volume | PIER Journals

Abstract

It is commonly believed that electromagnetic waves cannot propagate in lossy conductive media and that they quickly decay inside such media over short length scales of the order of the so-called skin depth. Here we prove that this common belief is incorrect if the conductive medium is stratified. We demonstrate that electromagnetic waves in stratified lossy conductive media may have propagating character, and that the propagation length of such waves may be considerably larger than the skin depth in homogeneous media. Our findings have broad implications in many fields of science and engineering. They enable radio communication and imaging in such strongly lossy conductive media as seawater, various soils, plasma and biological tissues. They also enable novel electromagnetic metamaterial designs by mediating the effect of losses on electromagnetic signal propagation in metamaterials. Our results demonstrate a new class of inherently non-Hermitian electromagnetic media with high dissipation, no gain, and no PT-symmetry, which nevertheless have almost real eigenvalue spectrum.

1. Blum, W. E. H., P. Schad, and S. Nortcliff, Essentials of Soil Science, Borntraeger Science Publishers, Stuttgart, 2018.

2. Vance, S., M. Bouffard, M. Choukroun, and C. Sotin, "Ganymede's internal structure including thermodynamics of magnesium sulfate oceans in contact with ice," Planetary and Space Science, Vol. 96, 62-70, 2014.
doi:10.1016/j.pss.2014.03.011 Google Scholar

3. Smolyaninov, I. I., "Surface electromagnetic waves at gradual interfaces between lossy media," Progress In Electromagnetics Research, Vol. 170, 177-186, 2021.
doi:10.2528/PIER21043006 Google Scholar

4. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, 77-79, 2001.
doi:10.1126/science.1058847 Google Scholar

5. Guo, A., G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, "Observation of PT-symmetry breaking in complex optical potentials," Phys. Rev. Letters, Vol. 103, 093902, 2009.
doi:10.1103/PhysRevLett.103.093902 Google Scholar

6. Smolyaninov, I. I., Q. Balzano, C. C. Davis, and D. Young, "Surface wave based underwater radio communication," IEEE Antennas and Wireless Propagation Letters, Vol. 17, 2503-2507, 2018.
doi:10.1109/LAWP.2018.2880008 Google Scholar

7. Landau, L. D. and E. M. Lifshitz, Quantum Mechanics, Elsevier, 1977.

8. Li, Y. and D. W. Oldenburg, "Aspects of charge accumulation in DC resistivity experiments," Geophysical Prospecting, Vol. 39, 803-826, 1991.
doi:10.1111/j.1365-2478.1991.tb00345.x Google Scholar

9. Bloch, F., "Uber die quantenmechanik der elektronen in kristallgittern," Zeitschrift fur Physik, Vol. 52, 555-600, 1929.
doi:10.1007/BF01339455 Google Scholar

10. Kittel, C., Introduction to Solid-state Physics, 173-196, John-Wiley, Singapore, 1996.

11. Bender, C. M. and S. Boettcher, "Real spectra in non-Hermitian Hamiltonians having PT Symmetry," Phys. Rev. Letters, Vol. 80, 5243, 1998.
doi:10.1103/PhysRevLett.80.5243 Google Scholar

12. Smolyaninov, I. I., "Gradient-index nanophotonics," Journal of Optics, Vol. 23, 095002, 2021.
doi:10.1088/2040-8986/ac1322 Google Scholar

13. Kozyrev, A. B., C. Qin, I. V. Shadrivov, Yu. S. Kivshar, I. L. Chuang, and D. W. van der Weide, "Wave scattering and splitting by magnetic metamaterials," Opt. Express, Vol. 15, 11714-11722, 2007.
doi:10.1364/OE.15.011714 Google Scholar

14. Smolyaninov, I. I., Hyperbolic Metamaterials, Morgan & Claypool/Institute of Physics, London, 2018.
doi:10.1088/978-1-6817-4565-7

15. Wangberg, R., et al. "Nonmagnetic nanocomposites for optical and infrared negative-refractive-index media," J. Opt. Soc. Am. B, Vol. 23, 498, 2006.
doi:10.1364/JOSAB.23.000498 Google Scholar

Dr. Igor I. Smolyaninov

Dr. Alexander B. Kozyrev