Diffractive interconnects: all-optical permutation operation using diffractive networks

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.

Massively parallel universal linear transformations using a wavelength-multiplexed diffractive optical network

“…For the implementation of the broadband diffractive designs in this paper, we fixed the mean value λm of this group of wavelengths {λ1,λ2,…,λNw}, i.e., λm=1Nw∑w=1Nwλw and assigned these wavelengths to be equally spaced between λ1=0.9125λm and λNw=1.0875λm. Unless otherwise specified, we chose λm to be 0.8 mm in our numerical simulations, as it aligns with the terahertz band that was experimentally used in several of our previous works 50 , 52 , 58 , 59 , 61 , 62 , 66 , 67 . Without loss of generality, the wavelengths used for the design of the broadband diffractive processors can also be selected at other parts of the electromagnetic spectrum, such as the visible band, for which the related simulation results and analyses can be found in Sec.…”

“…Unless otherwise specified, we chose λ m to be 0.8 mm in our numerical simulations, as it aligns with the terahertz band that was experimentally used in several of our previous works. 50,52,58,59,61,62,66,67 Without loss of generality, the wavelengths used for the design of the broadband diffractive processors can also be selected at other parts of the electromagnetic spectrum, such as the visible band, for which the related simulation results and analyses can be found in Sec. 3 to follow.…”

“…Diffractive neural networks have been used to perform various optical information processing tasks, including, object classification, 22 , 46 – 57 image reconstruction, 52 , 58 , 59 all-optical phase recovery and quantitative image phase imaging, 60 class-specific imaging, 61 super-resolution image displays, 62 and logical operations 63 – 65 Employing successive spatially engineered diffractive surfaces as the backbone for inverse design of deterministic optical elements also enabled numerous applications, such as spatially controlled wavelength demultiplexing, 66 pulse engineering, 67 and orbital angular momentum multiplexing/demultiplexing 68 …”

Snapshot multispectral imaging using a diffractive optical network

“…The former might be partially mitigated by using highaccuracy 3D fabrication tools such as two-photon polymerization; the latter, on the other hand, could potentially be addressed with anti-reflective coatings frequently used in the fabrication of high-quality lenses. We should also note that some of the earlier studies on multi-layer diffractive networks showed that surface reflections, in general, did not lead to a significant discrepancy between the outputs predicted by the numerical forward models/ designs and their experimental counterparts 51,57,[63][64][65] . Furthermore, some of these error sources, e.g., layer-tolayer misalignments, can directly be incorporated into the optical training forward model as random variables to drive and shape the deep learning-based evolution of the diffractive surfaces towards robust solutions that exhibit relatively flat performance curves within the possible error ranges 53 .…”

Super-resolution image display using diffractive decoders

“…Stated differently, a diffractive decoder can implement any arbitrary complex-valued linear transformation between its input and output FOVs, covering any desired set of spatially variant point spread functions, which forms a superset of spatially invariant imaging systems. Deep learning-trained diffractive networks were shown to all-optically perform an arbitrary complex-valued linear transformation, including space-variant operations such as permutation (45), with negligible error provided that the light modulation surfaces forming the diffractive network contain a sufficiently large number of trainable diffractive features (46)(47)(48). In this sense, the presented diffractive PSR image displays can be viewed as a hybrid (electronicoptical) network system that is composed of an electronic encoder (front-end), followed by a complex-valued all-optical matrix operator (the diffractive back-end) that decodes the input encoded fields in a way that the light intensity distribution at the output plane approximates the high-resolution target images.…”