Diffractive interconnects: all-optical permutation operation using diffractive networks - PubMed (original) (raw)
Diffractive interconnects: all-optical permutation operation using diffractive networks
Deniz Mengu et al. Nanophotonics. 2022.
Abstract
Permutation matrices form an important computational building block frequently used in various fields including, e.g., communications, information security, and data processing. Optical implementation of permutation operators with relatively large number of input-output interconnections based on power-efficient, fast, and compact platforms is highly desirable. Here, we present diffractive optical networks engineered through deep learning to all-optically perform permutation operations that can scale to hundreds of thousands of interconnections between an input and an output field-of-view using passive transmissive layers that are individually structured at the wavelength scale. Our findings indicate that the capacity of the diffractive optical network in approximating a given permutation operation increases proportional to the number of diffractive layers and trainable transmission elements in the system. Such deeper diffractive network designs can pose practical challenges in terms of physical alignment and output diffraction efficiency of the system. We addressed these challenges by designing misalignment tolerant diffractive designs that can all-optically perform arbitrarily selected permutation operations, and experimentally demonstrated, for the first time, a diffractive permutation network that operates at THz part of the spectrum. Diffractive permutation networks might find various applications in, e.g., security, image encryption, and data processing, along with telecommunications; especially with the carrier frequencies in wireless communications approaching THz-bands, the presented diffractive permutation networks can potentially serve as channel routing and interconnection panels in wireless networks.
Keywords: diffractive deep neural networks; diffractive permutation networks; optical computing; optical interconnects; optical machine learning; optical networks.
© 2022 the author(s), published by De Gruyter, Berlin/Boston.
Figures
Figure 1:
The schematic of a 5-layer diffractive permutation network, all-optically realizing 0.16 million interconnects between an input and output field-of-view. The presented diffractive permutation network was trained to optically realize an arbitrarily selected permutation operation between the light intensities over N i = 400 = 20 × 20 input and N o = 400 = 20 × 20 output pixels, establishing N i N o = 0.16 million desired interconnections based on 5 phase-only diffractive layers, each containing 40K(200 × 200) diffractive neurons/features.
Figure 2:
Input–output intensity pairs generated by the diffractive permutation network shown in Figure 1. (A) The diffractive permutation network shown in Figure 1 was tested on two different datasets. The first blind testing dataset contains 20K randomly generated inputs. 6 examples from this randomly created testing data are shown here for demonstrating input–output intensity pairs with low, moderate and high signal sparsity levels. Beyond successfully permuting randomly generated intensity patterns, the performance of the diffractive permutation network was also quantified using permuted EMNIST images. None of these test samples were used in the training phase. (B) Output intensity image PSNR with respect to the ground truth intensity patterns as a function of the input signal sparsity in randomly generated test dataset. (C) Same as (B), except for EMNIST test images.
Figure 3:
The impact of the number of diffractive layers on the approximation accuracy of D2NN for a given intensity permutation operation. (A) The average SSIM and PSNR values achieved by the diffractive permutation network designs based on L = 2, L = 3, L = 4 and L = 5 diffractive layers, containing 200 × 200, i.e., 40K, phase-only diffractive neurons/features per layer for the task of optically recovering permuted EMNIST images. (B) The transformation error between the desired intensity permutation (P) and its optically realized counterpart (
PD2NN
) for the diffractive networks with L = 2, L = 3, L = 4 and L = 5 diffractive layers. The transformation error decreases as a function of the number of layers in the diffractive network architecture. The L = 4-layer diffractive permutation network design represents a critical point as it matches the space-bandwidth product requirement of the desired permutation operation, i.e., N = N i N o = 4 × 40K = 160K, and further increasing the number of layers to L = 5 brings only a minor improvement. (C) Examples of EMNIST test images demonstrating the performance of the diffractive permutation networks as a function of L.
Figure 4:
The sensitivity of the diffractive permutation networks against various levels of physical misalignments (A) SSIM values achieved by 5-layer diffractive permutation networks with and without vaccination. (B) Transformation errors between the desired 100 × 100 permutation operation (P) and its optically synthesized counterpart (
PD2NN
) at different levels of misalignments denoted by v test. (C) The layers of a nonvaccinated diffractive permutation network, i.e., v tr = 0, along with the examples of EMNIST test images recovered optically through the diffractive permutation operation. (D) Same as (C), except for a vaccinated diffractive permutation network based on v tr = 0.25.
Figure 5:
Experimental demonstration of a diffractive permutation network. (A) The material thickness profiles of the diffractive surfaces of the fabricated diffractive permutation network. (B) The schematic of the experimental architecture illustrating the forward optical model of the diffractive permutation network. (C) 3D printed diffractive permutation network operating at THz part of the spectrum. (D) The schematic of our experimental system.
Figure 6:
Experimental results. (A) (left) The desired 25 × 25 permutation matrix, P, (middle) the optically realized permutation operation predicted by the numerical forward model,
PD2NN
, and (right) the absolute error map between the two matrices. (B) Comparison between the numerically predicted and the experimentally measured output images for the task of recovering intensity patterns describing the letters “U,” “C,” “L,” and “A”.
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