The Motion of a Charged Particle in the Electromagnetic Field of a Polarization-Modulated Wave

Abstract

This article presents an exact solution of the equation of motion of a charged particle in the electromagnetic field of a high-intensity polarization-modulated wave. Expressions for the average kinetic energy of a particle without regard to its rest energy in the case of circular and linear polarization of a modulated wave are obtained. The motion of a charged particle in the field was analyzed and expressed in terms of dependences of its average kinetic energy on the electromagnetic wave intensity and on various types of modulation depths. The contribution of each type of modulation to the energy characteristics of a charged particle was demonstrated. Solving the equation of motion of a charged particle in the electromagnetic field of a plane wave opens up possibilities for various applications related, in particular, to various developments of multi-frequency lasers and laser modulation technology. This study was proposed due to the growing interest in experiments using high-intensity femtosecond laser radiation and high-temperature plasma

This work was financially supported by the Russian Foundation for Basic Research and an Administration of the Krasnodar Region (project no. 19-44-230026)

Please cite this article as:

Kopytov G.Ph., Kudryavtsev D.I., Brazhko V.A. The motion of a charged particle in the electromagnetic field of a polarization-modulated wave. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2022, no. 6 (105), pp. 106--122. DOI: https://doi.org/10.18698/1812-3368-2022-6-106-122

Литература

[1] Gupta V.K., Kornfield J.A., Ferencz A., et al. Controlling molecular order in "Hairy-Rod" Langmuir --- Blodgett films: a polarization-modulation microscopy study. Science, 1994, vol. 265, no. 5174, pp. 940--942. DOI: https://doi.org/10.1126/science.265.5174.940

[2] Popovsky V.V., Kuzminich I.V. Method of polarization modulation and multiplexing in fiber-optic communication lines. Vestnik nauchnykh konferentsiy [Bulletin of Scientific Conferences], 2016, no. 10-2, pp. 94--100 (in Russ.).

[3] Knyazkov A.V. Polarize-optical light modulation. Nauchno-tekhnicheskie vedomosti SPbGPU. Fiziko-matematicheskie nauki [St. Petersburg State Polytechnical University Journal. Physics and Mathematics], 2013, no. 3, pp. 156--161 (in Russ.).

[4] Lopez-Ortega A., Zapata-Herrera M., Maccaferri N., et al. Enhanced magnetic modulation of light polarization exploiting hybridization with multipolar dark plasmons in magnetoplasmonic nanocavities. Light Sci. Appl., 2020, vol. 9, art. 49. DOI: https://doi.org/10.1038/s41377-020-0285-0

[5] Lyu Z., Wang C. All-optically phase-induced polarization modulation by means of holographic method. Sci. Rep., 2020, vol. 10, no. 1, art. 5657. DOI: https://doi.org/10.1038/s41598-020-62549-z

[6] Kovalev A.A., Yakunin V.V., Glazkov Yu.B. Spacial-polarization modulation of laser electromagnetic irradiation. Lazernaya meditsina [Laser Medicine], 2011, vol. 15, no. 2, pp. 120--121 (in Russ.).

[7] Li S., Li G., Ain Q., et al. A laser-plasma accelerator driven by two-color relativistic femtosecond laser pulses. Sci. Adv., 2019, vol. 5, no. 11. DOI: https://doi.org/10.1126/sciadv.aav7940

[8] Malka V., Fritzlerer S., Lefebvre E., et al. Electron acceleration by a wake field forced by an intense ultrashort laser pulse. Science, 2002, vol. 298, no. 5598, pp. 1596--1600. DOI: https://doi.org/10.1126/science.1076782

[9] Pompili R., Anania M., Bisesto F., et al. Femtosecond dynamics of energetic electrons in high intensity laser-matter interactions. Sci. Rep., 2016, vol. 6, art. 35000. DOI: https://doi.org/10.1038/srep35000

[10] Orlov A.B., Lutin E.A., Zhelyaeva L.E., et al. Mikropoloskovaya antennaya reshetka s polyarizatsionnoy adaptatsiey [Adaptive-polarization microstrip antenna array]. Patent RU 2156526. Appl. 27.11.1998, publ. 20.09.2000 (in Russ.).

[11] Frenkel Ya.I. Sobranie izbrannykh trudov. T. 1. Elektrodinamika [Collection of selected works. Vol. 1. Electrodynamics]. Moscow, Leningrad, ONTI-GTTI Publ., 1934.

[12] Volkov D.M. Electron in the field of plane polarized electromagnetic waves from the point of view of the Dirac equation. ZhETF, 1937, vol. 7, no. 11, pp. 1286--1289 (in Russ.).

[13] Landau L.D., Lifshitz E.M. The classical theory of fields. Course of theoretical physics. Vol. 2. The classical theory of fields. Butterworth-Heinemann, 1975.

[14] Boldyrev E.M. Motion of a particle in a static magnetic field and the field of a monochromatic electromagnetic plane wave. Tech. Phys., 1999, vol. 44, no. 5, pp. 575--579. DOI: https://doi.org/10.1134/1.1259386

[15] Chikhachev A.S., Chulkov V.V. Dependence of the motion of a charged particle on the phase of flight in the field of a powerful electromagnetic wave. J. Commun. Technol. Electron., 2007, vol. 52, no. 12, pp. 1373--1376. DOI: https://doi.org/10.1134/S106422690712011X

[16] Andreyev S.N., Makarov V.P., Rukhadze A.A. On the motion of a charged particle in a plane monochromatic electromagnetic wave. Quantim Electron., 2009, vol. 39, no. 1, pp. 68--72.

[17] Kopytov G.F., Martynov A.A., Akintsov N.S. A charged particle moves in the field of the plane elliptically polarized electromagnetic wave. Fundamentalnye issledovaniya [Fundamental Research], 2014, no. 9-5, pp. 1013--1018 (in Russ.).

[18] Kopytov G.F., Martynov A.A., Akintsov N.S. Motion of a charged particle in the field of a circularly polarized amplitude-modulated electromagnetic wave. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva [Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation], 2014, vol. 11, no. 2, pp. 39--43 (in Russ.).

[19] kintsov N.S., Kopytov G.F., Martynov A.A., et al. Motion of a charged particle in the field of an arbitrarily polarized amplitude-modulated electromagnetic wave. Fizicheskoe obrazovanie v vuzakh [Physical Education in Universities], 2015, vol. 21, no. S1, pp. 14--15 (in Russ.).

[20] Kopytov G.F., Martynov A.A., Akintsov N.S. The motion of a charged particle in the field by a frequency-modulated electromagnetic wave. Nanosistemy: fizika, khimiya, matematika [Nanosystems: Physics, Chemistry, Mathematics], 2015, vol. 6, no. 5, pp. 661--671. DOI: https://doi.org/10.17586/2220-8054-2015-6-5-661-671

[21] Akintsov N.S. Spectral characteristics of polarization-modulated electromagnetic wave in vacuum. Fizicheskoe obrazovanie v vuzakh [Physical Education in Universities], 2016, vol. 22, no. S1, pp. 35--37 (in Russ.).

[22] Bateman G., Erdelyia. Higher transcendental functions. McGraw-Hill, 1953.

[23] Sim S., Jang H., Koirala N., et al. Ultra-high modulation depth exceeding 2,400 % in optically controlled topological surface plasmons. Nat. Commun., 2015, vol. 6, art. 8814. DOI: https://doi.org/10.1038/ncomms9814