Fischbach,

Betz,

Asadova

et al. 2024

Advcd Theory and Sims

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Numerous natural and technological phenomena are governed by resonances. In nanophotonics, resonances often result from the interaction of several optical elements. Controlling these resonances is an excellent opportunity to provide light with properties on demand for applications ranging from sensing to quantum technologies. The inverse design of large, distributed resonators, however, is typically challenged by high computational costs when discretizing the entire system in space. Here, this limitation is overcome by harnessing prior knowledge about the individual scatterers that form the resonator and their interaction. In particular, a transition matrix multi‐scattering framework is coupled with the state‐of‐the‐art adaptive Antoulas–Anderson (AAA) algorithm to identify complex poles of the optical response function. A sample refinement strategy suitable for accurately locating a large number of poles is introduced. The AAA algorithm is tied into an automatic differentiation framework to efficiently differentiate multi‐scattering resonance calculations. The resulting resonance solver allows for efficient gradient‐based optimization, demonstrated here by the inverse design of an integrated exciton‐polariton cavity. This contribution serves as an important step towards efficient resonance calculations in a variety of multi‐scattering scenarios, such as inclusions in stratified media, periodic lattices, and scatterers with arbitrary shapes.

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Quasi-normal mode theory of the scattering matrix, enforcing fundamental constraints for truncated expansions

Cited by 27 publications

References 29 publications

Inverse Design of Metasurfaces Based on Coupled-Mode Theory and Adjoint Optimization

Inverse Design of Metasurfaces Based on Coupled-Mode Theory and Adjoint Optimization

Efficient perturbative framework for coupling of radiative and guided modes in nearly periodic surfaces

A Framework to Compute Resonances Arising from Multiple Scattering

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