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Analog computing by Brewster effect

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 Publication date 2016
and research's language is English




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Optical computing has emerged as a promising candidate for real-time and parallel continuous data processing. Motivated by recent progresses in metamaterial-based analog computing [Science 343, 160 (2014)], we theoretically investigate realization of two-dimensional complex mathematical operations using rotated configurations, recently reported in [Opt. Lett. 39, 1278 (2014)]. Breaking the reflection symmetry, such configurations could realize both even and odd Greens functions associated with spatial operators. Based on such appealing theory and by using Brewster effect, we demonstrate realization of a first-order differentiator. Such efficient wave-based computation method not only circumvents the major potential drawbacks of metamaterials, but also offers the most compact possible device compared to the conventional bulky lens-based optical signal and data processors.



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Developing mixed-signal analog-digital neuromorphic circuits in advanced scaled processes poses significant design challenges. We present compact and energy efficient sub-threshold analog synapse and neuron circuits, optimized for a 28 nm FD-SOI process, to implement massively parallel large-scale neuromorphic computing systems. We describe the techniques used for maximizing density with mixed-mode analog/digital synaptic weight configurations, and the methods adopted for minimizing the effect of channel leakage current, in order to implement efficient analog computation based on pA-nA small currents. We present circuit simulation results, based on a new chip that has been recently taped out, to demonstrate how the circuits can be useful for both low-frequency operation in systems that need to interact with the environment in real-time, and for high-frequency operation for fast data processing in different types of spiking neural network architectures.
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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)].
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Efficient solutions to NP-complete problems would significantly benefit both science and industry. However, such problems are intractable on digital computers based on the von Neumann architecture, thus creating the need for alternative solutions to tackle such problems. Recently, a deterministic, continuous-time dynamical system (CTDS) was proposed (Nat.Phys. {bf 7}(12), 966 (2011)) to solve a representative NP-complete problem, Boolean Satisfiability (SAT). This solver shows polynomial analog time-complexity on even the hardest benchmark $k$-SAT ($k geq 3$) formulas, but at an energy cost through exponentially driven auxiliary variables. This paper presents a novel analog hardware SAT solver, AC-SAT, implementing the CTDS via incorporating novel, analog circuit design ideas. AC-SAT is intended to be used as a co-processor and is programmable for handling different problem specifications. It is especially effective for solving hard $k$-SAT problem instances that are challenging for algorithms running on digital machines. Furthermore, with its modular design, AC-SAT can readily be extended to solve larger size problems, while the size of the circuit grows linearly with the product of the number of variables and number of clauses. The circuit is designed and simulated based on a 32nm CMOS technology. SPICE simulation results show speedup factors of $sim$10$^4$ on even the hardest 3-SAT problems, when compared with a state-of-the-art SAT solver on digital computers. As an example, for hard problems with $N=50$ variables and $M=212$ clauses, solutions are found within from a few $ns$ to a few hundred $ns$.
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