FDTD Simulations of Modulated Metasurfaces with Arbitrarily Shaped Meta-atoms by Surface Impedance Boundary Condition

Authors

  • Yanmeng Hu Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China
  • Quanen Zhou Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China limengmeng@njust.edu.cn
  • Xinyu Fang Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China limengmeng@njust.edu.cn
  • Mengmeng Li Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China

DOI:

https://doi.org/10.13052/2021.ACES.J.361201

Keywords:

Thin-layer model, metasurface, FDTD, impedance boundary condition

Abstract

In this paper, we propose a reduced-complexity finite difference time domain (FDTD) simulations of modulated metasurfaces with arbitrary unit cells.  The three dimensional (3D) physical structure of the metasurface is substituted by a spatially varying surface impedance boundary condition (IBC) in the simulation; as the mesh size is not dictated by sub-wavelength details, considerable advantage in space- and time-step is achieved. The local parameters of the IBC are obtained by numerical simulation of the individual unit cells of the physical structure, in a periodic environment approximation, in the frequency domain. As the FDTD requires an appropriate time domain impulse-response, the latter is obtained by broad-band frequency simulations, and vector fitting to an analytic realizable time response. The approach is tested on metasurface structures with complex unit cells and extending over 10 ××10 wavelengths, using a standard PC with 64GB RAM.

Downloads

Download data is not yet available.

Author Biographies

Yanmeng Hu, Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China

Yanmeng Hu received the B.S. degree in Electronic Information Science and Technology from the Henan University Minshen College, Kaifeng China, in 2017. She is pursuing the master’s degree in integrated circuit engineering in the Nanjing University of Science and Technology, Nanjing, China. Ms. Hu’s current research interest is electromagnetic analysis of multiscale problems.

Mengmeng Li, Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China

Mengmeng Li received the B.S. degree (Hons.) in physics from Huaiyin Normal College, Huai’an, China, in 2007, and the Ph.D. degree in electromagnetic field and microwave technology from the Nanjing University of Science and Technology, Nanjing, China, in 2014. From 2012 to 2014, he was a Visiting Student

with the Electronics Department, Politecnico di Torino, Turin, Italy, and also with the Antenna and EMC Laboratory (LACE), Istituto Superiore Mario Boella, Turin, where he carried out fast solver for multiscale simulations. Since 2014, he has been with the Department of Communication Engineering, Nanjing University of Science and Technology, where he has been an Assistant Professor, Associate Professor, and Professor since 2020. In 2017, he was a Visiting Scholar with Pennsylvania State University, Pennsylvania, PA, USA. His current research interests include fast solver algorithms, computational electromagnetic solvers for circuits, signal integrity analysis, and multiscale simulations.

Dr. Li was a recipient of the Doctoral Dissertation Award of Jiangsu Province in 2016, the Young Scientist Award at the ACES-China Conference in 2019, and five student paper/contest awards at the international conferences with the students. He is an active reviewer for many IEEE journals and conferences. He is an Associate Editor of the IEEE Antennas and Propagation Magazine, IEEE Open Journal of Antennas and Propagation (OJAP), and IEEE Access, and a Guest Editor of OJAP.

References

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nature Materials, vol. 13, no. 2, pp. 139-150, 2014.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: the two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag., vol. 54, no. 2, pp. 10-35, Feb. 2012.

S. Zhou, X. Fang, M. Li, and R. S. Chen, “S/X dual-band real-time modulated frequency selective surface based absorber,” Acta Physica Sinica, vol. 69, no. 20, pp. 204101, 2020.

Y. Liu, K. Li, Y. Jia, Y. Hao, S. X. Gong, and Y. J. Guo, “Wideband RCS reduction of a slot array antenna using polarization conversion metasurfaces,” IEEE Trans. Antennas Propag., vol. 64, no. 1, pp. 326-331, Jan. 2016.

G. Minatti, F. Caminita, M. Casaletti, and S. Maci, “Spiral leakywave antennas based on modulated surface impedance,” IEEE Trans. Antennas Propag., vol. 59, no. 12, pp. 4436-4444, Dec. 2011.

