Abstract
In the present work, we study the rotations of the polarization of light propagating in right and left-handed films and layered structures. Through the use of complex values representing the rotations we analyze the transmission (Faraday effect) and reflections (Kerr effect) of light. It is shown that the real and imaginary parts of the complex angle of Faraday and Kerr rotations are odd and even functions for the refractive index n, respectively. In the thin film case with left-handed materials there are large resonant enhancements of the reflected Kerr angle that could be obtained experimentally. In the magnetic clock approach, used in the tunneling time problem, two characteristic time components are related to the real and imaginary portions of the complex Faraday rotation angle . The complex angle at the different propagation regimes through a finite stack of alternating right and left-handed materials is analyzed in detail. We found that, in spite of the fact that Re(θ) in the forbidden gap is almost zero, the Im(θ) changes drastically in both value and sign.
References
[1] Padilla, W. J., D. N. Basov, and D. R. Smith. Negative refractive index metamaterials. Materials Today, Vol. 9, No. 7-8, 2006, pp. 28–35.10.1016/S1369-7021(06)71573-5Search in Google Scholar
[2] Veselago, V. G. The electrodynamics of substances with simultaneously negative values of ϵ and µ. Soviet Physics - Uspekhi, Vol. 10, No. 4, 1968, pp. 509–514.10.1070/PU1968v010n04ABEH003699Search in Google Scholar
[3] Smith, D. R., W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz. Composite medium with simultaneously negative permeability and permittivity. Physical Review Letters, Vol. 84, No. 18, 2000, pp. 4184-4187.10.1103/PhysRevLett.84.4184Search in Google Scholar PubMed
[4] Garcia Pomar, J. L., Negative and anomalous refraction in meta-materials and photonic crystals, PhD thesis, Madrid, Spain, 2009.Search in Google Scholar
[5] Smith, D. R., J. B. Pendry, and M. C. K. Wiltshire. Metamaterials and negative refractive index. Science, Vol. 305, No. 5685, 2004, pp. 788–792.Search in Google Scholar
[6] Pendry, J. B. Negative refraction makes a perfect lens. Physical Review Letters, Vol. 85, No. 18, 2000, pp. 3966–3969.10.1103/PhysRevLett.85.3966Search in Google Scholar PubMed
[7] Yang, S., P. Liu, M. Yang, Q. Wang, J. Song, and L. Dong. From Flexible and Stretchable Meta-Atom to Metamaterial: A Wearable Microwave Meta-Skin with Tunable Frequency Selective and Cloaking Effects. Scientific Reports, Vol. 6, No. 1, 2016, id. 21921.10.1038/srep21921Search in Google Scholar PubMed PubMed Central
[8] Schurig, D., J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith. Metamaterial electromagnetic cloak at microwave frequencies. Science, Vol. 314, No. 5801, 2006, pp. 977–980.Search in Google Scholar
[9] Leonhardt, U. Optical conformal mapping. Science, Vol. 312, No. 5781, 2006, pp. 1777–1780.Search in Google Scholar
[10] Yang, Y., J. Xu, H. Chen, and S. Zhu. Quantum interference enhancement with left-handed materials. Physical Review Letters, Vol. 100, No. 4, 2008, id. 043601.10.1103/PhysRevLett.100.043601Search in Google Scholar PubMed
[11] Papasimakis, N., and N. I. Zheludev. Metamaterial-induced transparency: Sharp Fano resonances and slow light. Optics and Photonics News, Vol. 20, No. 10, 2009, pp. 22–27.10.1364/OPN.20.10.000022Search in Google Scholar
[12] Zhang, L., S. Liu, L. Li, and T. J. Cui. Spin-Controlled Multiple Pencil Beams and Vortex Beams with Different Polarizations Generated by Pancharatnam-Berry Coding Metasurfaces. Appl. Mater. Interfaces, Vol. 9, No. 41, 2017, pp. 36447–36455.10.1021/acsami.7b12468Search in Google Scholar PubMed
[13] Ahamed, E., M. R. I. Faruque, M. J. Alam, M. F. B. Mansor, and M. T. Islam. Digital metamaterial filter for encoding information. Scientific Reports, Vol. 10, No. 1, 2020, id. 3289, DOI: 10.1038/s41598-020-60170-8.10.1038/s41598-020-60170-8Search in Google Scholar PubMed PubMed Central
[14] Asatryan, A. A., L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, et al. Suppression of Anderson localization in disordered metamaterials. Physical Review Letters, Vol. 99, No. 19, 2007, id. 193902.10.1103/PhysRevLett.99.193902Search in Google Scholar PubMed
[15] del Barco, O., and M. Ortuño. Localization length of nearly periodic layered metamaterials. Physical Review A, Vol. 86, No. 2, 2012, id. 023846.10.1103/PhysRevA.86.023846Search in Google Scholar
[16] del Barco, O., V. Gasparian, and Z. Gevorkian. Localization-length calculations in alternating metamaterial-birefringent disordered layered stacks. Physical Review A, Vol. 91, No. 6, 2015, id. 063822.10.1103/PhysRevA.91.063822Search in Google Scholar
