Time-varying materials in the presence of dispersion: plane-wave propagation in a Lorentzian medium with temporal discontinuity

Diego M. Solís; Raphael Kastner; Nader Engheta

doi:10.1364/PRJ.427368

[1] N. Engheta, R. W. Ziolkowski. Metamaterials: Physics and Engineering Explorations(2006).

[2] T. Tanabe, M. Notomi, H. Taniyama, E. Kuramochi. Dynamic release of trapped light from an ultrahigh-Q nanocavity via adiabatic frequency tuning. Phys. Rev. Lett., 102, 043907(2009).

[3] M. Silveirinha, N. Engheta. Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials. Phys. Rev. Lett., 97, 157403(2006).

[4] B. Edwards, A. Alù, M. E. Young, M. Silveirinha, N. Engheta. Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide. Phys. Rev. Lett., 100, 033903(2008).

[5] T. Kodera, D. L. Sounas, C. Caloz. Artificial faraday rotation using a ring metamaterial structure without static magnetic field. Appl. Phys. Lett., 99, 031114(2011).

[6] M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, A. B. Khanikaev. Far-field probing of leaky topological states in all-dielectric metasurfaces. Nat. Commun., 9, 909(2018).

[7] Z. Yu, S. Fan. Complete optical isolation created by indirect interband photonic transitions. Nat. Photonics, 3, 91-94(2009).

[8] V. Bacot, M. Labousse, A. Eddi, M. Fink, E. Fort. Time reversal and holography with spacetime transformations. Nat. Phys., 12, 972-977(2016).

[9] A. M. Shaltout, V. M. Shalaev, M. L. Brongersma. Spatiotemporal light control with active metasurfaces. Science, 364, eaat3100(2019).

[10] K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, S. Zhang, A. Alù, C.-W. Qiu. A reconfigurable active Huygens’ metalens. Adv. Mater., 29, 1606422(2017).

[11] K. Lee, J. Son, J. Park, B. Kang, W. Jeon, F. Rotermund, B. Min. Linear frequency conversion via sudden merging of meta-atoms in time-variant metasurfaces. Nat. Photonics, 12, 765-773(2018).

[12] L. Zhang, X. Q. Chen, R. W. Shao, J. Y. Dai, Q. Cheng, G. Castaldi, V. Galdi, T. J. Cui. Breaking reciprocity with space-time-coding digital metasurfaces. Adv. Mater., 31, 1904069(2019).

[13] E. Yablonovitch. Self-phase modulation of light in a laser-breakdown plasma. Phys. Rev. Lett., 32, 1101-1104(1974).

[14] F. R. Morgenthaler. Velocity modulation of electromagnetic waves. IRE Trans. Microw. Theory Tech., 6, 167-172(1958).

[15] Y. Xiao, D. N. Maywar, G. P. Agrawal. Reflection and transmission of electromagnetic waves at a temporal boundary. Opt. Lett., 39, 574-577(2014).

[16] C. Caloz, Z. Deck-Léger. Spacetime metamaterials-part ii: theory and applications. IEEE Trans. Antennas Propag., 68, 1583-1598(2020).

[17] R. L. Fante. Transmission of electromagnetic waves into time-varying media. IEEE Trans. Antennas Propag., 19, 417-424(1971).

[18] R. L. Fante. On the propagation of electromagnetic waves through a time-varying dielectric layer. Appl. Sci. Res., 27, 341-354(1973).

[19] Y. Xiao, G. P. Agrawal, D. N. Maywar. Spectral and temporal changes of optical pulses propagating through time-varying linear media. Opt. Lett., 36, 505-507(2011).

[20] Y. Xiao, D. N. Maywar, G. P. Agrawal. Optical pulse propagation in dynamic Fabry–Perot resonators. J. Opt. Soc. Am. B, 28, 1685-1692(2011).

[21] A. G. Hayrapetyan, J. B. Gãtte, K. K. Grigoryan, S. Fritzsche, R. G. Petrosyan. Electromagnetic wave propagation in spatially homogeneous yet smoothly time-varying dielectric media. J. Quant. Spectrosc. Radiat. Transfer, 178, 158-166(2016).

[22] M. Chegnizadeh, K. Mehrany, M. Memarian. General solution to wave propagation in media undergoing arbitrary transient or periodic temporal variations of permittivity. J. Opt. Soc. Am. B, 35, 2923-2932(2018).

[23] F. A. Harfoush, A. Taflove. Scattering of electromagnetic waves by a material half-space with a time-varying conductivity. IEEE Trans. Antennas Propag., 39, 898-906(1991).

[24] D. Holberg, K. Kunz. Parametric properties of fields in a slab of time-varying permittivity. IEEE Trans. Antennas Propag., 14, 183-194(1966).

[25] D. E. Holberg, K. S. Kunz. Parametric properties of dielectric slabs with large permittivity modulation. Radio Sci., 3, 273-286(1968).

