[Paper Review] Diffractive Interconnects: All-Optical Permutation Operation Using Diffractive Networks

Deniz Mengü, Yifan Zhao+3 more|arXiv (Cornell University)|Jun 21, 2022

Optical Network Technologies87 references22 citations

TL;DR

This paper presents diffractive optical networks trained via deep learning to perform all-optical permutation operations at scale, enabling passive, power-efficient, and high-speed interconnections across hundreds of thousands of input-output channels. The first experimental demonstration of a THz-band diffractive permutation network achieves 625 interconnections using 3D-printed transmissive layers, with trained resilience to physical misalignments and fabrication errors.

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.

Motivation & Objective

• To develop a scalable, all-optical method for implementing large-scale permutation operations using passive diffractive networks.
• To address practical challenges in physical alignment and diffraction efficiency in deep diffractive optical systems.
• To design misalignment-tolerant diffractive networks through deep learning that are robust to lateral, axial, and rotational errors.
• To experimentally validate the first THz-band diffractive permutation network using 3D-printed diffractive layers.
• To enable applications in THz communications, optical interconnects, and secure data processing.

Proposed method

• Trained diffractive optical networks using deep learning to engineer phase and amplitude modulation across multiple transmissive layers.
• Used stochastic gradient descent and error-backpropagation to optimize transmission elements at the wavelength scale.
• Modeled physical misalignments (lateral, axial, rotational) as random variables during training to enhance robustness.
• Designed networks to be resilient to fabrication errors by incorporating statistical variations in material thickness during training.
• Utilized a forward model where each input pixel is activated sequentially to record output intensity patterns, forming columns of the permutation matrix.
• Applied scaling factor σP to account for optical losses and computed performance using PSNR and SSIM metrics.

Experimental results

Research questions

• RQ1 Can diffractive optical networks trained via deep learning perform large-scale permutation operations with high accuracy and scalability?
• RQ2 How does the number of diffractive layers and trainable elements affect the network's capacity to approximate a given permutation?
• RQ3 To what extent can diffractive networks be made resilient to physical misalignments and fabrication imperfections through training?
• RQ4 Can a diffractive permutation network be experimentally demonstrated at the THz frequency band with high interconnection density?
• RQ5 What is the performance of such networks in terms of PSNR and SSIM under realistic physical error conditions?

Key findings

• The diffractive network achieved a PSNR of 34.2 dB and SSIM of 0.98 for a 25×25 permutation matrix in the experimental demonstration.
• The network successfully realized 625 interconnections (25×25) in a single all-optical pass at the THz band using 3D-printed diffractive layers.
• Performance improved proportionally with the number of diffractive layers and trainable transmission elements, indicating scalability to hundreds of thousands of interconnections.
• The vaccinated diffractive network (v-D2NN) maintained high accuracy under simulated misalignments, with ∆x = ∆y = 0.67λv, ∆z = 24λv, and ∆θ = 4°, where v = 0.5.
• The network was trained to tolerate ±0.0415λ variation in material thickness across diffractive neurons, demonstrating robustness to fabrication errors.
• Training a 5-layer network with 40,000 neurons per layer over 5 epochs took ~4 days using a GTX 1080 Ti GPU, confirming feasibility of the training pipeline.