Solving constant-coefficient differential equations with dielectric metamaterials

Zhang, Weixuan; Qu, Che; Zhang, Xiangdong

doi:10.1088/2040-8978/18/7/075102

Cited by 37 publications

(29 citation statements)

References 21 publications

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“…Constant-coefficient ordinary differential and integro-differential equations represent a vast variety of basic engineering systems and physical phenomena in virtually any field of science and engineering, including temperature diffusion processes, physical problems of motion subject to acceleration inputs and frictional forces, time-domain circuit responses and so on [3]. In order to solve differential equations in photonic domain, exploiting from an all-optical differentiator or integrator is indispensable.…”

Section: Introductionmentioning

confidence: 99%

“…Fiber gratings [5], silicon micro-ring resonator [7], and all-optical differentiator [6] have been proposed as some candidates for implementation of these solutions. However, in addition to involving either a redundant loop [8] or an additional optical pump [9], the configuration of these schemes suffer from microelectronic limitations regarding operational speed, power consumption and significantly larger size, which is inappropriate in the new generation of optical systems [3,10]. Besides, the proposals in [4,5] only investigate the first-order differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…Unlike bulky designs arising from additional Fourier sub-blocks in the former case, in the GF strategy, the computing metamaterial directly realizes the desired spatial impulse response at the output without any additional subblocks [17][18][19]. Nevertheless, most of the metamaterial-assisted proposals for solving integro-differential equations are based on the bulky Fourier designs [3,10]. For instance, Zhang et al proposed and designed the dielectric metamaterial blocks to solve some particular forms of the ordinary differential equations [3].…”

Section: Introductionmentioning

confidence: 99%

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Parallel integro-differential equation solving via multi-channel reciprocal bianisotropic metasurface augmented by normal susceptibilities

et al. 2019

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Analog optical signal processing has dramatically transcended the speed and energy limitations accompanied with its digital microelectronic counterparts. Motivated by recent metasurface's evolution, the angular scattering diversity of a reciprocal passive bianisotropic metasurface with normal polarization is utilized in this paper to design a multi-channel meta-computing surface, performing multiple advanced mathematical operations on input fields coming from different directions, simultaneously. Here, the employed ultra-thin bianisotropic metasurface computer is theoretically characterized based on generalized sheet transition conditions and susceptibility tensors. The operators of choice are deliberately dedicated to asymmetric integro-differential equations and image processing functions, like edge detection and blurring. To clarify the concept, we present several illustrative simulations whereby diverse wave-based mathematical functionalities have been simultaneously implemented without any additional Fourier lenses. The performance of the designed metasurface overcomes the nettlesome restrictions imposed by the previous analog computing proposals such as bulky profiles, asserting only single mathematical operation, and most importantly, supporting only the even-symmetric operations for normal incidences. Besides, the realization possibility of the proposed metasurface computer is conceptually investigated via picturing the angular scattering behavior of several candidate meta-atoms. This work opens a new route for designing ultra-thin devices executing parallel and accelerated optical signal/image processing.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Parallel integro-differential equation solving via multi-channel reciprocal bianisotropic metasurface augmented by normal susceptibilities

et al. 2019

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“…This progress sheds light on the potential development of optical analog processors based on metasurfaces.There already exist a few potential application examples about metasurface-based analog optical spatial devices such as differentiators, [18][19][20][21][22][23][24][25][26][27][28] integrators, [18,19,25] and even equation solvers. [29][30][31] The artificial materials utilized in these studies could be classified into three categories: multilayer films, [18,21,22] 1D gratings, [23,24,26] and general 2D metasurfaces. [19,20,25,[27][28][29][30][31] Among these structures, the general 2D metasurfaces with strong modulation flexibility are widely employed to realize the desired spatial operation functions mathematically defined by different Green's functions.…”

mentioning

confidence: 99%

“…[29][30][31] The artificial materials utilized in these studies could be classified into three categories: multilayer films, [18,21,22] 1D gratings, [23,24,26] and general 2D metasurfaces. [19,20,25,[27][28][29][30][31] Among these structures, the general 2D metasurfaces with strong modulation flexibility are widely employed to realize the desired spatial operation functions mathematically defined by different Green's functions. For practice, simple structures are more preferable, for example by a single layer of resonant metasurface.…”

