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A perfect absorber using an all-dielectric metasurface

1 A perfect absorber using an all-dielectric metasurface

Metasurfaces, which may modify the amplitude, phase, and polarisation of incident light, are the two-dimensional counterpart of bulk metamaterials. They are optically tiny scatterers (known as meta-atoms) arranged in periodic or aperiodic two-dimensional (2D) configurations that are typically seen on a thin substrate (around a few hundred micrometer).

In this article, OptiFDTD is used to model an all-dielectric metasurface composed of crystalline silicon (\(c-Si\)) meta-atoms on a silica (\(SiO_{2}\)) substrate to exhibit perfect absorption at a specified wavelength (0.46 \(\mu\)m) as reported in [1].

1.2 Design

The 3D design of the metasurface is modelled by a unit cell consisting of one meta-atom. The meta-atom is an elliptic cylinder with major, minor axis and thickness equal to 0.190 \(\mu\)m, 0.176 \(\mu\)m and 0.108 \(\mu\)m, respectively. The periodicity of the metasurface is 0.280 \(\mu\)m along the x and y axes. Figure 1 shows the 3D editor image (left) and the schematic (right) of the unit cell with corresponding dimensions. Figure 2 shows the structure in the OptiFDTD layout view.

The wafer dimensions in the simulation region are chosen as length = 1 \(\mu\)m and width = 0.28 \(\mu\)m. The boundary conditions at z = 0. \(\mu\)m and z = 1.0 \(\mu\)m are chosen as absorbing perfectly matched layer (APML), while the boundary conditions in x and y directions are periodic boundary condition (PBC) positioned at x (y) = -0.140 \(\mu\)m and x (y) = 0.140 \(\mu\)m. The substrate is created using a linear waveguide set to a channel waveguide profile (WG_channel_example) from z = 0.5 to 1.0 \(\mu\)m. The elliptic cylinder is a linear waveguide set to a fiber profile (WG_fiber_example) with Rx = 0.095 \(\mu\)m and Ry = 0.088 \(\mu\)m.

The optical source was configured using the input plane (positioned at z = 0.3 \(\mu\)m) with a rectangular distribution, see table 1 for further details.

Details of the optical source employed in the simulation
Optical source features Value
Wavelength ( \(\mu\)m ) 0.60
Half Width ( \(\mu\)m ) 0.28
Polarization X
Time domain shape Sine-Modulated Gaussian Pulse

The absorption (A) is calculated through observation areas recording the reflection (\(R\)) and transmission (\(T\)) and

\[\begin{equation}A = 1-R-T.\end{equation}\]

The observation areas (XY) used were located at z = 0.2 \(\mu\)m and z = 0.8 \(\mu\)m for reflection and transmission respectively.

The c-Si is represented as a dispersive material based on the experimental data taken from [2-3] shown in Figure 3. The material fit is achieved using a Lorentz-Drude material with 3 resonances shown in table 2.

The 3D editor image of the unit cell in OptiFDTD (left). The schematic of the unit cell with corresponding dimensions (right). d_{1} = 0.190 \mu\text{m}, d_{2} = 0.176 \mu\text{m}, h = 0.108 \mu\text{m} and p = 0.280 \mu\text{m}.
The layout for the simulation of the metasurface with the input plane (red line) and two XY observation areas for calculating reflection and transmission.
Lorentz-Drude fit data for c-Si
Strength Plasma Frequency
( rad/s )
Resonant Frequency
( rad/s )
Damping
( rad/s )
7.140530 7.057110e+15 7.057110e+15 2.643950e+12
3.702920 5.280530e+15 5.280530e+15 3.106500e+14
1.000000 4.557600e+14 0.000000e+00 1.102740e+11
The n and k terms the refractive index for both the experimental data taken from [2-3] as well as the fit shown as the hollow circles.

After convergence testing, the spatial mesh parameters (\(\Delta\)x, \(\Delta\)y and \(\Delta\)z) were chosen as 1.5 nm. Testing also confirmed that 35e3 time-steps are required for accurate results.

1.3 Results

The normalized reflection and transmission spectra obtained from the simulation of the metasurface are shown in Fig. 4. At 0.467 \(\mu\)m, it can be observed that both the transmission and reflection vanish and perfect absorption (A = 1) is achieved. Physically, it is originated by the interference of induced electric and magnetic quadrupoles inside the mata-atoms around \(\lambda\) = 0.46 \(\mu\)m [1].

The absorption, reflection, and transmission spectra for the metasurface illuminated by an x-polarized plane wave. The grey dashed line corresponds to 0.467 \mum, the wavelength at which perfect absorption occurs.

References:

  1. Xu, Rongyang, and Junichi Takahara. “All-dielectric perfect absorber
    based on quadrupole modes.” Optics Letters 46, no. 15, pp. 3596-3599,
    2021.
  2. Aspnes, David E., and A. A. Studna. “Dielectric functions and
    optical parameters of si, ge, gap, gaas, gasb, inp, inas, and insb from
    1.5 to 6.0 ev.” Physical review B 27, no. 2, p. 985, 1983.
  3. M. Polyanskiy. “Optical constants of Si (Silicon).”
    refractiveindex.info. https://refractiveindex.info/?shelf =
    main&book = Si&page = Aspnes (accessed Nov. 30, 2022).

Files:

  1. A perfect absorber using an all-dielectric metasurface: main.pdf (163113 KB)

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