Scattering by circularly symmetric structured optical fields in stratified media

Jungho Mun, Hongyoon Kim, Seong-Won Moon, and Junsuk Rho

Phys. Rev. B 106, 184414 – Published 16 November 2022

Abstract

Structured optical fields (SOFs) with spatially inhomogeneous phase, amplitude, or polarization can excite substantially different optical responses in nanoscale scattering particles. Inhibition of low-order multipolar resonances, excitation of dark modes and anapoles, and spin and orbital angular momenta dichroism have been demonstrated, broadening the scope of nanoscale manipulations of optical resonances by using these engineered external SOFs. However, studying scattering effects illuminated by SOFs is more complicated than conventional plane wave illuminations, and the difficulty increases for scattering particles on a substrate. In this paper, we present explicit expressions of SOFs propagating through stratified media, or multilayered systems, and provide their beam-shape coefficients. Specifically, simple analytic expressions are provided for circularly symmetric Bessel beams passing through an interface. Then, scattering calculations for a dielectric sphere on a substrate illuminated by an evanescent optical vortex are performed via the $T$ -matrix method, which yields accurate and efficient results as compared with finite element analysis. This paper will find practical applications in modeling SOFs for realistic configurations of scattering of particles on a substrate at nonplanar nonparaxial external light source illuminations.

Received 1 September 2022
Revised 26 October 2022
Accepted 1 November 2022

DOI:https://doi.org/10.1103/PhysRevB.106.184414

Physics Subject Headings (PhySH)

Structured light Wave scattering

Polarization

Electromagnetic wave theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jungho Mun ^1,*, Hongyoon Kim¹, Seong-Won Moon¹, and Junsuk Rho ^1,2,†

¹Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang 37673, Republic of Korea
²Department of Chemical Engineering, Pohang University of Science and Technology, Pohang 37673, Republic of Korea

^*mjh92@postech.ac.kr
^†jsrho@postech.ac.kr

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Vol. 106, Iss. 18 — 1 November 2022

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Images

Figure 1
Gaussian beams passing through a Fabry-Pérot resonator, inserted from left to right. (a), (b) The near-field distributions of (a) collimated ( $w_{0} = 6 λ_{0}$ ) and (b) focused ( $w_{0} = λ_{0}$ ) Gaussian beams at $λ_{0} = 0.5 μ m \approx 600 THz$ . (c) Transmittance spectra of the collimated (black) and focused (blue) Gaussian beams and plane wave (red). The refractive index of glass substrate is 1.43, and the interfaces are illustrated by black solid lines. Scale bar: $1 μ m = 2 λ_{0}$ .
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Figure 2
Structured Bessel beams passing through an interface. Left panels show the $x O z$ plane and right panels show the $x y$ plane at $z = 100 nm$ . (a) Vortex Bessel beam with $(p_{x}, p_{y}) = (1, 0), l = 1$ , and $a_{0} = 20^{\circ}$ . The inset shows the phase of $E_{x}$ . (b) Cylindrical vector Bessel beam with $(p_{ρ}, p_{ϕ}) = (1, 1), l = 0$ , and $a_{0} = 20^{\circ}$ . (c) Evanescent Bessel beam with $(p_{x}, p_{y}) = (1, 0), l = 0$ , and $a_{0} = 45^{\circ}$ . (d) Evanescent vortex Bessel beam with $(p_{x}, p_{y}) = (1, i) / \sqrt{2}, l = 1$ , and $a_{0} = 45^{\circ}$ . Red and green arrows illustrate electric field vectors with $π / 2$ phase difference. Scale bar: $1 μ m = λ_{0}$ .
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Figure 3
Benchmark of scattering of a sphere on substrate illuminated by an evanescent optical vortex. (a) Schematic illustration of the scattering configuration. (b) Multipole-decomposed scattering cross sections calculated semianalytically and numerically with finite element analysis. (c), (d) Near fields calculated at $λ_{0} = 350$ nm (c) semianalytically and (d) numerically with FEM. The incident SOF is an evanescent vortex Bessel beam with $l = 1, α_{0} = 45^{\circ}$ , and polarization state $(p_{x}, p_{y}) = (1, i) / \sqrt{2}$ ; the sphere has refractive index 3.5, positioned at $r_{p} = (80 nm, 50 nm, 100 nm)$ .
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Figure 4
Parametric studies on scattering of a dielectric sphere on a substrate illuminated by a circularly symmetric Bessel beam. (a) Schematic illustration of the scattering configuration. (b) Multipole strength depending on the gap distance $g$ . The particle is at $r_{p} = (80 nm, 50 nm, g + R)$ . (c) Multipole strength depending on the offset distance $Δ x$ . The particle is at $r_{p} = (Δ x, 0, 100 nm)$ . (d) Multipole strength depending on the inclination angle $α_{0}$ . The particle is at $r_{p} = (80 nm, 50 nm, 100 nm)$ . The inclination angle $α_{0}$ is $45^{\circ}$ for (b) and (c); the polarization state is $(p_{x}, p_{y}) = (1, i) / \sqrt{2}$ .
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Figure 5
(a) Schematic illustration of the far-field scattering configuration. (b)–(d) Far-field radiation patterns at wavelengths (b) 450 nm, (c) 500 nm, and (d) 650 nm. The radial part of power flow normalized by the sphere circular area $\hat{r} \cdot \frac{1}{2} Re (E \times H) / (π R^{2})$ is plotted at $r = 1 m$ .
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