Advanced Numerical and Experimental Analysis of Ultra-Miniature Surface Resonators

Authors

  • Yakir Ishay Schulich Faculty of Chemistry Technion - Israel Institute of Technology, Haifa, 3200003, Israel
  • Yaron Artzi Schulich Faculty of Chemistry Technion - Israel Institute of Technology, Haifa, 3200003, Israel
  • Nir Dayan Schulich Faculty of Chemistry Technion - Israel Institute of Technology, Haifa, 3200003, Israel
  • David Cristea Schulich Faculty of Chemistry Technion - Israel Institute of Technology, Haifa, 3200003, Israel
  • Aharon Blank Schulich Faculty of Chemistry Technion - Israel Institute of Technology, Haifa, 3200003, Israel https://orcid.org/0000-0003-4056-8103

DOI:

https://doi.org/10.13052/2022.ACES.J.370604

Keywords:

Electric Field Integral Equation, Electron Spin Resonance, Surface resonators

Abstract

Many scientific and technological applications make use of strong microwave fields. These are often realized in conjunction with microwave resonators that have small geometric features in which such fields are generated. For example, in magnetic resonance, large microwave and RF magnetic fields make it possible to achieve fast control over the measured electron or nuclear spins in the sample and to detect them with high sensitivity. The numerical analysis of resonators with small geometric features can pose a significant challenge. This paper describes a general method of analysis and characterization of surface microresonators in the context of electron spin resonance (ESR) spectroscopy and spin-based quantum technology. Our analysis is based on the Electric Field Integral Equation (EFIE) and the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation. In particular, we focus on a class of resonator configurations that possesses extremely small subwavelength features, which normally would require an ultra-fine mesh. We present several efficient techniques to numerically model, solve, and analyze these types of configurations for both normal and superconducting structures. The validation of these techniques is established both numerically and experimentally by the S11 parameters as well as the provision of direct mapping of the resonator’s microwave magnetic field component using a unique electron spin resonance micro-imaging method.

Downloads

Download data is not yet available.

Author Biographies

Yakir Ishay, Schulich Faculty of Chemistry Technion - Israel Institute of Technology, Haifa, 3200003, Israel

Yakir Ishay received BSc, MSc, and Ph.D. degrees in electrical engineering and physical chemistry from the Technion - Israel Institute of Technology in 2011, 2014, and 2020, respectively. He is currently working as an algorithm researcher and developer for Israel’s defense industry. His research interests include numerical methods in electromagnetics, design of microwave resonators for magnetic resonance imaging (MRI), and image processing and machine learning algorithms.

Yaron Artzi, Schulich Faculty of Chemistry Technion - Israel Institute of Technology, Haifa, 3200003, Israel

Yaron Artzi is a Ph.D. student of physical chemistry at the Technion – Israel Institute of Technology’s Department of Chemistry. He obtained his BSc and MSc degrees in physics at that same institution. His research interests include the development of advanced methodologies in the field of electron spin resonance (ESR) for quantum technology applications.

Nir Dayan, Schulich Faculty of Chemistry Technion - Israel Institute of Technology, Haifa, 3200003, Israel

Nir Dayan obtained his BSc in chemistry and biology and his MSc in chemistry from Tel Aviv University. Currently, he is a Ph.D. candidate at the Schulich Faculty of Chemistry at the Technion – Israel Institute of Technology. His projects in the Blank group are focused on the development of advanced techniques in electron spin resonance (ESR) for structural biology.

David Cristea, Schulich Faculty of Chemistry Technion - Israel Institute of Technology, Haifa, 3200003, Israel

David Cristea is a senior researcher at the Schulich Faculty of Chemistry, Technion - Israel Institute of Technology. He holds a BSc in electronics and MSc and Ph.D. degrees in electrical engineering from the Politehnica University of Timisoara, Romania. His research interests include R&D of new resonators in the field of nuclear magnetic resonance (NMR) and electron spin resonance (ESR).

