All-optical information-processing capacity of diffractive surfaces

Abstract

The precise engineering of materials and surfaces has been at the heart of some of the recent advances in optics and photonics. These advances related to the engineering of materials with new functionalities have also opened up exciting avenues for designing trainable surfaces that can perform computation and machine-learning tasks through light–matter interactions and diffraction. Here, we analyze the information-processing capacity of coherent optical networks formed by diffractive surfaces that are trained to perform an all-optical computational task between a given input and output field-of-view. We show that the dimensionality of the all-optical solution space covering the complex-valued transformations between the input and output fields-of-view is linearly proportional to the number of diffractive surfaces within the optical network, up to a limit that is dictated by the extent of the input and output fields-of-view. Deeper diffractive networks that are composed of larger numbers of trainable surfaces can cover a higher-dimensional subspace of the complex-valued linear transformations between a larger input field-of-view and a larger output field-of-view and exhibit depth advantages in terms of their statistical inference, learning, and generalization capabilities for different image classification tasks when compared with a single trainable diffractive surface. These analyses and conclusions are broadly applicable to various forms of diffractive surfaces, including, e.g., plasmonic and/or dielectric-based metasurfaces and flat optics, which can be used to form all-optical processors. Layers of materials that diffract light with variable spacing between them can be adjusted or “trained” to perform information-processing tasks using light alone. Diffraction is the alteration of the propagation of light waves by structural features of the materials they encounter. Aydogan Ozcan and colleagues at the University of California, Los Angeles, USA, performed an analysis of optical neural networks composed of spatially engineered diffractive surfaces. They explored the power of multilayered networks to perform optical processing tasks, including image recognition and classification. They also determined mathematical rules describing the performance limits of the networks in relation to the number of diffractive surfaces they contained. Their work is relevant to various diffractive surfaces, including metasurfaces patterned with features smaller than the wavelength of light, and plasmonic materials governed by the coherent behavior of surface electrons.