mentioning

confidence: 99%

Analog Optical Spatial Differentiators Based on Dielectric Metasurfaces

Zhou

Chen

et al. 2019

Advanced Optical Materials

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Analog spatial differentiator is an important optical computational device that can be potentially used in the field of high‐speed edge detection and optical image processing. In the current stage, a general method is still required to robustly design compact devices for various spectrum or complex situation. In this work, a dielectric metasurface method is proposed and experimentally demonstrated to build optical spatial differentiators. This is physically realized by a high‐quality magnetic resonance mode that is hybridized with the classic bounded surface wave via grating coupling. Experimentally, a well‐defined first‐order differentiation effect is observed at oblique light incidence. The application potential of this device is evaluated by inputting various figures. It is shown that it can perform an optical processor to trace the profiles of the figure content with a resolution better than 30.8 µm. This work may pave a robust way to build ultracompact optical computation devices for real‐time image processors, which can be freely extended to various frequencies.

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Implementing Quantum Search Algorithm with Metamaterials

Zhang

Cheng

et al. 2017

Advanced Materials

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[17] quantum metamaterials, [18][19][20] and so on. [21][22][23][24][25][26][27] Recently, the concept of "computational metamaterials" has been proposed. [28][29][30][31][32][33] Mathematical operations, such as spatial differentiation, integration, and convolution, can be performed by using designed metamaterial blocks. The dimension at wavelength scale of such kind of computing machines offers the possibility of miniaturized fullwave computing systems that are several orders of magnitude thinner than conventional bulky lens-based optical processors.On the other hand, quantum computation has been the focus of numerous studies and is expected to play an important role in future information processing since it outperforms classical computation at many tasks. [34] The excitement over quantum computation is based on just a few algorithms, the best known being Shor's factorization algorithm [35] and Grover's search algorithm. [36] The latter is extremely important, both from a fundamental standpoint, as it is usually more efficient than the best classical algorithm, and from a practical standpoint, because fast searching is central to solving difficult problems. Up to now, Grover's search algorithm has been implemented under many standard circuit models, such as optical experiments, [37,38] NMR systems, [39,40] trapped ion, [41] and so on. The problem is whether Grover's search algorithm can be performed by using designed metamaterials. In this work, we numerically and experimentally demonstrate the implementation of Grover's search algorithm through dielectric metamaterials at microwave frequencies.The general protocol is graphically shown in Figure 1a with different colors being used to distinguish the structural regions that perform different functions. In this metamaterial-based searching protocol, the electric field amplitude of the incident microwave "E(y)" is recognized as the probability amplitude of the equivalent quantum state, spatial positions "y" are used to label the items in the database, and the maximum number of the database is fixed by the full width at half-maximum (FWHM) "D" of the incident intensity profile with near-Gaussian distribution. The designed metamaterial is comprised of four cascaded subblocks: an oracle subblock (red area, U m ), two Fourier transform subblocks (green areas, F), and a phase plate subblock (blue area, U 0 ). The role of the oracle subblock is to mark the targeted item (red arrow) |y = m〉 Metamaterials, artificially structured electromagnetic (EM) materials, have enabled the realization of many unconventional EM properties not found in nature, such as negative refractive index, magnetic response, invisibility cloaking, and so on. Based on these man-made materials with novel EM properties, various devices are designed and realized. However, quantum analog devices based on metamaterials have not been achieved so far. Here, metamaterials are designed and printed to perform quantum search algorithm. The structures, comprising of an array of 2D subwavelength air holes wit...

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Solving constant-coefficient differential equations with dielectric metamaterials

Cited by 37 publications

References 21 publications

Parallel integro-differential equation solving via multi-channel reciprocal bianisotropic metasurface augmented by normal susceptibilities

Parallel integro-differential equation solving via multi-channel reciprocal bianisotropic metasurface augmented by normal susceptibilities

Analog Optical Spatial Differentiators Based on Dielectric Metasurfaces

Implementing Quantum Search Algorithm with Metamaterials

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