Metasurface design by a Hopfield network: finding a customized phase response in a broadband

In this paper, we proposed a method of designing metasurfaces that finding the meta-atoms by Hopfield Network. Hopfield network as part of an iterative design process to filter out unreasonable designs without having to go through a full-wave simulation. The undesired meta-atom patterns are effectively filtered by Hopfied Network that can reduce search steps. To demonstrate the validity and reliability of this method, we searched meta-atoms that can achieve customized phase profiles in a broad band for achieving two functional metasurfaces, ie, abnormal reflection and diffusive scattering. The generated meta-atoms are combined to form phase profiles for the metasurfaces. The calculated, simulated and measured results are roughly the same, which convincingly verifies the competency of this method. The proposed method provides an effective phase-search strategy to get desired phase responses intelligently for the design of functional metasurfaces.

[1]  Philip S. Yu,et al.  Top 10 algorithms in data mining , 2007, Knowledge and Information Systems.

[2]  Qiang Cheng,et al.  Coding metamaterials, digital metamaterials and programmable metamaterials , 2014, Light: Science & Applications.

[3]  Houtong Chen,et al.  Anomalous Terahertz Reflection and Scattering by Flexible and Conformal Coding Metamaterials , 2015 .

[4]  Dejan Pangercic,et al.  Optimization of simulated production process performance using machine learning , 2009, 2009 IEEE Conference on Emerging Technologies & Factory Automation.

[5]  David R. Smith,et al.  Learned Integrated Sensing Pipeline: Reconfigurable Metasurface Transceivers as Trainable Physical Layer in an Artificial Neural Network , 2019, Advanced science.

[6]  K. Aihara,et al.  Chaotic neural networks , 1990 .

[7]  Jinde Cao,et al.  Quantized Synchronization of Chaotic Neural Networks With Scheduled Output Feedback Control , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Ana Díaz-Rubio,et al.  From the generalized reflection law to the realization of perfect anomalous reflectors , 2016, Science Advances.

[9]  Stefan Balint,et al.  Complex and chaotic dynamics in a discrete-time-delayed Hopfield neural network with ring architecture , 2009, Neural Networks.

[10]  Xiang Wan,et al.  Machine‐Learning Designs of Anisotropic Digital Coding Metasurfaces , 2018, Advanced Theory and Simulations.

[11]  Jiafu Wang,et al.  Spin‐to‐Orbital Angular Momentum Conversion with Quasi‐Continuous Spatial Phase Response , 2019, Advanced Optical Materials.

[12]  Jinglei Du,et al.  Pure magnetic resonances controlled by the relative azimuth angle between meta-atoms. , 2015, Optics express.

[13]  Shoichi Hasegawa,et al.  Development and investigation of efficient GA/PSO-HYBRID algorithm applicable to real-world design optimization , 2009, IEEE Comput. Intell. Mag..

[14]  Wansheng Tang,et al.  Some novel double-scroll chaotic attractors in Hopfield networks , 2010, Neurocomputing.

[15]  Yongfeng Li,et al.  Deep Learning: A Rapid and Efficient Route to Automatic Metasurface Design , 2019, Advanced science.

[16]  David R. Smith,et al.  Learned Integrated Sensing Pipeline: Reconfigurable Metasurface Transceivers as Trainable Physical Layer in an Artificial Neural Network , 2019, Advanced science.

[17]  Chih-Ming Wang,et al.  High-efficiency broadband anomalous reflection by gradient meta-surfaces. , 2012, Nano letters.

[18]  Yi Yang,et al.  Nanophotonic particle simulation and inverse design using artificial neural networks , 2018, Science Advances.

[19]  A. Kildishev,et al.  Broadband Light Bending with Plasmonic Nanoantennas , 2012, Science.

[20]  Yoshifumi Nishio,et al.  Effective Search with Hopping Chaos for Hopfield Neural Networks Solving QAP , 2007, 2007 IEEE International Symposium on Circuits and Systems.

[21]  Christopher J. Hillar,et al.  Robust Exponential Memory in Hopfield Networks , 2014, The Journal of Mathematical Neuroscience.