Aharon Blank, Schulich Faculty of Chemistry Technion - Israel Institute of Technology, Haifa, 3200003, Israel

Aharon Blank is a full professor at the Schulich Faculty of Chemistry, Technion - Israel Institute of Technology. He holds BSc degrees in mathematics, physics, and chemistry from the Hebrew University of Jerusalem, an MSc in electrical engineering from Tel Aviv University, and a Ph.D. in physical chemistry from the Hebrew University. His research interests include the development and application of new methodologies in the field of nuclear magnetic resonance (NMR) and electron spin resonance (ESR).

References

T. Ōkoshi, Planar Circuits for Microwaves and Lightwaves, Springer-Verlag, Berlin, New York, 1985.

J.-S. Hong, Microstrip Filters for RF/microwave Applications, 2nd ed., Wiley, Hoboken, NJ, 2011.

L. Young-Taek, L. Jong-Sik, K. Chul-Soo, A. Dal, and N. Sangwook, “A compact-size microstrip spiral resonator and its application to microwave oscillator,” IEEE Microwave and Wireless Components Letters, vol. 12, pp. 375-377, 2002.

J. Garcia-Garcia, J. Bonache, I. Gil, F. Martin, M. C. Velazquez-Ahumada, and J. Martel, “Miniaturized microstrip and CPW filters using coupled metamaterial resonators,” IEEE Transactions on Microwave Theory and Techniques, vol. 54, pp. 2628-2635, 2006.

R. Vrijen, E. Yablonovitch, K. Wang, H. W. Jiang, A. Balandin, V. Roychowdhury, T. Mor, and D. DiVincenzo, “Electron-spin-resonance transistors for quantum computing in silicon-germanium heterostructures,” Phys. Rev. A, vol. 62, pp. 012-306, 2000.

V. Ranjan, S. Probst, B. Albanese, A. Doll, O. Jacquot, E. Flurin, R. Heeres, D. Vion, D. Esteve, J. J. L. Morton, and P. Bertet, “Pulsed electron spin resonance spectroscopy in the Purcell regime,” J. Magn. Reson., vol, 310, pp. 106-662, 2020.

V.-C. Su, C. H. Chu, G. Sun, and D. P. Tsai, “Advances in optical metasurfaces: fabrication and applications [Invited],” Opt Express, vol. 26, pp. 13148-13182, 2018.

J. A. Weil and J. R. Bolton, Electron Paramagnetic Resonance: Elementary Theory and Practical Applications, 2nd ed., Wiley-Interscience, Hoboken, NJ, 2007.

Y. Twig, E. Suhovoy, and A. Blank, “Sensitive surface loop-gap microresonators for electron spin resonance,” Rev. Sci. Instrum., vol. 81, pp. 104-703, 2010.

Y. Artzi, Y. Twig, and A. Blank, “Induction-detection electron spin resonance with spin sensitivity of a few tens of spins,” Appl. Phys. Lett., vol. 106, pp. 84-104, 2015.

S. Probst, A. Bienfait, P. Campagne-Ibarcq, J. J. Pla, B. Albanese, J. F. D. Barbosa, T. Schenkel, D. Vion, D. Esteve, K. Molmer, J. J. L. Morton, R. Heeres, and P. Bertet, “Inductive-detection electron-spin resonance spectroscopy with 65 spins/root Hz sensitivity,” Appl. Phys. Lett., vol. 111, 2017.

K. Lips, P. Kanschat, and W. Fuhs, “Defects and recombination in microcrystalline silicon,” Sol. Energy Mater., vol. 78, pp. 513-541, 2003.

M. Mannini, D. Rovai, L. Sorace, A. Perl, B. J. Ravoo, D. N. Reinhoudt, and A. Caneschi, “Patterned monolayers of nitronyl nitroxide radicals,” Inorg. Chim. Acta, vol. 361, pp. 3525-3528,2008.

P. P. Borbat, A. J. Costa-Filho, K. A. Earle, J. K. Moscicki, and J. H. Freed, “Electron spin resonance in studies of membranes and proteins,” Science, vol. 291, pp. 266-269, 2001.

A. Blank, Y. Twig, and Y. Ishay, “Recent trends in high spin sensitivity magnetic resonance,” J. Magn. Reson., vol. 280, pp. 20-29, 2017.

