Vol. 112

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2022-07-25

Spatiotemporal Localized Waves and Accelerating Beams in a Uniformly Moving Dielectric Medium

By Ioannis Besieris
Progress In Electromagnetics Research M, Vol. 112, 55-65, 2022
doi:10.2528/PIERM22050907

Abstract

A study is presented of several types of nondiffracting and slowly diffracting spatiotemporally localized waves supported by a simple dielectric medium moving uniformly with speed smaller or larger than the phase speed of light in the rest frame of the medium. The Minkowski material relations are not independent in the case that the speed of motion equals the phase speed of the medium; hence, the electric displacement and magnetic induction vectors cannot be uniquely determined from them. Following, however, a waveguide-theoretic approach, separate equations can be written for the longitudinal and transverse (with respect to the direction of motion) electromagnetic field intensities. The fundamental solutions associated with these equations provide a uniform transition between the cases of ordinary and Čerenkov-Vavilov radiation. The equation satisfied by the longitudinal field components in the absence of sources is examined in detail. In the temporal frequency domain one has an exact parabolic equation which supports accelerating beam solutions. The space-time equation supports several types of nondiffracting and slowly diffracting spatiotemporally localized waves. Comparisons are also made with the acoustic pressure equation in the presence of a uniform flow.

Citation


Ioannis Besieris, "Spatiotemporal Localized Waves and Accelerating Beams in a Uniformly Moving Dielectric Medium," Progress In Electromagnetics Research M, Vol. 112, 55-65, 2022.
doi:10.2528/PIERM22050907
http://jpier.org/PIERM/pier.php?paper=22050907

References


    1. Minkowski, H., "Die Grundgleichungen fur die electromagnetichen vorhange in bewegten Korpern," Kgl. Ges. Wiss., Vol. 1, 53-116, 1908.

    2. Tai, C. T., "The dyadic Green's function in a moving isotropic medium," IEEE Antennas Propag., Vol. 13, 322-323, 1965.
    doi:10.1109/TAP.1965.1138414

    3. Besieris, I. M. and R. T. Compton, "Time-dependent Green's function for electromagnertic waves in moving conducting media," J. Math. Phys., Vol. 8, 2445-2451, 1967.
    doi:10.1063/1.1705178

    4. Brittingham, J. N., "Focus wave modes in homogeneous Maxwell equations: Transverse electric mode," J. Appl. Phys., Vol. 54, 1179-1189, 1983.
    doi:10.1063/1.332196

    5. Kiselev, A. P., "Modulated Gaussian beams," Radio Phys. Quant. Electron., Vol. 26, 1014-1020, 1983.
    doi:10.1007/BF01034667

    6. Ziolkowski, R. W., "Localized transmission of electromagnetic energy," Phys. Rev. A, Vol. 39, 2005-2033, 1989.
    doi:10.1103/PhysRevA.39.2005

    7. Besieris, I. M., A. M. Shaarawi, and R. W. Ziolkowski, "A bidirectional traveling plane wave representation of exact solutions of the scalar wave equation," J. Math. Phys., Vol. 30, 1254-1269, 1989.
    doi:10.1063/1.528301

    8. Lu, J. Y. and J. F. Greenleaf, "Nondiffracting X waves-exact solutions to the free space scalar wave equation and their finite aperture realization," IEEE Trans. Ultrason. Ferroelectr. Freq. Contr., Vol. 39, 19-31, 1992.
    doi:10.1109/58.166806

    9. Ziolkowski, R. W., I. M. Besieris, and A. M. Shaarawi, "Aperture realizations of the exact solutions to homogeneous-wave equations," J. Opt. Soc. Am. A, Vol. 10, 75-87, 1993.
    doi:10.1364/JOSAA.10.000075

    10. Saari, P. and K. Reivelt, "Evidence of X-shaped propagation-invariant localized light waves," Phys. Rev. Lett., Vol. 79, 4135-4137, 1997.
    doi:10.1103/PhysRevLett.79.4135

    11. Besieris, I., M. Abdel-Rahman, A. Shaarawi, and A. Chatzipetros, "Two fundamental represen- tations of localized pulse solutionsto the scalar wave equation," Progress In Electromagnetics Research, Vol. 19, 1-48, 1998.
    doi:10.2528/PIER97072900

    12. Salo, J., J. Fagerholm, A. T. Friberg, and M. M. Saloma, "Unified description of X and Y waves," Phys. Rev. E, Vol. 62, 4261, 2000.
    doi:10.1103/PhysRevE.62.4261

    13. Grunwald, R., V. Kebbel, U. Neumann, A. Kummrow, M. Rini, E. T. Nibbering, M. Piche, G. Rousseau, and M. Fortin, "Generation and characterization of spatially and temporally localized few-cycle optical wave packets," Phys. Rev. A, Vol. 67, 063820 1-5, 2003.
    doi:10.1103/PhysRevA.67.063820

    14. Saari, P. and K. Reivelt, "Generation and classification of localized waves by Lorentz transformations in Fourier space," Phys. Rev. E, Vol. 68, 036612 1-12, 2004.

    15. Longhi, S., "Spatial-temporal Gauss-Laguerre waves in dispersive media," Phys. Rev. E, Vol. 68, 066612 1-6, 2003.
    doi:10.1103/PhysRevE.68.066612

    16. Conti, C., S. Trillo, P. di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett., Vol. 90, 170406 1-4, 200.

    17. Kiselev, A. P., "Localized light waves: Paraxial and exact solutions of the wave equation (review)," Opt. Spectrosc., Vol. 102, 603-622, 2007.
    doi:10.1134/S0030400X07040200

    18. Hernandez-Figueroa, H. E., M. Zamboni-Rached, and E. Recami, Localized Waves, Wiley- Interscience, Hoboken, NJ, 2008.
    doi:10.1002/9780470168981

    19. Hernandez-Figueroa, H. E., M. Zamboni-Rached, and E. Recami, Non-Diffracting Waves, Wiley-VCH, 2014.

    20. Sen Gupta, N. D., "Electrodynamics of moving media and Cerenkov radiation," J. Phys. A (Proc. Phys. Soc.), Vol. 1, 340, 1968.

    21. Sancer, M., "Potentials for cylindrical warm plasmas," Radio Sci., Vol. 1, 799, 1966.
    doi:10.1002/rds1966191067

    22. Siviloglou, G. A. and D. N. Christodoulides, "Accelerating finite-energy Airy beams," Opt. Lett., Vol. 32, 979-981, 2007.
    doi:10.1364/OL.32.000979

    23. Siviloglou, G. A., J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of accelerating Airy beams," Phys. Rev. Lett., Vol. 99, 2139011-4, 2007.
    doi:10.1103/PhysRevLett.99.213901

    24. Saari, P., "Laterally accelerating Airy pulses," Opt. Express, Vol. 16, 10303-10308, 2008.
    doi:10.1364/OE.16.010303