[22]  Hugh G. Lewis,et al.  Super-resolution target identification from remotely sensed images using a Hopfield neural network , 2001, IEEE Trans. Geosci. Remote. Sens..

[23]  Bin Liang,et al.  Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces , 2013, Scientific Reports.

[24]  Wen-feng Sun,et al.  Generation of Radial Polarized Lorentz Beam with Single Layer Metasurface , 2018 .

[25]  Paulo C. Rech.  Chaos and hyperchaos in a Hopfield neural network , 2011, Neurocomputing.

[26]  Jin Liang An,et al.  An Improved Algorithm for TSP Problem Solving with Hopfield Neural Networks , 2010 .

[27]  Lei Zhang,et al.  Shaping electromagnetic waves using software-automatically-designed metasurfaces , 2017, Scientific Reports.

[28]  Tom J. Smy,et al.  Finite-Difference Modeling of Broadband Huygens’ Metasurfaces Based on Generalized Sheet Transition Conditions , 2017, IEEE Transactions on Antennas and Propagation.

[29]  Xuesong Jin,et al.  Global stability analysis in delayed Hopfield neural network models , 2000, Neural Networks.

[30]  George V. Eleftheriades,et al.  Reflectionless Wide-Angle Refracting Metasurfaces , 2016, IEEE Antennas and Wireless Propagation Letters.

[31]  Mohammad Bagher Menhaj,et al.  A new set of sufficient conditions based on coupling parameters for synchronization of Hopfield like Chaotic Neural Networks , 2011 .

[32]  Harry A. Atwater,et al.  Low-Loss Plasmonic Metamaterials , 2011, Science.

[33]  Zongfu Yu,et al.  Training Deep Neural Networks for the Inverse Design of Nanophotonic Structures , 2017, 2019 Conference on Lasers and Electro-Optics (CLEO).

[34]  J. L. A. Quijano,et al.  Self-Complementary Metasurface for Designing Narrow Band Pass/Stop Filters , 2013, IEEE Microwave and Wireless Components Letters.

[35]  Mahesan Niranjan,et al.  A theoretical investigation into the performance of the Hopfield model , 1990, IEEE Trans. Neural Networks.

[36]  Qiang Cheng,et al.  Broadband diffusion of terahertz waves by multi-bit coding metasurfaces , 2015, Light: Science & Applications.

[37]  Pauline van den Driessche,et al.  Global Attractivity in Delayed Hopfield Neural Network Models , 1998, SIAM J. Appl. Math..

[38]  N. Yu,et al.  Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction , 2011, Science.

[39]  Xindong Wu,et al.  10 Challenging Problems in Data Mining Research , 2006, Int. J. Inf. Technol. Decis. Mak..

[40]  Sumio Hosaka,et al.  Associative memory realized by a reconfigurable memristive Hopfield neural network , 2015, Nature Communications.

[41]  Shihua Chen,et al.  Existence and stability of equilibria of the continuous-time Hopfield neural network , 2004 .

[42]  Andrea Alù,et al.  Machine-learning reprogrammable metasurface imager , 2019, Nature Communications.

[43]  Jianquan Yao,et al.  Manipulation of Terahertz Wave Using Coding Pancharatnam–Berry Phase Metasurface , 2018, IEEE Photonics Journal.

[44]  Tianping Chen,et al.  Global exponential stability of delayed Hopfield neural networks , 2001, Neural Networks.

[45]  Tie Jun Cui,et al.  Intelligent Electromagnetic Sensing with Learnable Data Acquisition and Processing , 2019, Patterns.

[46]  Martin Bohner,et al.  Exponential synchronization of chaotic neural networks with mixed delays and impulsive effects via output coupling with delay feedback , 2010, Math. Comput. Model..

[47]  Jordan M. Malof,et al.  Deep learning for accelerated all-dielectric metasurface design. , 2019, Optics express.

[48]  S. Tcvetkova,et al.  Perfect control of reflection and refraction using spatially dispersive metasurfaces , 2016, 1605.02044.