Symmetry constraints for vector scattering and transfer matrices containing evanescent components: Energy conservation, reciprocity, and time reversal

Byrnes, Niall; Foreman, Matthew R.

doi:10.1103/physrevresearch.3.013129

Cited by 10 publications

(15 citation statements)

References 60 publications

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“…The similar forms of γ 1 and γ 3 reflect the reciprocal symmetry present between scattering of an incoming plane wave scattering into an outgoing plane wave [74].…”

Section: Mean Enhancement Factorsmentioning

confidence: 80%

Role of Multiple Scattering in Single Particle Perturbations in Absorbing Random Media

Berk,

Foreman

2021

Preprint

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Speckle patterns produced by disordered scattering systems exhibit a sensitivity to addition of individual particles which can be used for sensing applications. Using a coupled dipole model we investigate how multiple scattering can enhance field perturbations arising in such random scattering based sensors. Three distinct families of multiple scattering paths are shown to contribute and the corresponding complex enhancement factors derived. Probability distributions of individual enhancement factors over the complex plane are characterised numerically within the context of surface plasmon polariton scattering in which absorption is shown to play an important role. We show that enhancements become more strongly dependent on individual scatterer properties when absorption losses are larger, however, amplitude enhancements ∼ 10 2 , comparable to low loss surface plasmons, are achievable through sensor optimisation. Approximate analytic expressions for the complex mean enhancements are also found, which agree well with simulations when loop contributions are negligible.

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“…The similar forms of γ 1 and γ 3 reflect the reciprocal symmetry present between scattering of an incoming plane wave scattering into an outgoing plane wave [74].…”

Section: Mean Enhancement Factorsmentioning

confidence: 80%

Role of Multiple Scattering in Single Particle Perturbations in Absorbing Random Media

Berk,

Foreman

2021

Preprint

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“…In this work, we used modes distributed on a Cartesian grid in k space, each having an equal weight given by w i = w = πk 2 /(2N k +1) for all i. Finally, we note that it is necessary to choose modes in inverse pairs to fully exploit scattering reciprocity [37].…”

Section: The Scattering Matrixmentioning

confidence: 99%

“…Finally, for mathematical convenience (see Ref. [37] for more details), we normalize the transmission and reflection matrices to t(j,i) and r(j,i) , which are given by t…”

Section: The Scattering Matrixmentioning

confidence: 99%

“…This matrix ensemble is the set of all scattering matrices corresponding to all possible microscopic configurations of a system with a given set of macroscopic properties, such as particle density, mean particle size etc. It is well known that for any non-absorbing system, physically admissible scattering matrices are constrained to be unitary due to energy conservation, with an additional symmetry constraint imposed when reciprocity or time reversal symmetry holds [36,37]. The earliest random matrix models for the scattering matrix, namely the circular ensembles, are based on the use of a uniform (Haar measure) distribution over the unitary group [38].…”

Section: Introductionmentioning

confidence: 99%

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Random matrix theory of polarized light scattering in disordered media

Byrnes¹,

Foreman²

2022

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In this work we present a method for generating random matrices describing electromagnetic scattering from disordered media containing dielectric particles with prescribed single particle scattering characteristics. Resulting scattering matrices automatically satisfy the physical constraints of unitarity, reciprocity and time reversal, whilst also incorporating the polarization properties of electromagnetic waves and scattering anisotropy. Our technique therefore enables statistical study of a variety of polarization phenomena, including depolarization rates and polarization-dependent scattering by chiral particles. In this vein, we perform numerical simulations for media containing isotropic and chiral spherical particles of different sizes for thicknesses ranging from the single to multiple scattering regime and discuss our results, drawing comparisons to established theory.

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“…This is because the loop paths associated with γ 2 are distinct from the scattering paths in γ 1,3 . In contrast, scattering trajectories contributing to γ 1 and γ 3 are partially related by reciprocity [44], such that a multiple scattering path from r N +1 to r i (associated with γ 1 ) has the same phase and amplitude as the reciprocal path going from r i to r N +1 (associated with γ 3 ). Correlation of |γ 1 | and |γ 3 | is hence dictated by the correlation between the additional propagation phases appearing in each enhancement factor, namely that of propagation of the scattered (incident) field from (to) the relevant scattering particle.…”

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confidence: 99%

Theory of Multiple Scattering Enhanced Single Particle Plasmonic Sensing

Berk,

Foreman

2021

Preprint

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Methods to increase the light scattered from small particles can help improve the sensitivity of many sensing techniques. Here, we investigate the role multiple scattering plays in perturbing the scattered signal when a particle is added to a random scattering environment. Three enhancement factors, parametrising the effect of different classes of multiple scattering trajectories on the field perturbation, are introduced and their mean amplitudes explored numerically in the context of surface plasmon polariton scattering. We demonstrate that there exists an optimum scatterer density at which the sensitivity enhancement is maximised, with factors on the order of 10 2 achievable. Dependence of the enhancement factors on scatterer properties are also studied.

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Symmetry constraints for vector scattering and transfer matrices containing evanescent components: Energy conservation, reciprocity, and time reversal

Cited by 10 publications

References 60 publications

Role of Multiple Scattering in Single Particle Perturbations in Absorbing Random Media

Role of Multiple Scattering in Single Particle Perturbations in Absorbing Random Media

Random matrix theory of polarized light scattering in disordered media

Theory of Multiple Scattering Enhanced Single Particle Plasmonic Sensing

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