Three-Dimensional Anisotropic Metamaterials as Triaxial Optical Inclinometers

Abstract

Split-ring resonators (SRRs) present an attractive avenue for the development of micro/nano scale inclinometers for applications like medical microbots, military hardware, and nanosatellite systems. However, the 180° isotropy of their two-dimensional structure presents a major hurdle. In this paper, we present the design of a three-dimensional (3D) anisotropic SRR functioning as a microscale inclinometer enabling it to remotely sense rotations from 0° to 360° along all three axes (X, Y, and Z), by employing the geometric property of a 3D structure. The completely polymeric composition of the cubic structure renders it transparent to the Terahertz (THz) light, providing a transmission response of the tilted SRRs patterned on its surface that is free of any distortion, coupling, and does not converge to a single point for two different angular positions. Fabrication, simulation, and measurement data have been presented to demonstrate the superior performance of the 3D micro devices.

Figure 1

Illustration of two- and three-dimensional split-ring resonators (SRRs) and their simulated transmission response. (a) A conventional, two-dimensional SRR with L = 36 µm, g = 4 µm, and a = 48 µm, that can be rotated along the X-, Y-, and Z-axis at angles θ_x, θ_y, θ_z degrees, respectively. At the initial position the resonator has the wave at normal incidence, magnetic field (H) polarized perpendicular to the gap and electric field (E) polarized parallel to the gap. (b) Showing the weak transmission observed when rotated about Y-axis (θ_y) as opposed to the strong first mode (θ = 0°) and second mode (θ_z = 90°) (c) Overlap of the resonance at 0.52 THz for rotations of 30°, 150°, 210°, and 330° about the Z-axis. (d) Transmission for the initial position (θ = 0°) and (θ_z = 180°), proving the isotropy of the transmission for any angle θ and nπ ± θ (n = 1, 2). (e) A cubic three-dimensional split ring resonator with L = 36 µm, g = 4 µm, and a = 110 µm, capable of maintaining a high SNR when rotated along all three-axes. (f–h) Simulated transmission response of the cube showing, (f) the high but ambiguous transmission response when rotated about Y-axis, (g) an isotropic transmission response for any angle θ and nπ ± θ (n = 1, 2) similar to the 2-D resonator, and (h) perfect overlap of the transmission at 0° and 180°. (i) A cubic rotation sensor with varying resonator length along each axis with L₁ = 72 µm, L₂ = 54 µm and L₃ = 36 µm while ‘g’ and ‘a’ are kept constant as before. (j–l) Simulated transmission response of the cube showing, (j) the ability of the cube to maintain the high transmission for Y-axis rotation, (k) significant changes in transmission between rotations of angle θ, and nπ ± θ (n = 1, 2), and (l) special case of a 180° rotation that perfectly overlaps the θ = 0° initial position.

Figure 2

Effect of the angular offset on the anisotropy of the 3D inclinometer. (a) Cubic rotation sensor with an angular offset of β_x, β_y, and β_z for each resonator L₃, L₁, and L₂, respectively. (b–d) Simulation results for the cubic sensor. (b) The variation in the first mode resonance strength as a function of the angular offset obtained by placing only 1 of the 3 resonators at a single time to avoid couplings; L₂ and L₃ have a 180° period but the L₁ resonator has no symmetry in its transmission. (c) Graph showing the anisotropic effect of adding angular offset; the resonator L₁ demonstrates a significant change in amplitude for a 180° rotation about any axis. (d) Zoomed in graph of (c) showing the variance in transmission of the L₁ resonator.

Figure 3

Simulation results for the rotation of the 3D cube. (a) Cubic inclinometer rotated about X-, Y-, and Z-axis at angles θ_x, θ_y, and θ_z, respectively. Variation in resonance strength of each resonator obtained by simulating rotations along (b) X-axis, (c) Y-axis, (d) Z-axis in steps of 15° from 0–360° proving that for no two angles do the values of all three resonators overlap each other. The resonance amplitudes are obtained at the resonant frequencies of the L₁ (0.28 THz), L₂ (0.38 THz), and L₃ (0.55 THz) resonators.

Figure 4

Fabrication process of the Triaxial inclinometer. (a) Illustration of the two dimensional planar configuration before the self-folding is initiated, showing the SU-8 panels, the Au SRRs and the SPR 220 hinges (b) Illustration of the self-folding process, demonstrating the melting of the hinge causing it to flow and generating a surface tension force that slowly lifts up and folds the panel to a 90° angle (c) Illustration of the folded 3D cubic structure through surface tension driven self-assembly, where the SU-8 panels form the faces of the cube once the hinges re-solidify (d) Optical images of the fabrication process for the cubic SRR inclinometer, starting with the patterning of Au SRRs, followed by the deposition of SU-8 panels and the SPR 220 hinges.

Figure 5

Optical Image of the 500 μm three-dimensional cubic inclinometer. (a) Three-dimensional cubic inclinometer with SU-8 panels, SPR 220 hinges, and Au SRRs of varying lengths with a tilt patterned on the surface. The cube consists of 5 × 5 array of 72 μm resonators (tilted at 20°), 6 × 6 array of 54 μm resonators (tilted at 15°), and 9 × 9 array of 36 μm resonators (tilted at 10°). Resonators on the opposite faces are identical. (b) A zoomed-in optical image of the 3D cubic inclinometer.

Figure 6

THz TDS measurement results for the cubic inclinometer. (a) Optical image of the experimental setup for THz transmission measurement, showing a 500 µm cube placed on the circular aperture with the inset showing the polarization direction of the THz wave. (b) Measured transmission response displaying the ability of the cube to distinguish various angles when rotated about any axis through a change in transmission. (c) Measured transmission response demonstrating a clear change in transmission and breaking of the 180° isotropy of the cube. (d) Measured frequency spectra of the cubic structure observed while rotating the cube about the direction of wave vector (k) in steps of 40° (e) Measured variation in the transmission response at the fundamental resonant frequency of the 3 resonators defined on the faces of a cube when rotated along the wave vector (k).