A 4 × 4 reconfigurable Mach-Zehnder interferometer (MZI)-based linear optical processor is investigated through its theoretical analyses and characterized experimentally. The linear transformation matrix of the structure is theoretically determined using its building block, which is a 2 × 2 reconfigurable MZI. To program the device, the linear transformation matrix of a given application is decomposed into that of the constituent MZIs of the structure. Thus, the required phase shifts for implementing the transformation matrix of the application by means of the optical processor are determined theoretically. Due to random phase offsets in the MZIs resulting from fabrication process variations, they are initially configured through an experimental protocol. The presented calibration scheme allows to straightforwardly characterize the MZIs to mitigate the possible input phase errors and determine the bar and cross states of each MZI for tuning it at the required sate before programming the device. After the configuration process, the device can be programmed to construct the linear transformation matrix of the application. In this regard, using the required bias voltages, the phase shifts obtained from the decomposition process are applied to the phase shifters of the MZIs in the device.

Abstract-This paper presents the design and performance analysis of an Analog Network Coding (ANC) scheme for multiuser Multi-Carrier Differential Chaos Shift Keying (MC-DCSK) modulation. The incentives to employ MC-DCSK system are to achieve a better spectral efficiency and more efficient energy consumption compared to that of a conventional DCSK system. The proposed scheme considers a network comprising L user nodes (L ≥ 2), and a single relay node R. In this scheme, called ANC-based two-way relay system, all users transmit their signals to the relay in the first time slot, and the relay forwards the superposition of the received signals each of the user nodes in the second time slot. At the receiver end, each user mitigates the overall interference by subtracting its own data signal from the received combined signal, and then starts the decoding process. The system design is analytically studied and the corresponding theoretical bit error rate expression for the multipath fading channel is derived. Additionally, the conventional ANC-DCSK scheme is analyzed and compared to the proposed ANC-based MC-DCSK scheme to show the improvement in the performance of our approach. Finally, to validate the accuracy of the methodology, the simulation results are compared to the related theoretical expressions.

Implementing any linear transformation matrix through the optical channels of an on-chip reconfigurable multiport interferometer has been emerging as a promising technique for various fields of study, such as information processing and optical communication systems. Recently, the use of multiport optical interferometric-based linear structures in neural networks has attracted a great deal of attention. Optical neural networks have proven to be promising in terms of computational speed and power efficiency, allowing for the increasingly large neural networks that are being created today. This paper demonstrates the experimental analysis of programming a 4 × 4 reconfigurable optical processor using a unitary transformation matrix implemented by a single layer neural network. To this end, the Mach-Zehnder interferometers (MZIs) in the structure are first experimentally calibrated to circumvent the random phase errors originating from fabrication process variations. The linear transformation matrix of the given application can be implemented by the successive multiplications of the unitary transformation matrices of the constituent MZIs in the optical structure. The required phase shifts to construct the linear transformation matrix by means of the optical processor are determined theoretically. Using this method, a single layer neural network is trained to classify a synthetic linearly separable multivariate Gaussian dataset on a conventional computer using a stochastic optimization algorithm. Additionally, the effect of the phase errors and uncertainties caused by the experimental equipment inaccuracies and the device components imperfections is also analyzed and simulated. Finally, the optical processor is experimentally programmed by applying the obtained phase shifts from the matrix decomposition process to the corresponding phase shifters in the device. The experimental results show that the optical processor achieves 72% classification accuracy compared to the 98.9% of the simulated optical neural network on a digital computer.

This paper presents the performance analysis of a phase error- and loss-tolerant multiport field-programmable MZI-based structure for optical neural networks (ONNs). Compared to the triangular (Reck) mesh, our proposed diamond mesh makes use of a larger number of MZIs, leading to a symmetric topology and adding additional degrees of freedom for the weight matrix optimization in the backpropagation process. Furthermore, the additional MZIs enable the diamond mesh to optimally eliminate the excess light intensity that degrades the performance of the ONNs through the tapered out waveguides. Our results show that the diamond topology is more robust to the inevitable imperfections in practice, i.e., insertion loss of the constituent MZIs and the phase errors. This robustness allows for better classification accuracy in the presence of experimental imperfections. The practical performance and the scalability of the two structures implementing different sizes of optical neural networks are analytically compared. The obtained results confirm that the diamond mesh is more error- and loss-tolerant in classifying the data samples in different sizes of ONNs.