Brillouin-Wigner perturbation theory in open electromagnetic systems

Muljarov, Egor A.; Langbein, Wolfgang Werner; Zimmermann, R.

doi:10.1209/0295-5075/92/50010

Cited by 165 publications

(297 citation statements)

References 20 publications

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“…It should be noted that this formulation of the normalization is slightly different than in most of our previous works on the resonant state expansion [10,[15][16][17][18][19][20][21]25,27,28], which is valid also for magnetic and bianisotropic materials [26]. This formulation can be reduced to our previous results for nonmagnetic materials that are solely described by the electric field, the electric permittivity, and the electric current as a special case.…”

Section: Resonant Statesmentioning

confidence: 78%

“…When normalizing the resonant states appropriately [10,[15][16][17][18][19][20][21]26,27], they can be used together with possible cuts to expand the Green's dyadic with outgoing boundary conditions as follows:…”

Section: Resonant Statesmentioning

confidence: 99%

“…Regarding the Green's dyadic, it has been shown that the residues of its pole expansion can be derived from the resonant electric field distributions of the resonant states when normalizing them appropriately [10]. Several approaches have been suggested for the normalization of resonant states [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

“…Several approaches have been suggested for the normalization of resonant states [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. This includes approximate formulations for highquality modes [23][24][25], the utilization of perfectly matched layers [14] or, equivalently, complex coordinates [11] in the exterior of the system, as well as numerical approaches [20,22].…”

Section: Introductionmentioning

confidence: 99%

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How to calculate the pole expansion of the optical scattering matrix from the resonant states

Weiß

Muljarov

2018

Phys. Rev. B

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We present a formulation for the pole expansion of the scattering matrix of open optical resonators, in which the pole contributions are expressed solely in terms of the resonant states, their wave numbers, and their electromagnetic fields. Particularly, our approach provides an accurate description of the optical scattering matrix without the requirement of a fit for the pole contributions, or the restriction to geometries, or systems with low Ohmic losses. Hence, it is possible to derive the analytic dependence of the scattering matrix on the wave number with low computational effort, which allows for avoiding the artificial frequency discretization of conventional frequency-domain solvers of Maxwell's equations and for finding the optical far-and near-field response based on the physically meaningful resonant states. This is demonstrated for three test systems, including a chiral arrangement of nanoantennas, for which we calculate the absorption and the circular dichroism.

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Section: Resonant Statesmentioning

confidence: 78%

Section: Resonant Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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How to calculate the pole expansion of the optical scattering matrix from the resonant states

Weiß

Muljarov

2018

Phys. Rev. B

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“…Based on the concept of RSs, a rigorous approach in electrodynamics called resonant-state expansion (RSE) has recently been developed [21], enabling accurate calculation of RSs in photonic systems [22][23][24][25][26]. The RSE calculates RSs of a given optical system using RSs of a basis system which is typically analytically treatable, as a basis for expansion, and maps Maxwell's wave equation onto a linear matrix eigenvalue problem.…”

Section: Formulation Of Wg-rsementioning

confidence: 99%

Resonant-state expansion of light propagation in nonuniform waveguides

et al. 2017

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A new rigorous approach for precise and efficient calculation of light propagation along nonuniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoingwave boundary conditions, form a natural basis for expansion of the local electromagnetic field. Using such an expansion at fixed frequency, we convert the wave equation for light propagation in a non-uniform waveguide into an ordinary second-order matrix differential equation for the expansion coefficients depending on the coordinate along the waveguide. We illustrate the method on several examples of non-uniform planar waveguides and evaluate its efficiency compared to the aperiodic Fourier modal method and the finite element method, showing improvements of one to four orders of magnitude. A similar improvement can be expected also for applications in other fields of physics showing wave phenomena, such as acoustics and quantum mechanics.

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Substrate‐Induced Maximum Optical Chirality of Planar Dielectric Structures

Gorkunov,

Antonov,

Mamonova

et al. 2024

Advanced Optical Materials

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Resonant dielectric planar structures can interact selectively with light of particular helicity thus providing an attractive platform for “chiral flat optics”. The absence of mirror‐symmetry planes defines geometric chirality, and it remains the main condition for achieving strong circular dichroism. For planar optical structures such as photonic‐crystal slabs and metasurfaces, breaking the out‐of‐plane mirror symmetry is especially challenging, as it requires to fabricate meta‐atoms with a tilt, variable height, or vertically shifted positions. Although transparent substrates formally break out‐of‐plane mirror symmetries, their optical effect is typically subtle being rarely considered for enhancing optical chirality. Here it is revealed that low‐refractive‐index substrates can induce up to maximum intrinsic optical chirality in otherwise achiral metastructures so that the transparency to waves of one helicity is combined with resonant blocking of waves of the opposite helicity. This effect originates from engineering twisted photonic eigenstates of different parities. The perturbation analysis developed in terms of the resonant‐state expansion reveals how the eigenstate coupling induced by a substrate gives rise to a pair of chiral resonances of opposite handedness. The general theory is confirmed by the specific examples of light transmission in the normal and oblique directions by a rotation‐symmetric photonic‐crystal slab placed on different transparent substrates.

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Brillouin-Wigner perturbation theory in open electromagnetic systems

Cited by 165 publications

References 20 publications

How to calculate the pole expansion of the optical scattering matrix from the resonant states

How to calculate the pole expansion of the optical scattering matrix from the resonant states

Resonant-state expansion of light propagation in nonuniform waveguides

Substrate‐Induced Maximum Optical Chirality of Planar Dielectric Structures

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