Signal propagation in electromagnetic media described by fractional-order models

• Published in: Communications in nonlinear science & numerical simulation 2020-03, Vol.82, p.105029, Article 105029
• Main Authors: Stefański, Tomasz P., Gulgowski, Jacek
• Format: Article
• Language: English
• Subjects: Algorithms; Attenuation; Computer simulation; Constitutive relationships; Electromagnetics; Fourier transforms; Fractional calculus; Marchaud derivative; Mathematical models; Maxwell's equations; Perturbation; Plane wave propagation; Plane waves; Propagation; Riemann–Liouville derivative; Signal processing; Time domain analysis; Wave propagation; Waveforms
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2019.105029

•In this paper, the signal propagation is analysed in electromagnetic media described by fractional-order (FO) models (FOMs). Maxwell’s equations with FO constitutive relations are introduced in the time domain.•With the use of the Fourier transformation, the algorithm for simulation of the non-monochromatic wave propagation is introduced. Its implementation in software allows for generation of time-domain waveforms of signals propagating in media described by FOMs.•It is demonstrated that despite high attenuation, a small perturbation of the time-derivative orders in Maxwell’s equations allows one to advance the time of signal arrival to the observation point.•In all the cases studied, the rate of pulse advancement increases, with simultaneous decrease of the value of the time-derivative orders in FO Maxwell’s equations. In this paper, signal propagation is analysed in electromagnetic media described by fractional-order (FO) models (FOMs). Maxwell’s equations with FO constitutive relations are introduced in the time domain. Then, their phasor representation is derived for one-dimensional case of the plane wave propagation. With the use of the Fourier transformation, the algorithm for simulation of the non-monochromatic wave propagation is introduced. Its implementation in Matlab allows for generation of time-domain waveforms of signals propagating in the media described by FOMs. It is demonstrated that despite high attenuation, a small perturbation of the time-derivative orders in Maxwell’s equations allows for tuning of the time of signal arrival to the observation point. In all the cases studied, the rate of pulse advancement increases, with simultaneous decrease of the value of the time-derivative orders in FO Maxwell’s equations.