M. Li, S. Li, Y, Yu, X, Ni, and R. S. Chen, “Design of random and sparse metalens with matrix pencil method,” Opt. Express, vol. 26, no. 19, pp. 24702-24711, Sep. 2018

M. Li, S. Li, L. K. Chin, Y. F. Yu, D. P. Tsai, and R. S. Chen, “Dual-layer achromatic metalens design with an effective Abbe number,” Opt. Express, vol. 28, no. 18, pp. 26041-26055, Aug. 2020

L. Li, H. Ruan, C. Liu, Y. Li, Y. Shuang, A. Alù, and T. J. Cui, “Machine-learning reprogrammable metasurface imager,” Nature Communications, vol. 10, no. 1, pp. 1082, 2019.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. OHara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: the two-dimensional equivalent of metamaterials,” Metamaterials, vol. 3, no. 2, pp. 100-112, 2009.

Y. Guo, T. Zhang, W. Y. Yin, and X. H. Wang, “Improved hybrid FDTD method for studying tunable graphene frequency-selective surfaces (GFSS) for THz-wave applications,” IEEE Trans. Terahertz Sci. Technol., vol. 5, no. 3, pp. 358-367, May 2015.

J. G. Maloney, G. S. Smith, “The use of surface impedance concepts in the finite-difference time-domain method,” IEEE Trans. Antennas Propag., vol. 40, no. 1, pp. 38-48, Jan. 1992.

M. A. Francavilla, E. Martini, S. Maci, and G. Vecchi, “On the numerical simulation of metasurfaces with impedance boundary condition integral equations,” IEEE Trans. Antennas Propag., vol. 63, no. 5, pp. 2153-2161, May 2015.

B. Stupfel and D. Poget, “Sufficient uniqueness conditions for the solution of the time harmonic maxwell’s equations associated with surface impedance boundary conditions,” J. Comput. Phys., vol. 230, no. 12, pp. 4571-4587, Jun. 2011.

E. F. Kuester, M. A. Mohamed, M. Piket-May and C. L. Holloway, “Averaged Transition Conditions for Electromagnetic Fields at a metafilm,” IEEE Trans. Antennas Propag., vol. 51, no. 10, pp. 2641-2651, Oct. 2003.

C. L. Holloway, D. C. Love, E. F. Kuester, J. A. Gordon, and D. A. Hill, “Use of generalized sheet transition conditions to model guided waves on metasurfaces/metafilms,” IEEE Trans. Antennas Propag., vol. 60, no. 11, pp. 5173-5186, Nov. 2012.

D. González-Ovejero and S. Maci, “Gaussian ring basis functions for the analysis of modulated metasurface antennas,” IEEE Trans. Antennas Propag., vol. 63, no. 9, pp. 3982-3993, Sep. 2015.

M. Bodehou, D. Gonzalez-Ovejero, C. Craeye, and I. Huynen, “Method of moments simulation of modulated metasurface antennas with a set of orthogonal entire-domain basis functions,” IEEE Trans. Antennas Propag., vol. 67, no. 2, 1119-1130, Feb. 2018.

M. Bodehou, C. Craeye, and I. Huynen, “Electric field integral equation-based synthesis of elliptical-domain metasurface antennas,” IEEE Trans. Antennas Propag., vol. 67, no. 2, pp. 1270-1274, Feb. 2019.

Q. Wu, “Characteristic mode analysis of composite metallic–dielectric structures using impedance boundary condition,” IEEE Trans. Antennas Propag., vol. 67, no. 12, pp. 7415-7424, Dec. 2019.

K. Achouri, M. A. Salem, and C. Caloz, “General metasurface synthesis based on susceptibility tensors,” IEEE Trans. Antennas Propag., vol. 63, no. 7, pp. 2977-2991, Jul. 2015.

C. Pfeiffer and A. Grbic, “Bianisotropic metasurfaces for optimal polarization control: Analysis and synthesis,” Phys. Rev. Appl., vol. 2, no. 4, p. 044011, Oct. 2014.

