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.
| 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.
| 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.](https://owkb.myws.site/wp-content/uploads/kb-articles/post-816_metasurface_v3-3/metasurface_v3/Images/c-Si.png)
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].
