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The rapid advancement and high integration of photonic integrated circuits (PICs) have enabled energy-efficient and fast computation in compact chip designs. A fundamental challenge in both classical and quantum information processing is the ability to create light wavefronts with complex spatial amplitude and phase distributions. Traditional methods that involve splitting light into multiple channels and modulating each one individually typically lead to chip area and power waste. We introduce a compact programmable PIC capable of generating arbitrary complex spatial states in a power-conserving manner. The proposed system harnesses multipath interference in an interlaced arrangement of phase modulator arrays and photonic lattices to transform excitation from a single input channel to a multi-channel output state with the required amplitude and phase profile. For an N-port device, we demonstrate that two layers of N phase shifters can approximate arbitrary N-dimensional amplitude states with sufficient accuracy, while three layers allow complete control over both amplitude and phase. Furthermore, we experimentally demonstrate arbitrary state generation with a silicon photonic platform by utilizing a measurement-and-feedback setting forin situprogramming of the device to optimize the desired output state. The present solution allows for a flexible design, compatible across various material platforms, for the integration of state generators used in future PICs that require arbitrarily complex inputs. 

We introduce a photonic integrated circuit solution for the direction-of-arrival estimation in the optical frequency band. The proposed circuit is built on discrete sampling of the phasefront of an incident optical beam and its analog processing in a photonic matrix-vector multiplier that maps the angle of arrival into the intensity profile at the output ports. We derive conditions for perfect direction-of-arrival sensing for a discrete set of incident angles and its continuous interpolation and discuss the angular resolution and field-of-view of the proposed device in terms of the number of input and output ports of the matrix multiplier. We show that while, in general, a non-unitary matrix operation is required for perfect direction finding, under certain conditions, it can be approximated with a unitary operation that simplifies the device complexity while coming at the cost of reducing the field of view. The proposed device will enable real-time direction-finding sensing through its ultra-compact design and minimal digital signal processing requirements. 

Abstract Random matrices are fundamental in photonic computing because of their ability to model and enhance complex light interactions and signal processing capabilities. In manipulating classical light, random operations are utilized for random projections and dimensionality reduction, which are important for analog signal processing, computing, and imaging. In quantum information processing, random unitary operations are essential to boson sampling algorithms for multiphoton states in linear photonic circuits. Random operations are typically realized in photonic circuits through fixed disordered structures or through large meshes of interferometers with reconfigurable phase shifters, requiring a large number of active components. In this article, we introduce a compact photonic circuit for generating random matrices by utilizing programmable phase modulation layers interlaced with a fixed mixing operator. We show that using only two random phase layers is sufficient for producing output optical signals with a white-noise profile, even for highly sparse input optical signals. We experimentally demonstrate these results using a silicon-based photonic circuit with tunable thermal phase shifters and waveguide lattices as mixing layers. The proposed circuit offers a practical method for generating random matrices for photonic information processing and for applications in data encryption.