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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. 

Recent investigations suggest that the discrete linear unitary group $U\left(N\right)$can be represented by interlacing a finite sequence of diagonal phase operations with an intervening unitary operator. However, despite rigorous numerical justifications, no formal proof has been provided. Here, we show that elements of $U\left(N\right)$can be decomposed into a sequence of $N$-parameter phases alternating with one-parameter propagators of a lattice Hamiltonian. The proof is based on building a Lie group by alternating these two operators and showing its completeness to represent $U\left(N\right)$for a finite number of layers. This is numerically verified by using Haar random matrices as targets, showing a convergence for exactly $N$layers. As a specific application, we propose an integrated all-optical logic gate device that performs OR, NAND, XOR, and XAND tasks within a lossless and passive optical circuit design. 

We demonstrate a compact multilayer GaAs–AlAs structure for passive optical edge detection at multiple wavelengths. Through the inverse design of the layer thicknesses, this structure manipulates spatial frequency components of an incoming wavefront, selectively reflecting high-frequency features while suppressing low-frequency intensity variations. Simulations reveal a reflectance transition from minimal to near-total as a function of numerical aperture, a property leveraged for enhancing edge contrast in optical imaging. For the first time, to our knowledge, we utilize molecular beam epitaxy (MBE) to fabricate edge detection devices, ensuring structural fidelity. Material characterization confirms high-quality interfaces, precise thickness control, and excellent uniformity, validating the suitability of MBE for this application. Experimental angle-resolved reflectance measurements closely align with theoretical predictions, demonstrating the feasibility of this approach for real-time, hardware-based optical image processing. The proposed design automatically works for at least two wavelengths and can be readily extended to operate at multiple wavelengths simultaneously. This work opens new possibilities for employing multilayer interference structures in high-performance optical imaging and real-time signal processing. 

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.