We consider a weakly nonlinear process of propagation of a modulated pulse with high-frequency filling in a plane graded-index waveguide layer. The transverse distribution of the refractive index is specified by a function of the hyperbolic-secant type, which is nonsymmetric relative to the layer axis. Due to this fact, the analysis includes not only the asymmetry of the waveguide layer, but also different properties of the cladding on both sides of the layer. Longitudinal inhomogeneity of the studied waveguide structure is also admissible. The transcendental characteristic equation is derived to determine the mode propagation constants, and the transverse wave fields are expressed in terms of a hypergeometric function. Numerical calculations demonstrate the possibility of the mode cutoff due to the asymmetry of the waveguide layer. The nonlinear Schrödinger equation is derived for the pulse envelope with the coefficients corresponding to the nonsymmetric waveguide layer.
Similar content being viewed by others
References
M. Diamond, J. Geophys. Res., 68, No. 11, 3459–3464 (1964). https://doi.org/10.1029/JZ068i011po3459
A. G. Sorokin and I. Y. Lobycheva, J. Atmos. Sol.-Terr. Phys., 73, No. 13, 1629–1635 (2011). https://doi.org/10.1016/j.jastp.2011.02.006
C. R. Wilson, J. Geophys. Res., 74, No. 7, 1812–1836 (1969). https://doi.org/10.1029/JA074i007p01812
V. M. Somsikov, Geomagn. Aeron., 51, No. 6, 707–719 (2011). https://doi.org/10.1134/S0016793211060168
N. T. Afanasiev and S. O. Chudaev, Sol.-Terr. Phys., 6, No. 4, 66–73 (2020). https://doi.org/10.12737/stp-64202010
S. S. Alsatkin, A. V. Medvedev, and K. G. Ratovsky, Sol.-Terr. Phys., 6, No. 1, 77–88 (2020). https://doi.org/10.12737/stp-61202009
V. Yu. Belashov and E. S. Belashova, Geomagn. Aeron., 56, No. 6, 716–723 (2016). https://doi.org/10.1134/S0016793216060049
N. V. Bakhmet’eva, G. I. Grigor’ev, A. V. Tolmacheva, et al., Radiophys. Quantum Electron., 60, No. 2, 103–112 (2017). https://doi.org/10.1007/s11141-017-9780-4
N. S. Petrukhin, E. N. Pelinovsky, and E. G. Didenkulova, Radiophys. Quantum Electron., 63, No. 1, 29–39 (2020). https://doi.org/10.1007/s11141-020-10032-0
K. M. Yusupov, N. V. Bakhmet’eva, V. L. Frolov, et al., in: XXVIth Russian Open Sci. Conf. on Radio Wave Propagation, July 1–6, 2019, Kazan, Russia, Vol. 2, pp. 124–127.
N. Yu. Zaalov and E. V. Moskaleva, Adv. Space Res., 64, No. 6, 1243–1255 (2019). https://doi.org/10.1016/j.asr.2019.06.034
B. G. Gavrilov, Yu. I. Zetser, A. N. Lyakhov, et al., Geomagn. Aeron., 57, No. 4, 461–470 (2017). https://doi.org/10.1134/S0016793217040065
E. D. Tereshchenko, V. A. Turyansky, B. Z. Khudukon, et al., Radiophys. Quantum Electron., 60, No. 8, 609–617 (2017). https://doi.org/10.1007/s11141-018-9831-5
E. N. Sergeev, S. M. Grach, V. L. Frolov and A. V. Shindin, Radiophys. Quantum Electron., 59, No. 11, 876–887 (2016). https://doi.org/10.1007/s11141-017-9758-2
T. M. Zaboronkova, N. F. Yashina, and C. Krafft, Phys. Plasmas, 26, No. 10, Art. no. 102104 (2019). https://doi.org/10.1063/1.5110958
H.-G. Unger, Planar Optical Waveguides and Fibres, Oxford Univ. Press, Oxford (1978).
A. D. Bezpaly, V. M. Shandarov, A. E. Mandel, et al., Russ. Phys. J., 62, No. 3, 387–392 (2019). https://doi.org/10.1007/s11182-019-01724-w
I. A. Molotkov, S. A. Vakulenko, and M. A. Bisyarin, Nonnlinear Localized Wave Processes [in Russian], Yanus-K, Moscow (1999).
S. V. Sazonov, JETP Lett., 112, No. 5, 283–289 (2020). https://doi.org/10.1134/S0021364020170087
A. I. Maimistov, Opt. Spectrosc., 129, No. 1, 110–115 (2021). https://doi.org/10.1134/S0030400X21010136
M. A. Bisyarin and I. A. Molotkov, Radiophys. Quantum Electron., 45, No. 6, 471–480 (2002). https://doi.org/10.1023/A:1019968702600
M. A. Bisyarin, Prikl. Mekh. Tekh. Fiz., 48, No. 6, 57–69 (2007).
N. N. Rozanov, Opt. Spectrosc., 128, No. 8, 1151–1154 (2020). https://doi.org/10.1134/S0030400X20080305
V. A. Svetlichny and O. V. Smirnova, in: XXVIth Russian Open Sci. Conf. on Radio Wave Propagation, July 1–6, 2019, Kazan, Russia, Vol. 1, pp. 414–417.
N. N. Zernov and A. V. Driuk, J. Atmos. Sol.-Terr. Phys., 205, 105313 (2020). https://doi.org/10.1016/j.jastp.2020.105313
A. V. Driuk and N. N. Zernov, J. Atmos. Sol.-Terr. Phys., 205, 105312 (2020). https://doi.org/10.1016/j.jastp.2020.105312
M. A. Bisyarin, Opt. Spectrosc., 114, No. 6, 904–908 (2013). https://doi.org/10.1134/S0030400X13060039
M. A. Bisyarin, Proc. Mozhaisky Mil. Space Acad., No. 670, 91–95 (2019).
F. W. J. Olver, Asymptotics and Special Functions, A K Peters/CRC Press, New York (1997),
R. H. J. Grimshaw and Y. A. Stepanyants, Radiophys. Quantum Electron., 63, No. 1, 21–28 (2020). https://doi.org/10.1007/s11141-020-10031-1
I. A. Molotkov and M. A. Bisyarin, Quantum Electron., 34, No. 2, 161–164 (2004). https://doi.org/10.1070/QE2004v034n02ABEH002603
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 64, Nos. 8–9, pp. 577–589, August–September 2021. Russian DOI: https://doi.org/10.52452/00213462_2021_64_08_577
Rights and permissions
About this article
Cite this article
Bisyarin, M.A. Mode Structure and the Envelope of a High-Power Pulse in a Nonsymmetric Graded-Index Waveguide Layer. Radiophys Quantum El 64, 521–532 (2022). https://doi.org/10.1007/s11141-022-10154-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11141-022-10154-7