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Register a new userComputing matrix inversion with optical networks
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With this paper we bring about a discussion on the computing potential of complex optical networks and provide experimental demonstration that an optical fiber network can be used as an analog processor to calculate matrix inversion. A 3x3 matrix is inverted as a proof-of-concept demonstration using a fiber network containing three nodes and operating at telecomm wavelength. For an NxN matrix, the overall solving time (including setting time of the matrix elements and calculation time of inversion) scales as O(N^2), whereas matrix inversion by most advanced computer algorithms requires ~O(N^2.37) computational time. For well-conditioned matrices, the error of the inversion performed optically is found to be less than 3%, limited by the accuracy of measurement equipment.
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We present a polarization-insensitive metasurface processor to perform spatial asymmetric filtering of an incident optical beam, thereby allowing for real-time parallel optical processing. To enable massive parallel processing, we introduce a novel Multi Input-Multi Output (MIMO) computational metasurface with an asymmetric optical response that can perform spatial differentiation on two distinct input signals regardless of their polarization. In our scenario, two distinct signals set in x and y directions, parallel and perpendicular to the incident plane, illuminate simultaneously the metasurface processor, and the resulting differentiated signals are separated from each other via appropriate Spatial Low Pass Filters (SLPF). By leveraging Generalized Sheet Transition Conditions (GSTCs) and surface susceptibility tensors, we design an asymmetric meta-atom augmented with normal susceptibilitiesto reach asymmetric optical response at normal beam illumination. Proof-of-principle simulations are also reported along with the successful realization of signal processing functions. The proposed metasurface overcomes major shortcomings imposed by previous studies such as large architectures arising from the need of additional subblocks, slow responses, and most importantly, supporting only a single input with a given polarization. Our results set the path for future developments of material-based analog computing using efficient and easy-to-fabricate MIMO processors for compact, fast, and integrable computing elements without any Fourier lens.
An optical neural network is proposed and demonstrated with programmable matrix transformation and nonlinear activation function of photodetection (square-law detection). Based on discrete phase-coherent spatial modes, the dimensionality of programmable optical matrix operations is 30~37, which is implemented by spatial light modulators. With this architecture, all-optical classification tasks of handwritten digits, objects and depth images are performed on the same platform with high accuracy. Due to the parallel nature of matrix multiplication, the processing speed of our proposed architecture is potentially as high as7.4T~74T FLOPs per second (with 10~100GHz detector)
Linear optical computing (LOC) with thermal light has recently gained attention because the problem is connected to the permanent of a Hermitian positive semidefinite matrix (HPSM), which is of importance in the computational complexity theory. Despite the several theoretical analyses on the computational structure of an HPSM in connection to LOC, the experimental demonstration and the computational complexity analysis via the linear optical system have not been performed yet. We present, herein, experimental LOC for estimating the permanent of an HPSM. From the linear optical experiments and theoretical analysis, we find that the LOC efficiency for a multiplicative error is dependent on the value of the permanent and that the lower bound of the computation time scales exponentially. Furthermore, our results are generalized and applied to LOC of permanents of unitary matrices, which can be implemented with a multi-port quantum interferometer involving single-photons at the input ports. We find that LOC with single-photons, for the permanent estimation, is on average less efficient than the most efficient classical algorithm known to date, even in ideal conditions.
A new approach to perform analog optical differentiation is presented using half-wavelength slabs. First, a half-wavelength dielectric slab is used to design a first order differentiator. The latter works properly for both major polarizations, in contrast to designs based on Brewster effect [Opt. Lett. 41, 3467 (2016)]. Inspired by the proposed dielectric differentiator, and by exploiting the unique features of graphene, we further design and demonstrate a reconfigurable and highly miniaturized differentiator using a half-wavelength plasmonic graphene film. To the best of our knowledge, our proposed graphene-based differentiator is even smaller than the most compact differentiator presented so far [Opt. Lett. 40, 5239 (2015)].
Hyperuniform disordered networks belong to a peculiar class of structured materials predicted to possess partial and complete photonic bandgaps for relatively moderate refractive index contrasts. The practical realization of such photonic designer materials is challenging however, as it requires control over a multi-step fabcrication process on optical length scales. Here we report the direct-laser writing of hyperuniform polymeric templates followed by a silicon double inversion procedure leading to high quality network structures made of polycrystalline silicon. We observe a pronounced gap in the shortwave infrared centered at a wavelength of $lambda_{text{Gap}}simeq $ 2.5 $mu$m, in nearly quantitative agreement with numerical simulations. In the experiments the typical structural length scale of the seed pattern can be varied between 2 $mu$m and 1.54 $mu$m leading to a blue-shift of the gap accompanied by an increase of the silicon volume filling fraction.
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