DOI: 10.5061/dryad.xksn02vm3
title: Circularly polarized photoluminescence from nanostructured arrays of light emitters

description: Strategically designed metamaterials can influence the properties of light
 emitters in several ways, including shaping of the directionality and
 polarization of luminescence. These properties, however, are limited in
 systems where the luminophores uniformly coat the metamaterial. Here, we
 study and design metamaterials comprised of both Au nanobars and
 nanopatterned light emitters. We systematically investigate the role of
 spatial averaging, dipole orientation, chirality, near-field effects, and
 other factors for these multi-material systems. Finally, we discuss
 multiple design routes to create metasurfaces that can emit
 photoluminescence of any circular polarization at any arbitrary angle.
 These systems simultaneously exhibit high photoluminescence intensity and
 tailored, directional, and polarized photoluminescence.
description: The FDTD
 simulations in this report were performed using commercial software
 provided by Lumerical FDTD solutions (Release: 2021
 R2).  Far-field data was collected by
 building a simulation made up of a 23 x 23 array of gold nanobars placed
 on top of an ITO-coated glass substrate. The light emitters were Gaussian dipole
 sources with an emission wavelength of 630 nm. For each spatial position
 of the dipole source, three simulations were
 performed with the dipole oriented along the x, y, or z directions. A
 uniform 8 nm meshing was applied over the nanostructure. Perfectly Matched
 Layer boundary conditions were used in all directions. The Lumerical
 function "farfieldpolar3d" was used to compute the far-field
 electric field components in polar coordinates (E<sub>r</sub>,
 E<sub>θ</sub>, E<sub>φ</sub>).  The data were
 further processed and visualized in MATLAB R2021a. From the electric field
 components we calculate the intensity of right and left circularly
 polarized (RCP and LCP) light at different directions in the far-field,
 using the formula: I<sub>RCP</sub> =
 E<sub style="font-family:'Times New Roman' , serif;">θ</sub>∗E<sub>θ</sub><sup>*</sup> - iE<sub>θ</sub><sup>*</sup>∗E<sub style="font-family:'Times New Roman' , serif;">φ</sub> + iEφ<sup>*</sup>∗E<sub style="font-family:'Times New Roman' , serif;">θ </sub>+ E<sub style="font-family:'Times New Roman' , serif;">φ</sub>∗Eφ<sup>*</sup> I<sub>LCP</sub> = E<sub style="font-family:'Times New Roman' , serif;">θ</sub>∗E<sub>θ</sub><sup>*</sup> - iE<sub>θ</sub><sup>*</sup>∗E<sub style="font-family:'Times New Roman' , serif;">φ</sub> + iEφ<sup>*</sup>∗E<sub style="font-family:'Times New Roman' , serif;">θ </sub>+ E<sub style="font-family:'Times New Roman' , serif;">φ</sub>∗Eφ<sup>*</sup><sub style="font-family:'Times New Roman' , serif;"><br></sub> To capture the total intensity of RCP or LCP light emitted from an ensemble of dipole sources, we incoherently add I<sub>RCP</sub> and I<sub>LCP</sub> for each dipole in the ensemble. The normalized photoluminescnce (PL) intensity and degree of circular polarization (DCP) of the emitted light can then be calculated using the formula: PL = (I<sub style="white-space:pre-wrap;">RCP </sub>+ I<sub style="white-space:pre-wrap;">LCP</sub>)/max((I<sub style="white-space:pre-wrap;">RCP </sub>+ I<sub style="white-space:pre-wrap;">LCP</sub>)) DCP = (I<sub style="text-align:center;white-space:pre-wrap;">RCP </sub>- I<sub style="text-align:center;white-space:pre-wrap;">LCP</sub>)/(I<sub style="text-align:center;white-space:pre-wrap;">RCP </sub>+ I<sub style="text-align:center;white-space:pre-wrap;">LCP</sub>) The Fourier-space DCP and PL data were plotted using MATLAB's 'imagesc' command. All of the post-processed simulation results were saved as MATLAB .mat files.  Near-field data was collected by building an FDTD simulation of a single unit cell of the 23 x 23 array. A circularly polarized light source, aligned along the z direction, was added to the simulation by combining two linear polarized light sources with polarization and phase shifts of ±90°. Periodic boundary conditions were used in the x and y directions and Perfectly Matched Layer boundary conditions were used in the z-direction. 
description: MATLAB is required to open the .mat files.