Employing quasidegenerate optical modes for chiral sensing

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Employing quasidegenerate optical modes for chiral sensing

S. F. Almousa, T. Weiss, and E. A. Muljarov

Phys. Rev. B 109, L041410 – Published 26 January 2024

Abstract

Chiral molecules cannot be superposed with their own mirror image. This yields two enantiomers of opposite handedness that are made out of the same building blocks, but interact differently with their environment. Hence, chiral sensing is of utmost importance for biology, chemistry, and life sciences. However, the impact of the handedness and chirality is very weak in most sensing schemes. Nevertheless, it has been demonstrated recently that chirality may result in strong coupling between resonant states with high quality factors. This is achieved by spectrally overlapping two quasibound states in the continuum in a periodic array of nanostructures. We demonstrate that this requires neither quasibound states in the continuum nor periodic arrays, which is exemplified for three achiral systems: a sphere with equal permittivity and permeability, a single core-shell structure, and a dielectric metasurface. For such achiral systems, we have shown previously that isolated resonant states exhibit a quadratic energy shift in the Pasteur parameter. However, for quasidegenerate states, we observe, using the rigorous resonant-state expansion and full-wave simulations, a linear energy shift and linear splitting in the presence of a chiral medium or molecule. Thus, the splitting is more sensitive to low concentrations of chiral molecules, which paves the way for novel chiral sensing schemes.

Received 14 September 2023
Revised 6 December 2023
Accepted 2 January 2024

DOI:https://doi.org/10.1103/PhysRevB.109.L041410

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Chirality Metamaterials

Nanoparticles Non-Hermitian systems Optical microcavities

Mode coupling theory Perturbative methods Whispering gallery mode resonators

Atomic, Molecular & OpticalAccelerators & BeamsCondensed Matter, Materials & Applied PhysicsFluid DynamicsInterdisciplinary PhysicsNonlinear DynamicsParticles & FieldsPhysics of Living SystemsPolymers & Soft MatterStatistical Physics & ThermodynamicsEnergy Science & TechnologyGravitation, Cosmology & AstrophysicsNetworksNuclear PhysicsPhysics Education ResearchPlasma PhysicsQuantum Information, Science & Technology

Authors & Affiliations

S. F. Almousa ^1,2, T. Weiss^3,4, and E. A. Muljarov¹

¹School of Physics and Astronomy, Cardiff University, Cardiff CF24 3AA, United Kingdom
²Department of Physics and Astronomy, King Saud University, Riyadh 11451, Saudi Arabia
³4th Physics Institute and SCoPE, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
⁴Institute of Physics, University of Graz, and NAWI Graz, Universitätsplatz 5, 8010 Graz, Austria

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Issue

Vol. 109, Iss. 4 — 15 January 2024

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Images

Figure 1
(a) Wave numbers (magenta crosses) of strictly degenerate TE and TM RSs with angular momentum number $l = 5$ of a basis sphere of radius $R$ and $ɛ = μ = 4$ , surrounded by vacuum. Right inset: radial dependence of tangential ( $∥$ ) and normal ( $⊥$ ) components of the normalized electric and magnetic fields of the fundamental WGM in TE (lines) and TM (triangles) polarizations, as defined in Eq. (28) of Ref. [29]. Left inset: Unperturbed degenerate (magenta cross) and perturbed split wave numbers of the fundamental WGM due to the dielectric ( $Δ ɛ = 0.01$ , green crosses), chiral ( $ϰ = 10^{- 3}$ , black squares), and simultaneous dielectric and chiral ( $Δ ɛ = 0.01$ , $ϰ = 10^{- 3}$ , blue squares) homogeneous perturbations of the basis sphere. (b) Real part of the wave-number splitting, $k_{+} - k_{-}$ (left axis), of the TE-TM degenerate fundamental WGM as a function of the Pasteur parameter $ϰ$ for chiral perturbations of the sphere (black), vacuum (blue), and sphere with an additional perturbation $Δ ɛ = 0.01$ (green), with the black-to-green chiral sensitivity enhancement factor (red, right axis, see main text for details) and the corresponding sketches of the system given on the right. Solid lines and squares are, respectively, the exact results and the RSE solution given by Eq. (7).
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Figure 2
(a) Real part of the wave numbers of $l = 200$ TE (blue) and TM (red) WGMs of a basis core-shell system, surrounded by vacuum, with $ɛ_{1} = 4$ in the core, shell thickness $Δ R = 0.1 R$ , and system radius $R$ , as functions of the shell permittivity $ɛ_{2}$ . (b) Real part of the unperturbed (dashed lines) and perturbed (black solid lines) wave numbers, and (c) square moduli of the TE (blue) and TM (red) expansion coefficients in Eq. (6) of the perturbed lower branch as functions of $ɛ_{2}$ , for a homogeneous chiral core perturbation of $ϰ = 10^{- 3}$ . (d) Real part of the normalized electric field of TE (blue) and the imaginary part of the magnetic field of TM (red) WGMs of the core-shell system at $ɛ_{2} = 2$ . The wave numbers of the TE and TM modes are, respectively, $k_{1} R = 179.409265396 - 3.08 \times 10^{- 7} i$ and $k_{2} R = 179.408443931 - 3.69 \times 10^{- 7} i$ . (e) Real part of the wave-number splitting, $k_{+} - k_{-}$ , of the TE-TM quasidegenerate WGMs in (d), as a function of the Pasteur parameter $ϰ$ for chiral perturbations of the core (black), shell (blue), and vacuum (green), with the corresponding sketches of the system given on the top. Note that the blue curves in (d) and (e) and the green one in (e) have been rescaled for the sake of clarity. The actual results can be obtained by multiplying the curves with the same-color factors.
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Figure 3
(a) Real part of the wave-number splitting, $k_{+} - k_{-}$ , for the TE-TM quasidegenerate WGMs in Fig. 2 with magnetic quantum numbers $m = 0$ (black) and $m = \pm 1$ (red), perturbed by a chiral molecule with effective volume $V_{p} / V = 10^{- 7}$ and $ϰ = 1$ placed near the shell at a distance $d$ , as a function of normalized center distance $(d + R) / R$ . (b) As in (a), but as a function of $ϰ$ for $d = - 0.005 R$ .
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Figure 4
(a) Schematic of a dielectric metasurface of high-index disks ( $n_{r} = 3.5$ ) with diameter $d$ , period $a$ , height $h$ , and interparticle distance $g$ . (b) Splitting of the wave number as a function of Pasteur parameter $ϰ$ . The splitting typically starts quadratically (gray lines), except for the case of quasidegeneracy (black lines), for which we have fine-tuned all parameters except for the refractive index of the disk. (c) Real and (d) imaginary parts of the wave numbers of the electric (red lines) and magnetic (blue lines) dipolar modes as a function of aspect ratio $h / d$ for $d = 505.1 nm$ , $g = 222.8 nm$ , and a surrounding medium with $n_{r} = 1.498$ . The quasidegeneracy occurs for $h = 221.7 nm$ . Insets in (c) show the resonant magnetic (top) and electric (bottom) fields of the magnetic and electric dipole mode, respectively, at $h = 219.7 nm$ , while arrows mark the aspect ratios for the curves in (b).
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