Dielectric Meta Surface¶

This is an example of simple but common meta-atom structure, a nano-disk on a substrate in a twofold periodic square lattice. The example and parameters are taken from Berzins et al. [1]. The material data employed for silicon is a freely available data set from http://www.refractiveindex.info/. The 3D unit cell is periodic in $x-$ and $y-$ direction. It contains a disk (or cylinder) situated on a substrate and is surrounded by a background material. The materials in the example are chosen according to [1] as silicon (disk), glass (substrate) and air (background).

The grating is illuminated from above by linear polarized plane waves with $s$ and $p$ polarization. JCMsuite computes the near field distributions.

The following figures show the near-fields and intensities within the structure for perpendicular plane wave incidence from the above at a wavelength of $550\mathrm{nm}$ .

Field vectors and intensity outside the scatterer.¶

_images/field_vectors_p_pol+both_planes.png

Field vectors for $p$ -polarized illumination in two planes overlayed over the geometry.¶

The post process FourierTransform computes the amplitudes of the transmitted diffraction orders. The post process ScatteringMatrix computes the scatterometric quantities from the plane wave decomposition obtained in the FourierTransform.

Spectral dependency

In the reference paper [1] the transmission spectrum is adapted to provide color-filtering. The script data_analysis/run_scan_illumination.py aims to reproduce the spectral plot in Fig.1. of this publication.

Phase profile

To re-shape the transmitted wave front one needs control over its phase locally. For a given structure we obtain this phase from the Jones matrices computed by the post process ScatteringMatrix. This yields a complex-valued transmission coefficient for p and s polarized components of the transmitted orders for any two linear independent incident fields. Its phase corresponds to the phase shift of the transmitted wave with respect to the incident wave. While the absolute phase is rarely of interest, its relative dependency on the atom’s parameters and the incident light typically is. The following figure depicts the amplitude and phase of the transmission coefficient (due to the symmetry this is polarization independent):

_images/spectral_scan_transmission_coefficient.png

This figure is generated by the script data_analysis/run_scan_illumination.py as well.

A change of the radius and height of the nano-disk influences the phase and transmission. This dependency is investigated with the script data_analysis/run_scan_geometry.py. Here, the diameter and height of the nano-disks are varied and the change in phase in and transmission is recorded.

_images/transmission_parameter_sensitivity.png

Bibliography

[1]	(1, 2, 3) Berzins, Jonas, Fabrizio Silvestri, Giampiero Gerini, Frank Setzpfandt, Thomas Pertsch, and Stefan MB Baeumer. “Color filter arrays based on dielectric metasurface elements.” In Metamaterials XI, vol. 10671, p. 106711F. International Society for Optics and Photonics, 2018.