Abstract
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 $4\times 4$ 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.
Highlights
Neural networks (NNs) have been impressively emerging since they have proven to be promising in solving complex computational functions [1]–[3]
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
The analytical implementation of an arbitrary unitary matrix by means of the optical processor is demonstrated through a stochastic optimization algorithm to determine the required phase shifts in the constituent Mach-Zehnder interferometers (MZIs)
Summary
Neural networks (NNs) have been impressively emerging since they have proven to be promising in solving complex computational functions [1]–[3]. On-chip multiport reconfigurable interferometers as optical processors with small footprint can implement linear operations between several optical channels They can be used to efficiently perform complex matrix multiplications in NNs by exploiting the inherent parallelism of optics which provides a linear time complexity as compared to digital NNs which scale matrix multiplications by polynomial time complexity [6]. Multiport programmable MZI-based interferometers which implement a unitary transformation matrix between the N input and N output ports are used as a new programming method in various applications [11]–[14] Their reconfigurability allows for performing complex and precise linear optical functions in information processing applications, such as optical neural networks [2], [14], [15]. The experimental results demonstrate that the optical processor achieves 72% accuracy in classifying 50 data samples which were correctly classified through simulation
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