Vol. 107

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2022-01-12

Analytical and Numerical Studies of Oblique Wave Incidence on Impedance-Matched Graded Interfaces Between RHM and LHM Media

By Brage B. Svendsen, Balwan Rana, and Mariana Dalarsson
Progress In Electromagnetics Research M, Vol. 107, 131-140, 2022
doi:10.2528/PIERM21112701

Abstract

This paper presents analytical and numerical studies of electromagnetic wave propagation through an interface between a regular right-handed material (RHM) and a left-handed metamaterial (LHM). The interface is graded along the direction perpendicular to the boundary plane between the two materials, chosen to be the x-direction. The permittivity ε(ω, x) and permeability μ(ω, x) are chosen to vary according to hyperbolic tangent functions. We show that the field intensities for both TE- and TM-cases satisfy the same differential equations, and we obtain remarkably simple exact analytical solutions to Helmholtz' equations for lossy media. The obtained exact analytical results for the field intensities along the graded RHM-LHM composite are in line with the expected properties of RHM-LHM structures. Finally, we perform a numerical study of the wave propagation over an impedance-matched graded RHM-LHM interface, using the software COMSOL Multiphysics, and obtain an excellent agreement between the numerical simulations and analytical results. The results obtained in the present paper are not limited to any particular application, and are generally useful for all cases of wave propagation over impedance-matched two- and three-dimensional interfaces between RHM and LHM media. The advantage of the present method is that it can model smooth realistic material transitions, while at the same time including the abrupt transition as a limiting case. Furthermore, unlike previously existing solutions, the interface width is included as a parameter in the analytical solutions in a very simple way. This enables the use of the interface width as an additional degree of freedom in the design of practical RHM-LHM interfaces.

Citation


Brage B. Svendsen, Balwan Rana, and Mariana Dalarsson, "Analytical and Numerical Studies of Oblique Wave Incidence on Impedance-Matched Graded Interfaces Between RHM and LHM Media," Progress In Electromagnetics Research M, Vol. 107, 131-140, 2022.
doi:10.2528/PIERM21112701
http://jpier.org/PIERM/pier.php?paper=21112701

References


    1. Smith, D. R., J. J. Mock, A. F. Starr, and D. Schurig, "A gradient index metamaterial," Phys. Rev. E, Vol. 71, 036609, March 2005, doi: 10.1103/PhysRevE.71.036609.
    doi:10.1103/PhysRevE.71.036609

    2. Litchinitser, N. M., A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, "Metamaterials: Electromagnetic enhancement at zero-index transition," Optics Letters, Vol. 33, No. 20, 2350-2352, 2008, doi: 10.1364/OL.33.002350.
    doi:10.1364/OL.33.002350

    3. Pinchuk, A. O. and G. C. Schatz, "Metamaterials with gradient negative index of refraction," Journal of the Optical Society of America A, Vol. 24, No. 10, A39-A44, 2007, doi: 10.1364/JOSAA.24.000A39.
    doi:10.1364/JOSAA.24.000A39

    4. Gaufillet, F., S. Marcellin, and E. Akmansoy, "Dielectric metamaterial-based gradient index lens in the terahertz frequency range," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 23, No. 4, 1-5, July/August 2017, Art no. 4700605, doi: 10.1109/JSTQE.2016.2633825.
    doi:10.1109/JSTQE.2016.2633825

    5. Zhang, N., W. X. Jiang, H. F. Ma, W. X. Tang, and T. J. Cui, "Compact high-performance lens antenna based on impedance-matching gradient-index metamaterials," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 2, 1323-1328, February 2019, doi: 10.1109/TAP.2018.2880115.
    doi:10.1109/TAP.2018.2880115

    6. Su, Y. and Z. N. Chen, "A flat dual-polarized transformation-optics beamscanning Luneburg lens antenna using PCB-stacked gradient index metamaterials," IEEE Transactions on Antennas and Propagation, Vol. 66, No. 10, 5088-5097, October 2018, doi: 10.1109/TAP.2018.2858209.
    doi:10.1109/TAP.2018.2858209

    7. Salami, P. D. and L. Yousefi, "Far-field subwavelength imaging using phase gradient metasurfaces," IEEE Journal of Lightwave Technology, Vol. 37, No. 10, 2317-2323, March 2019, doi: 10.1109/JLT.2019.2902544.
    doi:10.1109/JLT.2019.2902544

