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SIGMA, 2012, Volume 8, 096, 21 pages (Mi sigma773)  

This article is cited in 8 scientific papers (total in 8 papers)

Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources

Gennadiy Burlaka, Vladimir Rabinovichb

a Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Cuernavaca, Mor. México
b National Polytechnic Institute, ESIME Zacatenco, D.F. México

Abstract: The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit expressions for the field amplitudes and simple relations for the field eigenfrequencies and the retardation time that become the coupled variables. The main features of the technique are illustrated by examples of the moving source fields in the plasma and the Cherenkov radiation. It is emphasized that the deeper insight to the wave effects in dispersive case already requires the explicit formulation of the dispersive material model. As the advanced application we have considered the Doppler frequency shift in a complex single-resonant dispersive metamaterial (Lorenz) model where in some frequency ranges the negativity of the real part of the refraction index can be reached. We have demonstrated that in dispersive case the Doppler frequency shift acquires a nonlinear dependence on the modulating frequency of the radiated particle. The detailed frequency dependence of such a shift and spectral behavior of phase and group velocities (that have the opposite directions) are studied numerically.

Keywords: dispersive media; two-dimensional stationary phase method; electromagnetic wave; moving modulated source


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ArXiv: 1212.1971
MSC: 78A25; 78A35
Received: July 29, 2012; in final form December 2, 2012; Published online December 10, 2012

Citation: Gennadiy Burlak, Vladimir Rabinovich, “Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources”, SIGMA, 8 (2012), 096, 21 pp.

Citation in format AMSBIB
\by Gennadiy~Burlak, Vladimir~Rabinovich
\paper Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources
\jour SIGMA
\yr 2012
\vol 8
\papernumber 096
\totalpages 21

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    This publication is cited in the following articles:
    1. Burlak G., Martinez-Sanchez E., “Change of Structure of the Cherenkov Emission at Modulated Source in Dispersive Metamaterials”, Prog. Electromagn. Res., 139 (2013), 277–288  crossref  isi  elib  scopus
    2. Burlak, G., Martinez-Sanchez, E., “Spatial resonances of the Cherenkov emission in dispersive metamaterials”, Materials Research Society Symposium Proceedings, 1617, 2013, 181–185  scopus
    3. Vladimir Vega Alcantar, Aura Jazmine and Rabinovich, “Electromagnetic Waves Propagation from Moving Sources in Waveguides Filled by a Dispersive Dielectric Media”, Communications in Mathematical Analysis, 16:2 (2014), 84–101  mathscinet  zmath
    4. E. Martinez-Sanchez, G. Burlak, V. Rabinovich, “The structure of the Cherenkov field emission in metamaterials”, Communications in Mathematical Analysis, 17:2 (2014), 253–262  mathscinet  zmath
    5. Burlak G., Rabinovich V., “Propagation of Electromagnetic Waves Generated By Modulated Moving Source in Dispersive Lossy Media”, Math. Meth. Appl. Sci., 38:10, SI (2015), 2012–2026  crossref  mathscinet  zmath  isi  elib  scopus
    6. Barrera-Figueroa V., Rabinovich V.S., “Cherenkov radiation in a planarly layered waveguide in the case of polarized waves”, Bol. Soc. Mat. Mex., 22:2, SI (2016), 431–459  crossref  mathscinet  zmath  isi
    7. Barrera-Figueroa V., Rabinovich V.S., “Electromagnetic field generated by a modulated moving point source in a planarly layered waveguide”, Russ. J. Math. Phys., 23:2 (2016), 139–163  crossref  mathscinet  zmath  isi  elib  scopus
    8. Lopez-Toledo J.A., Oviedo-Galdeano H., “Reflection and Transmission of a Gaussian Beam For An Inhomogeneous Layered Medium Using Spps Method”, J. Electromagn. Waves Appl., 32:17 (2018), 2210–2227  crossref  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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