Abstract
In this study, the propagation characteristics of electromagnetic waves in a parity-time (PT)-symmetrical 1D photonic crystal comprising dispersed silver layers are investigated. Based on the transmission matrix theory, the total reflection and transmission coefficients of the structure are obtained. It was found that, due to the PT-symmetrical structure, the reflections of the left and right incident waves are nonreciprocal. Numerical simulations indicated that the width of the band gap decreases with the increase in the gain and loss factor ρ in the PT medium, and the band gap ultimately disappears when ρ reaches a critical value, i. e.,
-
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
-
Research funding: None declared.
-
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
[1] C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry”, Phys. Rev. Lett., vol. 80, pp. 5243–5246, 1998, https://doi.org/10.1103/physrevlett.80.5243.Search in Google Scholar
[2] C. M. Bender, S. Boettcher, and P. N. Meisinger, “PT-symmetric quantum mechanics”, J. Math. Phys., vol. 40, pp. 2201–V2229, 1999, https://doi.org/10.1063/1.532860.Search in Google Scholar
[3] Z. Ahmed, “Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential”, Phys. Lett. A., vol. 282, pp. 343–348, 2001, https://doi.org/10.1016/s0375-9601(01)00218-3.Search in Google Scholar
[4] S. A. Maiera and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures”, J. Appl. Phys., vol. 98., p. 011101, nos. 1–10, 2005, https://doi.org/10.1063/1.1951057.Search in Google Scholar
[5] L. Feng, Y. L. Xv, W. S. Fegadolli, et al., “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies”, Nature Mat., vol. 12, p. 108, 2012, https://doi.org/10.1038/nmat3495.Search in Google Scholar PubMed
[6] C. M. Bender, B. K. Berntson, D. Parker, and E. Samuel, “Observation of PT phase transition in a simple mechanical system”, Am. J. of Phys., vol. 81, p. 173, 2013, https://doi.org/10.1119/1.4789549.Search in Google Scholar
[7] V. Achilleos, G. Theocharis, O. Richoux, and V. Pagneux, “Non-Hermitian acoustic metamaterials: Role of exceptional points in sound absorption”, Phys. Rev. B., vol. 95, p. 144303, 2017, https://doi.org/10.1103/physrevb.95.144303.Search in Google Scholar
[8] L. Feng, Y. L. Xu, W. S. Fegadolli, et al., “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies”, Nat. Mater., vol. 12, no. 2, pp. 108–113, 2013, https://doi.org/10.1038/nmat3495.Search in Google Scholar
[9] J. Zhang, B. Peng, S. K. Ozdemir, et al., “A phonon laser operating at an exceptional point”, Nat. Photonics, vol. 12, pp. 479–484, 2018, https://doi.org/10.1038/s41566-018-0213-5.Search in Google Scholar
[10] S. K. Ozdemir, S. Rotter, F. Nori, and L. Yang, “Parity Ctime symmetry and exceptional points in photonics”, Nature Materials, vol. 18, pp. 783–798, 2019, https://doi.org/10.1038/s41563-019-0304-9.Search in Google Scholar PubMed
[11] J. Gear, Y. Sun, S. Y. Xiao, et al., “Unidirectional zero reflection as gauged parity-time symmetry”, New J. Phys., vol. 19, p. 123041, 2017, https://doi.org/10.1088/1367-2630/aa9b56.Search in Google Scholar
[12] Y. T. Fang, Y. Y. Wang, and J. Xia, “Large-range electric field sensor based on parity-time symmetry cavity structure”, Acta. Phys. Sin., vol. 68, no. 19, p. 194201, 2019, https://doi.org/10.7498/aps.68.20190784.Search in Google Scholar
[13] Y. Sun, W. Tan, H. Li, J. Li, and H. Chen, “Experimental Demonstration of a Coherent Perfect Absorber with PT Phase Transition”, Phys. Rev. Lett., vol. 112, p. 143903, 2014, https://doi.org/10.1103/physrevlett.112.143903.Search in Google Scholar
[14] P.J. Ma and L. Gao, “Large and tunable lateral shifts in one-dimensional PT-symmetric layered structures”, Opt. Exp., vol. 27 no. 6, pp. 9679–9688, 2017, https://doi.org/10.1364/OE.25.009676.Search in Google Scholar PubMed
[15] Y.Y. Cao, Y. Y. Fu, Q.J. Zhou, Y.D. Xu, L. Gao, and H.Y. Chen, “Giant Goos-H?nchen shift induced by bounded states in optical PT-symmetric bilayer structures”, Opt. Exp., vol. 25, no. 9, pp. 7857–7867, 2019, https://doi.org/10.1364/oe.27.007857.Search in Google Scholar PubMed
[16] S. Longhi, “Invisibility in PT-symmetric complex crystals”, J. Phys A-Math. Theor., vol. 44, p. 485302, 2011, https://doi.org/10.1088/1751-8113/44/48/485302.Search in Google Scholar
[17] H. Ramezani, T. Kotto, R. El-Ganainy, and D. N. Christodoulides, “Unidirectional Nonlinear PT-symmetric Optical Structures”, Phys. Rev. A, vol. 82, p. 043803, 2010, https://doi.org/10.1103/physreva.82.043803.Search in Google Scholar
[18] S. L. Ding and G. P. Wang, “Extraordinary reflection and transmission with direction dependent wavelength selectivity based on parity-time-symmetric multilayers”, J. App. Phys., vol. 117, p. 023104, 2015, https://doi.org/10.1063/1.4905319.Search in Google Scholar
[19] Y. T. Fang, Y. C. Zhang, and J. J. Wang, “Resonance-dependent extraordinary reflection and transmission in PC-symmetric layered structure”, Opt. Commun., vol. 407, pp. 255–261, 2018, https://doi.org/10.1016/j.optcom.2017.09.049.Search in Google Scholar
[20] Y. T. Fang, Y. Y. Wang, and Y. C. Zhang, “Twofold unidirectional properties of parity-time symmetry structure under magneto-optical modulation”, Opt. Eng., vol. 57, no. 2, p. 027102, 2018, https://doi.org/10.1117/1.oe.57.2.027102.Search in Google Scholar
[21] Y. Y. Fu, Y. D Xu, and H.Y Chen, “Zero index metamaterials with PT symmetry in a waveguide system”, Opt. Exp., vol. 24, no. 2, 1648–1657, 2016, https://doi.org/10.1364/oe.24.001648.Search in Google Scholar
[22] J. Y. Dong, G. X. Yu, J. J. Fu, M. Luo and W. W. Du, “Design of Multi-Resonant Cavities Based on Metal-Coated Dielectric Nanocylinders”, Z. Naturforsch, vol. 73, no. 6, pp. 559–563, 2018, https://doi.org/10.1515/zna-2018-0063.Search in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
