Optical Phenomena in Time Dependent Medium


  • Cícero Julião Instituto Federal de Alagoas, BR-104, 111, Murici-AL, 57820-000, Brazil


Photonic Time Crystal, Periodic, Maxwell Equations, Dielectric Constant


How to deal with optical phenomena if the physical quantities are time-dependent? When a light wave propagating in space meets an interface between two media, a transmitted and a reflected wave appears. However, if a medium abruptly changes the value of its dielectric constant, even without an interface dividing space, we also have the phenomenon of reflection and refraction. Thinking of time as a coordinate similar to the spatial coordinates, the interface found also provides a change in the medium. But a change in time. Thus, known relationships, such as Snell’s Law, should be reviewed for such phenomena. This article deals with some situations where we have non-fixed dielectric constants, changing with time. From Maxwell’s equations, we demonstrate how to simulate the propagation of an electromagnetic wave in a medium that varies its dielectric constant over time. We used the finite difference method in the time domain (FDTD). We show the interesting phenomenon of temporal refraction and reflection.


. Mendonça, J. T., and P. K. Shukla., “Time Refraction and Time Reflection: Two Basic Concepts,” Phys. Scr, vol. 65, 2002.

. C. F. Bohren, “Scattering of electromagnetic waves by an optically active cylinder,” J. Colloid Interface Sci., vol. 66, no. 1, pp. 105–109, 1978.

. J. R. Zurita-Sánchez et al., “Pulse propagation through a slab with time-periodic dielectric function ε(t),” Opt. Express, vol. 20, no. 5, p. 5586, 2012.

. J. R. Zurita-Sánchez and P. Halevi, “Resonances in the optical response of a slab with time-periodic dielectric function ε(t),” Phys. Rev. A - At. Mol. Opt. Phys., vol. 81, no. 5, pp. 0–8, 2010.

. J. R. Zurita-Sánchez, P. Halevi, and J. C. Cervantes-González, “Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function (t),” Phys. Rev. A - At. Mol. Opt. Phys., vol. 79, no. 5, pp. 1–13, 2009.

. L. Zeng et al., “Photonic time crystals,” Sci. Rep., vol. 7, no. 1, pp. 1–9, 2017.

. F. R. Morgenthaler, “Velocity Modulation of Electromagnetic Waves,” IEEE Trans. Microw. Theory Tech., vol. 6, no. 2, pp. 167–172, 1958.

. F. Biancalana, A. Amann, A. V Uskov, and E. P. O’Reilly, “Dynamics of light propagation in spatiotemporal dielectric structures,” Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys., vol. 75, no. 4, 2007.

. E. J. Reed, M. Soljačić, and J. D. Joannopoulos, “Reversed doppler effect in photonic crystals,” Phys. Rev. Lett., vol. 91, no. 13, 2003.

. S. Juršenas, S. Miasojedovas, G. Kurilčik, A. Žukauskas, and P. R. Hageman, “Luminescence decay in highly excited GaN grown by hydride vapor-phase epitaxy,” Appl. Phys. Lett., vol. 83, no. 1, pp. 66–68, 2003.

. E. Lustig, Y. Sharabi, and M. Segev, “Topology of photonic time-crystals.”

. E. Lustig, Y. Sharabi, and M. Segev, “Topological aspects of photonic time crystals,” 2018.

. J. A. Richards, “Solutions to Periodic Differential Equations,” in Analysis of Periodically Time-Varying Systems, Berlin, Heidelberg: Springer Berlin Heidelberg, 1983, pp. 27–49.

. J. Ma and Z.-G. Wang, “Band structure and topological phase transition of photonic time crystals,” Opt. Express, vol. 27, no. 9, p. 12914, 2019.

. F. A. Harfoush and A. Taflove, “Scattering of electromagnetic waves by a material half-space with a time-varying conductivity,” IEEE Trans. Antennas Propag., vol. 39, no. 7, pp. 898–906, 1991.

. M. N. O. Sadiku, Computational Electromagnetics with MATLAB®. 2018.

. J. Nagel, “The One-Dimensional Finite-Difference Time-Domain (FDTD) Algorithm Applied to the Schrödinger Equation,” Bitbucket.Org, vol. 2, no. 3, pp. 1–5, 2012.

. Y. Hao and R. Mittra, FDTD Modeling of Metamaterials, no. January 2008. 2009.




How to Cite

Julião , C. . (2021). Optical Phenomena in Time Dependent Medium. American Scientific Research Journal for Engineering, Technology, and Sciences, 77(1), 135–144. Retrieved from https://www.asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/6736