[17] Torres-Herrera, E. J., F. M. Izrailev, and N. M. Makarov. Non-conventional Anderson localization in a matched quarter stack with metamaterials. New Journal of Physics, Vol. 15, No. 5, 2013, id. 055014.10.1088/1367-2630/15/5/055014Search in Google Scholar
[18] Landau, L. D., and E. M. Lifshitz. Electrodynamics of Continuous Media, Elsevier, United Kingdom, 1984.10.1016/B978-0-08-030275-1.50007-2Search in Google Scholar
[19] Thouless, D. Electrons in disordered systems and the theory of localization. Physics Reports, Vol. 13, No. 3, 1974, pp. 93-142.10.1016/0370-1573(74)90029-5Search in Google Scholar
[20] Gasparian, V., M. Ortuño, J. Ruiz, and E. Cuevas. Faraday rotation and complex-valued traversal time for classical light waves. Physical Review Letters, Vol. 75, No. 12, 1995, pp. 2312–2315.10.1103/PhysRevLett.75.2312Search in Google Scholar PubMed
[21] Inoue, M., K. Nishimura, and T. Fujii. Localization and hopping of magnetoelastic waves in highly magnetostrictive strings with random chain structures (abstract). Journal of Applied Physics, Vol. 81, No. 8, 1997, id. 5692.10.1063/1.364639Search in Google Scholar
[22] Sadatgol, M., M. Rahman, E. Forati, M. Levy, and D. O. Guney. Enhanced Faraday rotation in hybrid magneto-optical metamaterial structure of bismuth-substituted-iron-garnet with embedded-gold-wires. Journal of Applied Physics, Vol. 119, No. 10, 2016, id. 103105.10.1063/1.4943651Search in Google Scholar
[23] Gevorkian, Z., V. Gasparian, and J. Lofy. Time dependent Faraday rotation. Laser Physics, Vol. 28, No. 1, 2018, id. 016001.10.1088/1555-6611/aa94deSearch in Google Scholar
[24] Caligiuri, V., R. Dhama, K. V. Sreekanth, G. Strangi, and A. De Luca. Dielectric singularity in hyperbolic metamaterials: The inversion point of coexisting anisotropies. Scientific Reports, Vol. 6, No. 1, 2016, id. 20002.10.1038/srep20002Search in Google Scholar PubMed PubMed Central
[25] Gevorkian, Z., and V. Gasparian. Plasmon-enhanced Faraday rotation in thin films. Physical Review A., Vol. 89, No. 2, 2014, id. 023830.10.1103/PhysRevA.89.023830Search in Google Scholar
[26] Sharipova, M., A. I. Musorin, T. D. Dolgova and A. Fedyanin. Ultrafast dynamics of Faraday rotation in thin films. Proceedings SPIE Optics+Optoelectronics, Prague, Czech Republic, Vol. 9502, 2015. Available from: DOI: 10.1117/12.218063510.1117/12.2180635Search in Google Scholar
[27] Enders, A., and G. Nimtz. On superluminal barrier traversal. Journal de Physique I, Vol. 2, 1992, pp. 1693–1698.10.1051/jp1:1992236Search in Google Scholar
[28] Enders, A., and G. Nimtz. Evanescent-mode propagation and quantum tunneling. Physical Review E, Vol. 48, 1993, pp. 632–634.10.1103/PhysRevE.48.632Search in Google Scholar
[29] Steinberg, A. M., P. G. Kwiat, and R. Y. Chiao. Measurement of the single-photon tunneling time. Physical Review Letters, Vol. 71, No. 5, 1993, pp. 708–711.10.1103/PhysRevLett.71.708Search in Google Scholar
[30] Spielman, Ch., R. Szipöcs, A. Stingl, and F. Krausz. Surface roughness scaling of plasma polymer films. Physical Review Letters, Vol. 73, 1994, pp. 708-711.10.1103/PhysRevLett.73.708Search in Google Scholar
[31] Hartman, E. Tunneling of a Wave Packet. Journal of Applied Physics, Vol. 33, No. 12, 1962, pp. 3427–3433.10.1063/1.1702424Search in Google Scholar
[32] Gasparian, V., M. Ortuño, G. Schön, and U. Simon. Handbook of Nanostructured Materials and Nanotechnology, Vol. 2, Nalwa, H. S., Ed. Academic Press, New York, 2000, pp. 513–569.10.1016/B978-012513760-7/50027-7Search in Google Scholar
[33] Muga, J. G., and C. R. Leavens. Arrival time in quantum mechanics. Physics Reports, Vol. 338, No. 4, 2000, pp. 353–438.10.1016/S0370-1573(00)00047-8Search in Google Scholar
[34] Balcou, Ph., and L. Dutriaux. Dual Optical Tunneling Times in Frustrated Total Internal Reflection. Physical Review Letters, Vol. 78, No. 5, 1997, pp. 851–854.10.1103/PhysRevLett.78.851Search in Google Scholar
[35] Gasparian, V., J. Ruiz, G. Schön, and M. Ortuño. Kramers-Kronig relations and the barrier interaction time problem. European Physical Journal B, Vol. 9, No. 2, 1999, pp. 283–287.10.1007/s100510050767Search in Google Scholar
[36] Aronov, A. G., V. M. Gasparian, and U. Gummich. Transmission of waves through one-dimensional random layered systems. Journal of Physics Condensed Matter, Vol. 3, No. 17, 1991, pp. 3023–3039.10.1088/0953-8984/3/17/017Search in Google Scholar
[37] Gasparian, V. Sov. Phys. Solid State 31 (1989) 266. Fiz. Tverd. Tela, Vol. 31, 1989, p. 162.Search in Google Scholar
[38] Carpena, P., V. Gasparian, and M. Ortuño. Finite periodic and quasiperiodic systems in an electric field. Zeitschrift für Physik B, Condensed Matter, Vol. 102, No. 3, 1997, pp. 425–431.10.1007/s002570050307Search in Google Scholar
© 2020 Josh Lofy et al., published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 International License.