D. M. Sullivan, Electromagnetic Simulation using the FDTD Method, 2nd ed., IEEE Press, John Wiley & Sons, Inc., Hoboken, New Jersey, 2013.

G. Meunier, The Finite Element Method for Electromagnetic Modeling, ISTE, Wiley, London, Hoboken, NJ, 2008.

R. F. Harrington, “The method of moments in electromagnetics,” Journal of Electromagnetic Waves and Applications, vol. 1, pp. 181-200, 1987.

A. W. Glisson, D. Kajfez, and J. James, “Evaluation of modes in dielectric resonators using a surface integral equation formulation,” IEEE Transactions on Microwave Theory and Techniques, vol. 31, pp. 1023-1029, 1983.

S. Rao, D. Wilton, and A. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Transactions on Antennas and Propagation, vol. 30, pp. 409-418, 1982.

V. Jandhyala, B. Shanker, E. Michielssen, and W. C. Chew, “Fast algorithm for the analysis of scattering by dielectric rough surfaces,” Journal of the Optical Society of America A, vol. 15, pp. 1877-1885, 1998.

A. J. Poggio and E. K. Miller, “Chapter 4 - Integral equation solutions of three-dimensional scattering problems,” in R. Mittra (Ed.), Computer Techniques for Electromagnetics, Pergamon, pp. 159-264, 1973.

P. Yla-Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general composite metallic and dielectric structures with junctions,” Progress in Electromagnetics Research, vol. 52, pp. 81-108, 2005.

J. R. Mautz and R. F. Harrington, “H-Field, E-Field, and combined field solutions for bodies of revolution,” in, Defence technical information center, 1977.

A. W. Glisson, “Electromagnetic scattering by arbitrarily shaped surfaces with impedance boundary conditions,” Radio Science, vol. 27, pp. 935-943, 1992.

R. D. Graglia, “On the numerical integration of the linear shape functions times the 3-D Green’s function or its gradient on a plane triangle,” IEEE Transactions on Antennas and Propagation, vol. 41, pp. 1448-1455, 1993.

N. Dayan, Y. Ishay, Y. Artzi, D. Cristea, E. Reijerse, P. Kuppusamy, and A. Blank, “Advanced surface resonators for electron spin resonance of single microcrystals,” Rev. Sci. Instrum., vol. 89, pp. 124-707, 2018.

A. Okaya and L. F. Barash, “The dielectric microwave resonator,” Proceedings of the IRE, vol. 50, pp. 2081-2092, 1962.

R. Prozorov and V. G. Kogan, “London penetration depth in iron-based superconductors,” Rep Prog Phys, vol. 74, pp. 124-505, 2011.

A. R. Kerr, “Surface impedance of superconductors and normal conductors in EM simulators,” in Electronics Division Internal Report, National Radio Astronomy Observatory, Green Bank, West Virginia, 1996.

Y. Artzi, Y. Yishay, M. Fanciulli, M. Jbara, and A. Blank, “Superconducting micro-resonators for electron spin resonance - the good, the bad, and the future,” J. Magn. Reson., vol. 334, pp. 107-102, 2022.

F. P. Andriulli, K. Cools, I. Bogaert, and E. Michielssen, “On a well-conditioned electric field integral operator for multiply connected geometries,” IEEE Transactions on Antennas and Propagation, vol. 61, pp. 2077-2087, 2013.

F. P. Andriulli, A. Tabacco, and G. Vecchi, “Solving the EFIE at low frequencies with a conditioning that grows only logarithmically with the number of unknowns,” IEEE Transactions on Antennas and Propagation, vol. 58, pp. 1614-1624, 2010.

C. Lu, X. Cao, and A. Frotanpour, “Method of moments for partially structured mesh,” 31st International Review of Progress in Applied Computational Electromagnetics (ACES), pp. 1-2, 2015.

M. F. Catedra, O. Gutierrez, I. Gonzalez, and F. S. De Adana, “Electric and magnetic dual meshes to improve moment method formulations,” Appl Comput Electrom, vol. 22, pp. 363-372, 2007.