    8. Badri, S. H., H. R. Saghai, and H. Soofi, "Multimode waveguide crossing based on a square Maxwell's fisheye lens," Applied Optics, Vol. 58, No. 17, 4647-4653, June 2019, doi: 10.1364/AO.58.004647.
    doi:10.1364/AO.58.004647

    9. Hajiahmadi, M. J., R. Faraji-Dana, and A. K. Skrivervik, "Far field superlensing inside biological media through a nanorod lens using spatiotemporal information," Nature, Scientific Reports, Vol. 11, 1-8, January 2021, Art no. 19534, doi: 10.1038/s41598-021-81091-0.

    10. Alibakshikenari, M., B. S. Virdee, L. Azpilicueta, M. Naser-Moghadasi, M. Olusola Akinsolu, C. H. See, B. Liu, R. A. Abd-Alhameed, F. Falcone, I. Huynen, T. A. Denidni, and E. Limiti, "A comprehensive survey of metamaterial transmission-line based antennas: Design, challenges, and applications," IEEE Access, Vol. 8, 144778-144808, August 2020, doi: 10.1109/ACCESS.2020.3013698.
    doi:10.1109/ACCESS.2020.3013698

    11. Alibakshikenari, M., F. Babaeian, S. Assa, C. H. See, A. A. Althuwayb, I. Huynen, R. A. Abd-Alhameed, F. Falcone, and E. Limiti, "A comprehensive survey on various decoupling mechanisms with focus on metamaterial and metasurface principles applicable to SAR and MIMO antenna systems," IEEE Access, Vol. 8, 192965-193004, November 2020, doi: 10.1109/ACCESS.2020.3032826.

    12. Alibakhshikenari, M., B. S. Virdee, and E. Limiti, "Compact single-layer traveling-wave antenna design using metamaterial transmission lines," Radio Science, Vol. 52, 1510-1521, December 2017, doi: 10.1002/2017RS006313.
    doi:10.1002/2017RS006313

    13. Alibakhshi-Kenari, M., M. Naser-Moghadasi, R. A. Sadeghzadeh, B. S. Virdee, and E. Limiti, "Periodic array of complementary artificial magnetic conductor metamaterials-based multiband antennas for broadband wireless transceivers," IET Microwaves, Antennas & Propagation, Vol. 10, No. 15, 1682-1691, June 2016, doi: 10.1049/iet-map.2016.0069.
    doi:10.1049/iet-map.2016.0069

    14. Alibakhshi-Kenari, M., M. Naser-Moghadasi, and R. A. Sadeghzadeh, "Bandwidth and radiation specifications enhancement of monopole antennas loaded with split ring resonators," IET Microwaves, Antennas & Propagation, Vol. 9, No. 14, 1487-1496, May 2015, doi: 10.1049/iet-map.2015.0172.
    doi:10.1049/iet-map.2015.0172

    15. Alibakhshi-Kenari, M., M. Naser-Moghadasi, and R. A. Sadeghzadeh, "Composite right-left-handed-based antenna with wide applications in very-high frequency-ultra-high frequency bands for radio transceivers," IET Microwaves, Antennas & Propagation, Vol. 9, No. 15, 1713-1726, July 2015, doi: 10.1049/iet-map.2015.0308.
    doi:10.1049/iet-map.2015.0308

    16. Alibakhshi-Kenari, M., M. Naser-Moghadasi, R. A. Sadeghzadeh, and B. S. Virdee, "Metamaterial-based antennas for integration in UWB transceivers and portable microwave handsets," International Journal of RF and Microwave Computer-Aided Engineering, Vol. 26, No. 1, 88-96, January 2016, doi: 10.1002/mmce.20942.
    doi:10.1002/mmce.20942

    17. Alibakhshi-Kenari, M., M. Naser-Moghadasi, and R. Sadeghzadeh, "The resonating MTM-based miniaturized antennas for wide-band RF-microwave systems," Microwave and Optical Technology Letters, Vol. 57, No. 10, 2339-2344, October 2015, doi: 10.1002/mop.29328.
    doi:10.1002/mop.29328

