WAVEFRONT CONTROL FOCUS large-scale networks have proven effective for the forecasting of chaotic time series, a task where prediction error grows exponentially with time, and where accuracy improves with reservoir size.
Complex optical propagation is a good match for this approach: light scattering can provide large-scale mode mixing while an SLM can encode the input information onto the wavefront of the light beam. A fundamental limitation is that light propagation through conventional optical components at low power is linear. While linear transformations are central to many computational tasks, such as matrix multiplication and Fourier transforms, nonlinear mappings are essential in machine
Figure 1. Optical reservoir computing framework using a static scattering material. A spatial light modulator encodes information, and the resulting speckle pattern intensity is measured with a camera.
learning to increase the expressivity of the resulting algorithm. Optical nonlinearities could provide a valuable resource for computing, but typically rely on the interaction of high-power optical fields with nonlinear materials. In practice, achieving sufficiently strong light-matter interactions can be challenging, and may introduce substantial optical losses, limiting their efficiency and scalability. Here, we show how wavefront shaping can be used to introduce structural nonlinearity into a system made entirely of linear optical components.
STRUCTURAL NON LINEARITY USING LINEAR OPTICAL COMPONENTS To introduce the concept of structural nonlinearity, we first consider the interaction of light with a scattering medium. A material with a spatially varying dielectric constant ε can be described by its scattering potential V = k 0
2
( ε-1). The scattering potential thus describes the spatial variations of the optical properties of the medium that affect the propagation of light through the material. For a monochromatic
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