[26] J. R. Zurita-Sánchez, P. Halevi, J. C. Cervantes-González. Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ε(t). Phys. Rev. A, 79, 053821(2009).

[27] J. R. Zurita-Sánchez, J. H. Abundis-Patiño, P. Halevi. Pulse propagation through a slab with time-periodic dielectric function ε(t). Opt. Express, 20, 5586-5600(2012).

[28] J. S. Martnez-Romero, P. Halevi. Standing waves with infinite group velocity in a temporally periodic medium. Phys. Rev. A, 96, 063831(2017).

[29] J. S. Martnez-Romero, P. Halevi. Parametric resonances in a temporal photonic crystal slab. Phys. Rev. A, 98, 053852(2018).

[30] J. Simon. Action of a progressive disturbance on a guided electromagnetic wave. IRE Trans. Microw. Theory Tech., 8, 18-29(1960).

[31] A. A. Oliner, A. Hessel. Wave propagation in a medium with a progressive sinusoidal disturbance. IRE Trans. Microw. Theory Tech., 9, 337-343(1961).

[32] R. S. Chu, T. Tamir. Wave propagation and dispersion in space-time periodic media. Proc. Inst. Electr. Eng., 119, 797-806(1972).

[33] R. L. Fante. Optical propagation in space–time-modulated media using many-space-scale perturbation theory. J. Opt. Soc. Am., 62, 1052-1060(1972).

[34] T. T. Koutserimpas, R. Fleury. Electromagnetic waves in a time periodic medium with step-varying refractive index. IEEE Trans. Antennas Propag., 66, 5300-5307(2018).

[35] T. T. Koutserimpas, A. Alù, R. Fleury. Parametric amplification and bidirectional invisibility in PT-symmetric time-Floquet systems. Phys. Rev. A, 97, 013839(2018).

[36] T. T. Koutserimpas, R. Fleury. Nonreciprocal gain in non-Hermitian time-Floquet systems. Phys. Rev. Lett., 120, 087401(2018).

[37] T. T. Koutserimpas, R. Fleury. Electromagnetic fields in a time-varying medium: exceptional points and operator symmetries. IEEE Trans. Antennas Propag., 68, 6717-6724(2020).

[38] L. Felsen, G. Whitman. Wave propagation in time-varying media. IEEE Trans. Antennas Propag., 18, 242-253(1970).

[39] M. Mirmoosa, G. Ptitcyn, V. Asadchy, S. Tretyakov. Time-varying reactive elements for extreme accumulation of electromagnetic energy. Phys. Rev. Appl., 11, 014024(2019).

[40] G. Ptitcyn, M. S. Mirmoosa, S. A. Tretyakov. Time-modulated meta-atoms. Phys. Rev. Res., 1, 023014(2019).

[41] M. S. Mirmoosa, G. A. Ptitcyn, R. Fleury, S. A. Tretyakov. Instantaneous radiation from time-varying electric and magnetic dipoles. Phys. Rev. A, 102, 013503(2020).

[42] M. S. Mirmoosa, T. T. Koutserimpas, G. A. Ptitcyn, S. A. Tretyakov, R. Fleury. Dipole polarizability of time-varying particles(2020).

[43] A. Taflove, S. C. Hagness. Computational Electrodynamics: The Finite-Difference Time-Domain Method(2005).

[44] D. M. Sols, N. Engheta. Functional analysis of the polarization response in linear time-varying media: a generalization of the Kramers-Kronig relations. Phys. Rev. B, 103, 144303(2021).

[45] A. V. Oppenheim, A. S. Willsky, H. Nawab. Signals and Systems(1996).

[46] D. M. Pozar. Microwave Engineering(2011).

[47] G. Eleftheriades, A. Iyer, P. Kremer. Planar negative refractive index media using periodically L-C loaded transmission lines. IEEE Trans. Microw. Theory Tech., 50, 2702-2712(2002).

[48] N. Engheta, A. Salandrino, A. Alù. Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors. Phys. Rev. Lett., 95, 095504(2005).

[49] M.-A. Parseval. Mémoire sur les séries et sur l’intégration complète d’une équation aux différences partielles linéaires du second ordre, à coefficients constants. Mém. prés. par divers savants, Acad. des Sciences, Paris, 1, 638-648(1806).

[50] M. Plancherel, M. Leffler. Contribution à l’étude de la représentation d’une fonction arbitraire par des intégrales définies. Rendiconti del Circolo Matematico di Palermo (1884-1940), 30, 289-335(1910).

[51] L. Rayleigh. LIII. On the character of the complete radiation at a given temperature. London, Edinburgh, Dublin Philos. Mag. J. Sci., 27, 460-469(1889).

[52] H. Lebesgue. Intégrale, longueur, aire. Ann. Mat. Pura Appl. (1898-1922), 7, 231-359(1902).

CLP Journals