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.

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_r, E_θ, E_φ).  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_RCP = E_θ∗E_θ^* - iE_θ^*∗E_φ + iEφ^*∗E_θ + E_φ∗Eφ^*

I_LCP = E_θ∗E_θ^* - iE_θ^*∗E_φ + iEφ^*∗E_θ + E_φ∗Eφ^*

To capture the total intensity of RCP or LCP light emitted from an ensemble of dipole sources, we incoherently add I_RCP and I_LCP 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_RCP + I_LCP)/max((I_RCP + I_LCP))

DCP = (I_RCP - I_LCP)/(I_RCP + I_LCP)

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. 

MATLAB is required to open the .mat files.