We report on the realization of an on-chip waveguide platform capable of creating arbitrary two-dimensional refractive index profiles in situ and in real-time. The device exhibits complex multimode dynamics which we train to perform machine learning. We tune the refractive index profile in situ using a backpropagation algorithm to perform audio and image classification with up to 50-dimensional inputs. The two-dimensional programmability is realized by sandwiching a photoconductive film and a lithium niobate slab waveguide between two flat electrodes. While applying voltage between the electrodes, we program the effective index of the waveguide by projecting different light patterns onto the photoconductive film. The effective index increases by 10^-3 in illuminated regions via the electro-optic effect, free from any measurable memory effects or cyclic degradation. In conclusion, we developed a photonics platform with versatile spatial programmability that opens new avenues for optical computing and photonic inverse-design.
Deep learning acceleration with integrated photonics has typically employed a circuit-centric approach with Mach-Zehnder interferometers. This requires a large spatial footprint, which has motivated the direct training of spatial refractive index distribution within a slab waveguide. Here, we demonstrate through simulations that nonlinear optical material platforms with large electro-optic coefficients can capitalize on this approach. We show that a linear device with realistic device parameters can perform 50 by 50 unitary matrix multiplications. We also performed MNIST digit classification, achieving 90.5% classification accuracy with minimal digital preprocessing. Finally, we comment on device implementation with Lithium Niobate or Barium Titanate slab waveguides.
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