Abstract
In this chapter, we first emphasize upon the unique properties of generic time-periodic permittivity-modulated media like momentum gaps and parametric amplification/absorption. Then we showcase the formulation of a state-transition matrix-based analytical approach for the studies on EM wave propagation in dielectric media having step-periodically varying permittivity (i.e. permittivity switching between two values). We further demonstrate how the numerical solution of system ODEs (ordinary differential equations) using MATLAB can assist in the performance prediction of infinitely extended space-invariant step-modulated dielectric medium. Finally, we deploy the 1D-FDTD-based computational framework developed in earlier chapters to shed light onto the interaction of EM waves with a step-modulated dielectric slab, considering various permittivity contrast, modulation frequency and slab-widths. We point out the main differences between step-periodic and sinusoidal permittivity variation cases in terms of imposed non-linear modulation on the carrier EM wave. We highlight and demonstrate the instability scenario that leads to parametric amplification through numerical examples.
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Notes
- 1.
Mathematically speaking, these special operating conditions are often interpreted using Floquet diabolic and exceptional points [16].
References
Collin RE (1966) Foundations for microwave engineering. McGraw-Hill, New York, NY, USA
Ramakrishna SA, Grzegorczyk TM (2009) Physics and applications of negative refractive index materials. Taylor & Francis Group and SPIE Press, CRC Press
Eleftheriades GV, Balmain KG (2005) Negative refraction metamaterials: fundamental principles and applications, Copyright: IEEE. Wiley, Hoboken, New Jersey
Caloz C, Itoh T (2006) Electromagnetic metamaterials: transmission line theory and microwave applications, the engineering approach. Wiley, Hoboken, New Jersey
Morgenthaler FR (1958) Velocity modulation of electromagnetic waves. IRE Trans Microw Theory Tech 6:167–172
Weinstein H (1965) Linear signal stretching in a time-variant system. IEEE Trans Circuit Theory 12:157–164
Holberg D, Kunz K (1966) Parametric properties of fields in a slab of time-varying permittivity. IEEE Trans Antennas Propag 14:183–194
Auld B, Collins J, Zapp H (1968) Signal processing in a nonperiodically time-varying magnetoelastic medium. Proc IEEE 56:258–272
Rezende SM, Morgenthaler FR (1969) Magnetoelastic waves in time-varying magnetic fields. I. theory. J App Phys 40:524–536
Felsen L, Whitman G (1970) Wave propagation in time-varying media. IEEE Trans Antennas Propag 18:242–253
Fante R (1971) Transmission of electromagnetic waves into time-varying media. IEEE Trans Antennas Propag 19:417–424
Budko VN (2009) Electromagnetic radiation in a time-varying background medium. Phys Rev A (Gen Phys) 80:053817
Zurita-Sanchez JR, Halevi P, Cervantes-Gonzalez JC (2009) Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function \(\varepsilon (t)\). Phys Rev A (Gen Phys) 79:053821
Xiao Y, Maywar DN, Agrawal GP (2014) Reflection and transmission of electromagnetic waves at a temporal boundary. Opt Lett 39:574
Hayrapetyan AG, Gotte JB, Grigoryan KK, Fritzsche S, Petrosyan RG (2016) Electromagnetic wave propagation in spatially homogeneous yet smoothly time-varying dielectric media. J Quant Spectrosc Radiat Transf 178:158–166
Koutserimpas TT, Fleury R (2018) Electromagnetic waves in a time periodic medium with step-varying refractive index. IEEE Trans Antennas Propag 66:5300–5307
Lurie KA, Yakovlev VV (2016) Energy accumulation in waves propagating in space-and time-varying transmission lines. IEEE Antennas Wirel Propag Lett 15:1681–1684
Lurie KA, Onofrei D, Sanguinet WC, Weekes SL, Yakovlev VV (2017) Energy accumulation in a functionally graded spatial temporal checkerboard. IEEE Antennas Wirel Propag Lett 16:1496–1499
Mirmoosa MS, Ptitcyn GA, Asadchy VS, Tretyakov SA (2019) Time-varying reactive elements for extreme accumulation of electromagnetic energy. Phys Rev A (Gen Phys) 11:014024
Koutserimpas TT, Fleury R (2018) Nonreciprocal gain in non-Hermitian time-Floquet systems. Phys Rev Lett 120:087401
Akbarzadeh A, Chamanara N, Caloz C (2018) Inverse prism based on temporal discontinuity and spatial dispersion. Opt Lett 43:3297
Martinez-Romero JS, Becerra-Fuentes OM, Halevi P (2016) Temporal photonic crystals with modulations of both permittivity and permeability. Phys Rev A (Gen Phys) 93:063813
Estep NA, Sounas DL, Soric J, Alu A (2014) Magnetic-free nonreciprocity and isolation based on parametrically modulated coupled resonator loops. Nat Phys 10:923–927
Hadad Y, Soric JC, Alu A (2016) Breaking temporal symmetries for emission and absorption. Proc Nat Acad Sci USA 113:3471–3475
Chegnizadeh M, Mehrany K, Memarian M (2018) General solution to wave propagation in media undergoing arbitrary transient or periodic temporal variations of permittivity. J Opt Soc Am B 35:2923–2932
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Sarkar, D. (2022). EM Wave Propagation in Dielectric Medium with Step-Periodic Modulation. In: FDTD Analysis of Guided Electromagnetic Wave Interaction with Time-Modulated Dielectric Medium. SpringerBriefs in Electrical and Computer Engineering(). Springer, Singapore. https://doi.org/10.1007/978-981-19-1630-4_4
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DOI: https://doi.org/10.1007/978-981-19-1630-4_4
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