Generalization of the Circular Dichroism from Metallic Arrays That Support Bloch-Like Surface Plasmon Polaritons

The broken mirror symmetry in subwavelength photonic systems has manifested many interesting chiroptical effects, such as optical rotation and circular dichroism. When such systems are placed periodically in a lattice form, in addition to intrinsic chirality, extrinsic chirality also takes part, and the overall effect depends not only on the basis and lattice but also the excitation configuration. Here, we study planar chiral nanohole arrays in square lattice that support Bloch-like surface plasmon polaritons (SPPs) and clarify how the system geometry and the excitation contribute to circular dichroism. By using temporal coupled mode theory, the dissymmetry factor and the scattering matrix of the arrays are analytically formulated. Remarkably, we find the dissymmetry factor depends only on the coupling polarization angle and the in-coupling phase difference between the p- and s-polarizations. Furthermore, the upper limit of the dissymmetry factor at ±2 can be reached simply by orienting the lattice of the arrays for properly exciting the Bloch-like SPPs and at the same time making the basis mimic two orthogonal and relatively displaced dipoles, demonstrating the interplay between extrinsic and intrinsic chirality. The models have been verified by numerical simulations and experiments, yielding dissymmetry factors of 1.82 and 1.55, respectively, from the proposed dual slot system.

Figure 1

(a) The setup for angle- and polarization-resolved optical microscopy where L, focusing lens; P, polarizer; BS, beam splitter; QWP, quarter-wave plate; BFP, back focal plane; OB, objective lens; S, sample; SP, spectrometer. The red beam indicates the incident beam path and the blue beam defines the scattered beam path from the sample. Inset: the plane-view SEM image of the FIB-fabricated L-shaped metallic nanohole array with the scale bar being 1 µm. (b) The schematic of the sample and the excitation configuration. The blue region is the glass substrate while the yellow region is the gold thin film. The incident polar angle is defined as θ with respect to the surface normal, or the z direction, along the incident plane and the incident azimuthal angle is defined as ϕ between the incident plane and the Γ-X direction, i.e., the x direction.

Figure 2

The measured $\varphi$-dependent mappings of (a) R_pp, (b) R_sp, (c) R_ps and (d) R_ss. The SPP dispersion relations deduced from the analytical phase-matching equation are shown as red dashed lines in (a) and are labelled as (n_x,,n_y). The mappings are not symmetric with respect to ϕ = 90° due to the chiral basis.

Figure 3

The measured $\varphi$-dependent absorption mappings of the (−1,0), (0,−1), and (1,0) SPP modes taken under (a) RCP and (b) LCP excitations. The color scale bars indicate the strength of absorption. (c) The plot of the dissymmetry factor g as a function of ϕ.

Figure 4

The simulated (a)–(d) amplitudes and (e)–(h) phases of the reflection coefficients r_pp, r_ps, r_sp, and r_ss for ϕ = 120° (forward incidence) and 300° (backward incidence). The solid lines are the best fits using the CMT deduced S. Inset: the schematic of the simulation unit cell with P = 550 nm, hole depth = 60 nm, a  = 400, b = 250 nm, w = 125 nm.

Figure 5

(a) The ${\alpha }^{\mathrm{in}}$ as a function of $\varphi$ obtained by fitting the simulation and the experimental results with the CMT-deduced S and by using the field manipulation method. (b) The ${{\delta }_p}^{\mathrm{in}}-{{\delta }_s}^{\mathrm{in}}$ plot obtained by fitting the simulation with the CMT deduced S and by using the field manipulation method. (c) The $g$ as a function of $\varphi$ calculated by direct FEM and by using the αⁱⁿ and ${{\delta }_p}^{\mathrm{in}}-{{\delta }_s}^{\mathrm{in}}$ given in (a) and (b) from CMT and field manipulation. The experimental results extracted from Fig. 3 are also overlaid for comparison. (d) The plot of ${\alpha }^{\mathrm{in}}-{\alpha }_{\mathrm{basis}}^{\mathrm{in}}$ as a function of ϕ. It is almost constant with ϕ when away from the cross points.

Figure 6

(a) The evolution of the basis with arm length along the Γ-X direction. The arm length b is varied from 125 to 625 nm. (b) The variation of ${\alpha }_{\mathrm{basis}}^{\mathrm{in}}$ with b provided ${\alpha }_{\mathrm{lattice}}^{\mathrm{in}}$ is 0° all the time. (c) The plot of the ratio of the field amplitude perpendicular to the SPPs propagation direction E_⊥ and the total field amplitude E as a function of b, showing a consistent behavior with ${\alpha }_{\mathrm{basis}}^{\mathrm{in}}$.

Figure 7

(a) The evolution of the basis with orientation along the Γ-X direction. The rotation angle is varied from 0 to 60° with respect to the vertical axis. (b) The variation of ${\alpha }_{\mathrm{basis}}^{\mathrm{in}}$ with rotation angle provided ${\alpha }_{\mathrm{lattice}}^{\mathrm{in}}$ is 0° all the time. (c) The plot of the ratio of the field amplitude perpendicular to the SPPs propagation direction E_⊥ and the total field amplitude E as a function of the rotation angle, showing a consistent trend.

Figure 8

(a) The unit cell of the proposed dual slot structure and the plane-view SEM image of the dual slot periodic structure fabricated by FIB with the scale bar = 1 µm. The plots of simulated (b) αⁱⁿ and ${{\delta }_p}^{\mathrm{in}}-{{\delta }_s}^{\mathrm{in}}$ and (d) g as a function of a. The plots of simulated (c) αⁱⁿ and ${{\delta }_p}^{\mathrm{in}}-{{\delta }_s}^{\mathrm{in}}$ and (e) g as a function of s. The highest g obtained from the two series are 1.52 and 1.82, respectively. (f) The absorption spectra of the (0,−1) SPP mode measured under LCP and RCP excitations, showing that g reaches 1.55.