Scattering and absorption invariance of nonmagnetic particles under duality transformations

Qingdong Yang, Weijin Chen, Yuntian Chen, and Wei Liu

Phys. Rev. A 102, 033517 – Published 18 September 2020

Abstract

We revisit the total scatterings (in terms of extinction, scattering, and absorption cross sections) by arbitrary clusters of nonmagnetic particles that support optically induced magnetic responses. Our reexamination is conducted from the perspective of the electromagnetic duality symmetry, and it is revealed that all total scattering properties are invariant under duality transformations. This secures that, for self-dual particle clusters, the total scattering properties are polarization independent for any fixed incident direction, while, for non-self-dual particle clusters, two scattering configurations that are connected to each other through a duality transformation would exhibit identical scattering properties. This electromagnetic duality induced invariance is irrelevant to specific particle distributions or wave incident directions, which is illustrated for both random and periodic clusters.

Received 21 May 2020
Accepted 31 August 2020

DOI:https://doi.org/10.1103/PhysRevA.102.033517

Physics Subject Headings (PhySH)

Dualities in field theory Light-induced magnetic effects Mie scattering Nanophotonics

Core-shell nanoparticles

Atomic, Molecular & Optical

Authors & Affiliations

Qingdong Yang¹, Weijin Chen¹, Yuntian Chen^1,2,*, and Wei Liu ^3,†

¹School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People's Republic of China
²Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People's Republic of China
³College for Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China

^*yuntian@hust.edu.cn
^†wei.liu.pku@gmail.com

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 102, Iss. 3 — September 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Scattering efficiency spectra (both total scattering and partial dipolar contributions from ED and MD) for the Ag core-dielectric ( $In = 3.4$ ) shell spherical particle ( $R_{1} = 61$ nm and $R_{2} = 208$ nm). The resonant position is marked at $λ_{A} = 1449$ nm. (b) A randomly chosen particle cluster consisting of four such particles, with three particles on the $x − y$ plane (one on the $x$ axis and the other two with position vectors making the same angle of $120^{\circ}$ with respect to the $x$ axis) and the fourth particle is placed at the $z$ axis. The distances between the particles and the coordinate origin are $o a = 800$ nm, $o b = 1000$ nm, $o c = 1200$ nm, and $o d = 1100$ nm. (c),(d) The scattering and extinction efficiency for three polarization directions ( $θ = 10^{\circ}, 50^{\circ}, 80^{\circ}$ with respect to the $x$ axis) when the incident plane wave is propagating along the $z$ axis. (e),(f) The efficiency for three polarization directions ( $θ = 10^{\circ}, 50^{\circ}, 80^{\circ}$ with respect to the $z$ axis) when the incident wave is propagating along the $- x$ axis.
Reuse & Permissions
Figure 2
Scattering efficiency spectra of (a) an E-particle with $R_{1} = 78$ nm and $R_{2} = 122$ nm and (b) an M-particle with $R_{1} = 40$ nm and $R_{2} = 140$ nm. The two particles support respectively pure ED and MD moments at the marked resonant point $λ_{B} = 984$ nm. (c),(d) The dual-paired configurations with a duality transformation of $β = π / 2$ (swapping the positions of E-particles and M-particles) with two different incident directions ( $k_{i} ∥ z$ and $k_{i} ∥ - x$ ). The particle position parameters are the same as those in Fig. 1. (e),(f) The scattering and extinction efficiency for the incidence along $z$ with polarization angles chosen as $θ = 30^{\circ}$ in (c) and $120^{\circ}$ in (d). (g),(h) The scattering and extinction efficiency for another incidence along $- x$ .
Reuse & Permissions
Figure 3
Scattering efficiency spectra of (a) an $H_{1}$ -particle with $R_{1} = 77$ nm and $R_{2} = 214$ nm and (b) an $H_{2}$ -particle with $R_{1} = 28$ nm and $R_{2} = 220$ nm. The two particles support both ED and MD moments at the marked resonant point $λ_{C} = 1560$ nm. (c),(d) The dual-paired configurations with a duality transformation of $α = π / 2$ (swapping the positions of $H_{1}$ -particles and $H_{2}$ -particles) with two different incident directions ( $k_{i} ∥ z$ and $k_{i} ∥ - x$ ). The position parameters are the same as those in Fig. 1. (e),(f) The scattering and extinction efficiency for the incidence along z with polarization angles chosen as $θ = 20^{\circ}$ in (c) and $110^{\circ}$ in (d). (g),(h) The scattering and extinction efficiency for another incidence along $- x$ .
Reuse & Permissions
Figure 4
(a) 1D lattice of D-particles with period $T = 1510$ nm. Extinction and scattering efficiency spectra are shown in (b) and (c) for a normal incidence ( $k_{i} ∥ z$ ) with polarization angle $θ = 10^{\circ}, 30^{\circ}, 45^{\circ}$ and in (d) and (e) for an oblique incidence ( $ϕ = 30^{\circ}$ ) with $θ = 0, 45^{\circ}, 90^{\circ}$ . The marked point A corresponds to the resonant wavelength ( $λ_{A} = 1449$ nm) of the D-particle.
Reuse & Permissions
Figure 5
(a),(b) Two dual-paired 1D lattices consist of E, M-particles of $T = 1020$ nm and $d = 80$ nm. Extinction and scattering efficiency spectra are shown: in (c) and (d) for a normal incidence ( $k_{i} ∥ z$ ), with polarization angles $θ = 20^{\circ}$ and $110^{\circ}$ for the configurations in (a) and (b), respectively; in (e) and (f) for an oblique incidence ( $ϕ = 20^{\circ}$ ), with polarization angles $θ = 90^{\circ}$ and 0 for (a) and (b), respectively. The marked point B corresponds to the common resonant wavelength ( $λ_{B} = 984$ nm) of the E, M-particles.
Reuse & Permissions
Figure 6
(a),(b) Two dual-paired 1D lattices consist of $H_{1}$ , $H_{2}$ -particles of $T = 1520$ nm and $d = 50$ nm. Extinction and scattering efficiency spectra are shown: in (c) and (d) for a normal incidence ( $k_{i} ∥ z$ ), with polarization angles $θ = 30^{\circ}$ and $120^{\circ}$ for the configurations in (a) and (b), respectively; in (e) and (f) for an oblique incidence ( $ϕ = 30^{\circ}$ ), with polarization angle $θ = 90^{\circ}$ and 0 for (a) and (b), respectively. The marked point C corresponds to the common resonant wavelength ( $λ_{C} = 1560$ nm) of the $H_{1}$ , $H_{2}$ -particles.
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information