PHYSICAL REVIEW LETTERS 123, 060401 (2019) 0031-9007=19=123(6)=060401 (7) 060401-1

Introducing structure into photon pair generation via spontaneous parametric down‐conversion (SPDC) is shown to be useful for controlling the output state and exploiting new degrees of freedom for quantum technologies. This paper presents a new method for simulating first‐ and second‐order correlations of the down‐converted photons in the presence of structured pump beams and shaped nonlinear photonic crystals. This method is nonperturbative, and thus accounts for high‐order effects, and can be made very efficient using parallel computing. Experimental results of photodetection and coincidence rates in complex spatial configurations are recovered quantitatively by this method. These include SPDC in 2D nonlinear photonic crystals, as well as with structured light beams such as Laguerre Gaussian and Hermite Gaussian beams. This simulation method reveals conservation rules for the down‐converted signal and idler beams that depend on the nonlinear crystal modulation pattern and the pump shape. This scheme can facilitate the design of nonlinear crystals and pumping conditions for generating non‐classical light with pre‐defined properties.

We report complete spatial shaping (both phase and amplitude) of the second-harmonic beam generated in a nonlinear photonic crystal. Using a collinear second-order process in a nonlinear computer generated hologram imprinted on the crystal, the desired beam is generated onaxis and in the near field. This enables compact and efficient one-dimensional beam shaping in comparison to previously demonstrated off-axis Fourier holograms. We experimentally demonstrate the second-harmonic generation of high-order Hermite-Gauss, top hats and arbitrary skyline-shaped beams.

In this Letter, we report the dynamic control of the spatial shape of the second harmonic (SH) beam generated in a nonlinear crystal, by controlling the phase of the input fundamental beam before entering the crystal. This method enables 2D beam shaping and does not require any special fabrication beforehand. We have shown in simulation and experiment that this is possible for both short and long crystals: for short crystals, we assume the transverse phase of the SH beam is doubled relative to the input phase of the fundamental beam; for longer crystals, genetic algorithms were used in order to solve the inverse phase problem, which generally does not have an analytical solution. The method we present enables us to dynamically shape a beam in a nonlinear process, using standard crystals and optical equipment, and without the need to use any optical element after the nonlinear crystal.

Harnessing the full complexity of optical fields requires complete control of all degrees-of-freedom within a region of space and time -an open goal for present-day spatial light modulators (SLMs), active metasurfaces, and optical phased arrays. Here, we solve this challenge with a programmable photonic crystal cavity array enabled by four key advances: (i) near-unity vertical coupling to high-finesse microcavities through inverse design, (ii) scalable fabrication by optimized, 300 mm full-wafer processing, (iii) picometer-precision resonance alignment using automated, closed-loop "holographic trimming", and (iv) out-of-plane cavity control via a high-speed µLED array. Combining each, we demonstrate near-complete spatiotemporal control of a 64-resonator, two-dimensional SLM with nanosecond-and femtojoule-order switching. Simultaneously operating wavelength-scale modes near the space-and time-bandwidth limits, this work opens a new regime of programmability at the fundamental limits of multimode optical control.