K. Hill and T. Van, “Fast converging graded mesh for bodies of revolution with tip singularities,” Appl Comput Electrom, vol. 19, pp. 93-99, 2004.

K. Sertel and J. L. Volakis, “Incomplete LU preconditioner for FMM implementation,” Microwave and Optical Technology Letters, vol. 26, pp. 265-267, 2000.

B. Carpentieri and M. Bollhöfer, “Symmetric inverse-based multilevel ILU preconditioning for solving dense complex non-hermitian systems in electromagnetics,” Progress in Electromagnetics Research-pier, vol. 128, pp. 55-74, 2012.

B. Carpentieri, I. S. Duff, L. Giraud, and G. Sylvand, “Combining fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations,” SIAM Journal on Scientific Computing, vol. 27, pp. 774-792, 2005.

F. P. Andriulli, K. Cools, H. Bagci, F. Olyslager, A. Buffa, S. Christiansen, and E. Michielssen, “A multiplicative calderon preconditioner for the electric field integral equation,” IEEE Transactions on Antennas and Propagation, vol. 56, pp. 2398-2412, 2008.

H. C. Snorre and J.-C. Nédélec, “A preconditioner for the electric field integral equation based on calderon formulas,” SIAM Journal on Numerical Analysis, vol. 40, pp. 1100-1135, 2003.

S. Sun, Y. G. Liu, W. C. Chew, and Z. Ma, “Calderón multiplicative preconditioned EFIE with perturbation method,” IEEE Transactions on Antennas and Propagation, vol. 61, pp. 247-255, 2013.

Q. S. Liu, S. Sun, and W. C. Chew, “Low-frequency CMP-EFIE with perturbation method for open capacitive problems,” Proceedings of the 2012 IEEE International Symposium on Antennas and Propagation, pp. 1-2, 2012.

J. Peeters, K. Cools, I. Bogaert, F. Olyslager, and D. D. Zutter, “Embedding calderón multiplicative preconditioners in multilevel fast multipole algorithms,” IEEE Transactions on Antennas and Propagation, vol. 58, pp. 1236-1250, 2010.

R. Zhao, Z. Huang, W. Huang, J. Hu, and X. Wu, “Multiple-traces surface integral equations for electromagnetic scattering from complex microstrip structures,” IEEE Transactions on Antennas and Propagation, vol. 66, pp. 3804-3809, 2018.

A. Ghai, C. Lu, and X. Jiao, “A comparison of preconditioned Krylov subspace methods for large-scale nonsymmetric linear systems,” Numerical Linear Algebra with Applications, vol. 26, e2215, 2019.

Y. Saad and M. Schultz, “GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAM Journal on Scientific and Statistical Computing, vol. 7, pp. 856-869, 1986.

R. Fletcher, “Conjugate gradient methods for indefinite systems,” in, Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 73-89, 1976.

P. Sonneveld, “CGS, A fast Lanczos-type solver for nonsymmetric linear systems,” SIAM Journal on Scientific and Statistical Computing, vol. 10, pp. 36-52, 1989.

R. W. Freund, “A transpose-free quasi-minimal residual algorithm for non-hermitian linear systems,” SIAM Journal on Scientific Computing, vol. 14, pp. 470-482, 1993.

H. A. v. d. Vorst, “Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM Journal on Scientific and Statistical Computing, vol. 13, pp. 631-644, 1992.

A. Blank, E. Suhovoy, R. Halevy, L. Shtirberg, and W. Harneit, “ESR imaging in solid phase down to sub-micron resolution: methodology and applications,” Phys. Chem. Chem. Phys., vol. 11, pp. 6689-6699, 2009.

Downloads

Published

2022-06-30

How to Cite

[1]
Y. . Ishay, Y. . Artzi, N. . Dayan, D. . Cristea, and A. . Blank, “Advanced Numerical and Experimental Analysis of Ultra-Miniature Surface Resonators”, ACES Journal, vol. 37, no. 06, pp. 679–691, Jun. 2022.

Issue

2022: Vol 37 Iss 6

Section

General Submission

Categories