Strong chiral optical response from planar arrays of subwavelength metallic structures supporting surface plasmon resonances

F. Eftekhari and T. J. Davis

Phys. Rev. B 86, 075428 – Published 13 August 2012

Abstract

A strong differential response in the scattering of left and right circularly polarized light from surface plasmons in planar metal nanostructures is investigated theoretically and experimentally. We show that a strong chiral optical response can be obtained by an interference effect arising from a combination of resonance phase shifts in the metal structures and phase shifts associated with the rotation of the electric field vector. The effect is modeled using an analytical theory of localized surface plasmon resonances which predicts a maximum in the chiral response when the nanostructure exhibits at least two resonant modes, separated in frequency by $Γ / \sqrt{3}$ , where $Γ$ is the FWHM of the resonance, and when the angle between the dipole moments of the modes is oriented at 45 degrees. The predictions of the model agree well with numerical simulations based on the finite-difference time-domain method. The interference effect is demonstrated by optical measurements on planar metamaterials consisting of subwavelength arrays of gold rods. The effect is not related to optical activity, circular dichroism, diffraction, or phase shifts on propagation. The failure to satisfy the conditions for interference explains why some geometrically chiral structures show little or no differential scattering with circularly polarized incident light. This work provides criteria for designing new plasmonic nanostructures with strong chiral optical response.

Received 25 May 2012

DOI:https://doi.org/10.1103/PhysRevB.86.075428

Published by the American Physical Society

Authors & Affiliations

F. Eftekhari and T. J. Davis

CSIRO Materials Science and Engineering, Private Bag 33 Clayton, Victoria 3168, Australia and Melbourne Centre for Nanofabrication 151 Wellington Road Clayton, Victoria 3168, Australia

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Vol. 86, Iss. 7 — 15 August 2012

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Images

Figure 1
Examples of planar plasmonic nanostructures that exhibit geometric chirality but varying degrees of optical chirality: (a)–(c) these structures have been shown to have no chiral optical response; (d)–(f) these structures are not obviously chiral but show quite strong differential response to left and right circularly polarized light.Reuse & Permissions
Figure 2
Diagrams showing the oscillations of two LSP modes relative to the incident field for (a) LCP and (b) RCP. The colors represent the two different LSP modes and the white arrows on the structures indicate the orientations of the LSP dipole moments. The dashed curves in the graphs show the LSP oscillations with time, in units of $ω t$ , excluding the resonance phase shifts. The relative phases of the oscillations change sign with incident light changing from LCP to RCP. The solid lines include the phase differences due to the resonances (mode 1: $φ_{r}^{1} = π / 4$ ; mode 2: $φ_{r}^{2} = 3 π / 4$ ). The combined phase difference $Δ φ$ determines the amplitude of the sum of the oscillations that affects the intensity in the far field.Reuse & Permissions
Figure 3
The geometry used in the analytical model. (a) The metal structure on the $x − y$ plane showing the circularly polarized incident light and the direction of the scattered light. (b) A representation of two LSP modes on a single metal nanostructure showing the directions of the dipole moments. The color indicates the relative surface charge of each mode. Note that the LSP dipole moments may not be parallel to the structural features.Reuse & Permissions
Figure 4
(a) The term $| f_{r}^{k} | | f_{r}^{j} | \sin (φ_{r}^{k} - φ_{r}^{j})$ as a function of normalized frequency $(ω - ω_{r}^{k}) / Γ$ for a range of resonance differences $(ω_{r}^{k} - ω_{r}^{j}) / Γ$ . The optimum frequency difference (solid line) occurs for $(ω_{r}^{k} - ω_{r}^{j}) / Γ = 1 / \sqrt{3} \approx 0.58$ . (b) The two nanorods used in the FDTD simulation, representing a single meta-atom. Both nanorods are 25 nm wide, 20 nm thick, and made from gold embedded in a medium with permittivity $ε = 2$ . Nanorod 1 is 75 nm long with an orientation fixed at $θ_{1}^{1} = 90^{\circ}$ and the length of nanorod 2 was varied. (c) The scattering intensity difference calculated using FDTD for different resonances of nanorod 2 with $θ_{1}^{2} = 45^{\circ}$ . The resonances were altered by changing its length: 60, 65, 66.5, 68, and 70 nm. (d) The calculated dependence of the scattering intensity difference on $θ_{1}^{2}$ with nanorod 2, $l_{2} = 66.5$ nm.Reuse & Permissions
Figure 5
(a) An SEM image of the ebeam resist pattern on a gold film prior to etching. After etching the exposed gold is removed leaving gold nanorods in the same pattern as the resist. (b) The extinction spectra from arrays of single nanorods obtained with linearly polarized light parallel and perpendicular to the long axes of the rods. Nanorod 1 is 100 nm long and nanorod 2 is 80 nm long. Both sets of rods are 30 nm thick and 40 nm wide (c) The difference in the extinction for LCP and RCP for sets of nanorods with rod 2 at different angles. (d) The difference in the extinction for sets of rods with nanorod 2 lengths of 60, 70, 80, 90, and 100 nm. This shifts the resonances so that the relative frequency differences are 0.92, 0.74, 0.33, $- 0.16$ , and $- 0.22$ respectively.Reuse & Permissions
Figure 6
The normalized peak extinction differences associated with left and right circularly polarized light as functions of (a) nanorod angle and (b) resonance difference, as obtained from FDTD numerical simulations (circles), experimental results (triangles), and theory (solid line). The size of the triangles relates to the approximate errors in the measurements.Reuse & Permissions

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