    18. Alibakhshikenari, M., B. S. Virdee, A. Ali, and E. Limiti, "A novel monofilar-Archimedean metamaterial inspired leaky-wave antenna for scanning application for passive radar systems," Microwave and Optical Technology Letters, Vol. 60, No. 10, 2055-2060, February 2018, doi: 10.1002/mop.31300.
    doi:10.1002/mop.31300

    19. Alibakshikenari, M., B. S. Virdee, P. Shukla, Y. Wang, L. Azpilicueta, M. Naser-Moghadasi, C. H. See, I. Elfergani, C. Zebiri, R. A. Abd-Alhameed, I. Huynen, J. Rodriguez, T. A. Denidni, F. Falcone, and E. Limiti, "Impedance bandwidth improvement of a planar antenna based on metamaterial-inspired T-matching network," IEEE Access, Vol. 9, 67916-67927, May 2021, doi: 10.1109/ACCESS.2021.3076975.
    doi:10.1109/ACCESS.2021.3076975

    20. Alibakhshikenari, M., B. S. Virdee, C. H. See, R. A. Abd-Alhameed, F. Falcone, and E. Limiti, "Impedance matching network based on metasurfaces (2-D metamaterials) for electrically small antennas," 2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, 1953-1954, 2020, doi: 10.1109/IEEECONF35879.2020.9330460.
    doi:10.1109/IEEECONF35879.2020.9330460

    21. Alibakhshikenari, M., B. S. Virdee, P. Shukla, C. H. See, R. A. Abd-Alhameed, F. Falcone, and E. Limiti, "Improved adaptive impedance matching for RF front-end systems of wireless transceivers," Scientific Reports, Vol. 10, 14065, 2020, doi: 10.1038/s41598-020-71056-0.
    doi:10.1038/s41598-020-71056-0

    22. Fu, Y., Y. Xu, and H. Chen, "Applications of gradient index metamaterials in waveguides," Nature, Scientific Reports, Vol. 5, 1-6, December 2015, Art no. 18223, doi: 10.1038/srep18223.

    23. El-Khozondar, H. J., R. J. El-Khozondar, A. Shama, K. Ahmed, and V. Dhasarathan, "Highly efficient solar energy conversion using graded-index metamaterial nanostructured waveguide," Journal of Optical Communications, eISSN 2191-6322, ISSN 0173-4911, February 2020, doi: 10.1515/joc-2019-0285.

    24. La Spada, L., T. M. McManus, A. Dyke, S. Haq, L. Zhang, Q. Cheng, and Y. Hao, "Surface wave cloak from graded refractive index nanocomposites," Nature: Scientific Reports, Vol. 6, 29363, July 2016, doi: 10.1038/srep29363.

    25. Wu, Q., J. P. Turpin, and D. H. Werner, "Integrated photonic systems based on transformation optics enabled gradient index devices," Nature, Light: Science & Applications, Vol. 1, 1-6, November 2012, Art no. 4700605, doi: 10.1038/lsa.2012.38.

    26. Luque-González, J. M., R. Halir, J. G. Wanguemert-Perez, J. de-Oliva-Rubio, J. H. Schmid, P. Cheben, I. Molina-Fernandez, and A. Ortega-Monux, "An ultracompact GRIN-lens-based spot size converter using subwavelength grating metamaterials," Laser Photonics Reviews, Vol. 13, 1-7, September 2019, doi: 10.1002/lpor.201900172.

    27. Dalarsson, M., Z. Jaksic, and P. Tassin, "Exact analytical solution for oblique incidence on a graded index interface between a right-handed and a left-handed material," Journal of Optoelectronics and Biomedical Materials, Vol. 1, No. 4, 345-352, December 2009.

    28. Dalarsson, M., M. K. Norgren, T. Asenov, and N. Doncov, "Arbitrary loss factors in the wave propagation between RHM and LHM media with constant impedance throughout the structure," Progress In Electromagnetics Research, Vol. 137, 527-538, 2013.
    doi:10.2528/PIER13013004

    29. Dalarsson, M., "General theory of wave propagation through graded interfaces between positive-and negative refractive-index media," Physical Review A, Vol. 96, 043848, October 2017, doi: PhysRevA.96.043848.
    doi:10.1103/PhysRevA.96.043848

    30. Dalarsson, M. and P. Tassin, "Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material," Optics Express, Vol. 17, 6747-6752, April 2009.

    31. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, Dover Books, New York, 1965.