Supplementary Information: Learning incoherent light emission steering from metasurfaces using generative models 1. Experimental Details 1.1. Design principles of the metasurface

Dielectric metasurfaces are made up of a sub-wavelength array of optical nano-resonators which can exert complete control over the phase, amplitude and polarization of light. Here we design a reconfigurable metasurface that can dynamically control the direction of light emission from within the metasurface. This design process is done using a commercial electromagnetic wave simulator Lumerical FDTD which solves Maxwell’s equations in the timedomain, and Fourier transforms the solution to gain information about the optical resonators based on the refractive index distribution. The reflection properties of a single unitcell (nano-pillar) of GaAs resonators sitting on a distributed Bragg reflector (DBR) stack are calculated using the ‘grating s-params’ module in Lumerical FDTD at the emission wavelength of the InAs quantum dots (QDs). We model the semiconductor alloy composition, refractive index distribution, the geometry (height, width, pitch etc.) of the resonator and DBR as optimization parameters. The properties of reflection (amplitude and phase) of this metasurface are used as the figure of merit to optimize for these geometries and refractive indices. Ideally a reconfigurable metasurface, we want to maximize the phase shift as a function of the absorbed pump intensity while minimizing the optical absorption losses due to the free-carrier generation. These metasurface are typically made up low quality factor (Qf ≃ 25) resonances which by design can change the phase of light near the resonances by nearly 2π with minimal absorption losses in the resonator. As the optical pump photons are absorbed by the GaAs resonators, we create populations of electrons and holes for a very short (carrier lifetime of 26ps [1, 2]) period of time with in the GaAs resonator. During this time period the refractive index of the resonators get modified based on the Drude free-carrier effect such that more carriers decreases the real part and increases the imaginary part of the index. We specifically chose GaAs as the resonator material due to its low-electron effective mass leading to large index change with minimal pump intensity. This change in the refractive index as a blue shift in the resonant wavelength while increasing the absorption of the same. Thus as the resonance blue shifts through the emission wavelength of the metasurface (1250nm), the phase of the light reflected form the metasurface shifts. The optical pump profile from the spatial light modulator (SLM) which translates into a refractive profile induces a spatial phase profile on the metasurface which ultimately forms the additional optical momentum steering the emission from the Figure 1. Experimental Details: A) Measurement setup for PL steering. The schematic shows how the optical pump pattern on the 800nm pulse is imaged onto the sample using the spatial light modulator (SLM). The PL from the sample is imaged in the backfocal-plane (BFP) of the objective lens to form the output of the system. The blue arrows indicate propagation of the input image from the SLM to be de-magnified and projected on to the metasurface sample. B) Metasurface Characteristics: Reflection (blue curve) of the metasurface with respect to gold and emission spectra (orange curve) from the metasurface during continuous wave pumping at 808nm. The peak in reflection coincides with the peak in emission from the metasurface. The inset at the top of the graph shows an SEM image of the fabricated metasurface