X. Du, H. Yu, and M. Li, “Effective modeling of tunable graphene with dispersive FDTD-GSTC method,” Applied Computational Electromagnetics Society Journal, (Special Issue of ACES, Beijing, 2018), vol. 31, no. 6, pp. 851-856, 2019.

X. Jia, F. Yang, X. Liu, M. Li, and S. Xu, “Fast nonuniform metasurface analysis in FDTD using surface susceptibility model,” IEEE Trans. Antennas Propag., vol. 68, no. 10, pp. 7121-7130, Oct. 2020.

V. Nayyeri, M. Soleimani, O. M. Ramahi, “Modeling graphene in the finite-difference time-domain method using a surface boundary condition,” IEEE Trans. Antennas Propag., vol. 61, no. 8, pp. 4176-4182, May 2013.

X. Liu, F. Yang, M. Li, and S. Xu, “Analysis of reflectarray antenna elements under arbitrary incident angles and polarizations using generalized boundary conditions,” IEEE Antennas Wirel. Propag. Lett., vol. 17, pp. 2208-2212, 2018.

O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. V. Räisänen, and S. A. Tretyakov, “Simple and accurate analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag., vol. 56, no. 6, pp. 1624-1632, Jun. 2008.

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag., vol. 14, no. 3, pp. 302-307, May 1966.

A. Taflove and S. C. Hagness, Computional Electrodynamics: The Finite-Difference Time-Domain Method, 3rd edition. Norwood, MA: Artech House, 2017.

K. Niu, Z. X. Huang, M. Li, and X. L. Wu, “Optimization of the artificially anisotropic parameters in WCS-FDTD method for reducing numerical dispersion,” IEEE Trans. Antennas Propag., vol. 65, no. 12, pp. 7389-7394, Dec. 2017.

K. Niu, Z. X. Huang, X. Ren, M. Li, B. Wu and X. L. Wu, “An optimized 3-D HIE-FDTD method with reduced numerical dispersion,” IEEE Trans. Antennas Propag., vol. 66, no. 11, pp. 6435-6440, Nov. 2018.

D. F. Kelley and R. J. Luebbers, “Piecewise Linear Recursive Convolution for Dispersive Media Using FDTD,” IEEE Trans. Antennas Propag., vol. 44, no. 6, pp. 792-797, Jun. 1996.

Y. Yang, L. Jing, B. Zheng, R. Hao, W. Yin, E. Li, C. M. Soukoulis, and H. Chen, “Full-polarization 3D metasurface cloak with preserved amplitude and phase,” Advanced Materials, vol. 28, no. 32, pp. 6866-6871, 2016.

S. A. Cummer, “An analysis of new and existing FDTD methods for isotropic cold plasma and a method for improving their accuracy,” IEEE Trans. Antennas Propag., vol. 45, pp. 392-400, 1997.

B. Gustavsen and A. Semlyen, “Rational approximation of frequency domain responses by vector fitting,” IEEE Transactions on Power Delivery, vol. 14, no. 3, pp. 1052-1061, Mar. 1999.

R. Luebbers, F. P. Hunsberger, K. S. Kunz, R. B. Standler, and M. Schaneider, “A frequency-dependent time-domain formulation for dispersive materials,” IEEE Trans. Electromagn. Compat., vol. 37, pp. 222-227, Aug. 1990

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, “Time-domain analysis of periodic structures at oblique incidence: Orthogonal and nonorthogonal FDTD implementations,” IEEE Trans. Microwave Theory Tech., vol. 46, pp. 420-427, Apr. 1998

X. Li, S. Xiao, B. Cai, Q. He, T. J. Cui, and L. Zhou, “Flat metasurfaces to focus electromagnetic waves in reflection geometry,” Opt. Letters, vol. 37, no. 23, pp. 4940-4942, 2012.

Downloads

Published

2021-12-01

How to Cite

[1]
Y. . Hu, Q. . Zhou, X. Fang, and M. Li, “FDTD Simulations of Modulated Metasurfaces with Arbitrarily Shaped Meta-atoms by Surface Impedance Boundary Condition”, ACES Journal, vol. 36, no. 12, pp. 1509–1517, Dec. 2021.