(44-4) 05 * << * >> * Russian * English * Content * All Issues

Necessary conditions for the propagation of two modes, LP01 and LP11, in a step-index optical fiber with a Kerr nonlinearity
V.A. Burdin 1, A.V. Bourdine 1, O.Yu. Gubareva 1

Povolzhskiy State University of Telecommunication and Informatics,
443090, Samara, Russia, Moskovskoye Shosse 77

 PDF, 979 kB

DOI: 10.18287/2412-6179-CO-699

Pages: 533-539.

Full text of article: English language.

This paper presents the results of an analysis of the necessary propagation conditions in a step-index optical fiber with a Kerr nonlinearity of two modes, LP01 and LP11, during the transmission of high-power optical pulses. All results were obtained by solving a system of two nonlinear equations for these modes, obtained by the Gauss approximation method, and the subsequent use of a procedure for refining estimates using the mixed finite elements method. The necessary conditions are determined, estimates of the boundaries for the range of normalised frequencies for which they are fulfilled are obtained, and an approximate formula is proposed for estimating the upper limit of this range.

optical fiber, refractive index profile, step-index optical fiber, equivalent mode spot radius, Kerr nonlinearity, propagation constant, Gauss approximation, system of nonlinear equations.

Burdin VA, Bourdine AV, Gubareva OYu. Necessary conditions for the propagation of two modes, LP01 and LP11, in a step-index optical fiber with a Kerr nonlinearity. Computer Optics 2020; 44(4): 533-539. DOI: 10.18287/2412-6179-CO-699.

This work was supported by RFBR, DST, NSFC and NRF (Project No. 19-57-80006 BRICS_t).


  1. Okamoto K, Marcatili EAJ. Chromatic dispersion characteristics of fibers with optical kerr-effect non-linearity. J Lightw Technol 1989; 1(12): 1988-1994.
  2. Debord B, Alharbi M, Vincetti L, Husako, A, Fourcade-Dutin C, Hoenninger C, Mottay E, Gérôme F, Benabid F. Multi-meter fiber-delivery and pulse self-compression of milli-Joule femtosecond laser and fiber-aided laser-micromachining. Opt Express 2014; 22(9): 10735-10746.
  3. Pouysegur J, Guichard F, Weichelt B, Delaigue M, Zaouter Y, Hönninger C, Mottay E, Georges P, Druon F. Single-stage Yb:YAG booster amplifier producing 2.3 mJ, 520 fs pulses at 10 kHz. Proc Adv Solid State Lasers 2015; hal-01359547.
  4. Debord B, Gerome F, Paul P-M, Husakou A, Benabid F. 2.6 mJ energy and 81 GW peak power femto-second laser pulse delivery and spectral broadening in inhibited coupling Kagome fiber. CLEO: 2015, OSA Technical Digest (online) (Optical Society of America, 2015): STh4L.7.
  5. Kryukov PG. Femtosecond pulses. The introduction of a new area of laser physics [In Russian]. Moscow: “Fizmatlit” Publisher; 2008.
  6. Stingl A. Femtosecond future. Nat Photon 2010; 4: 158.
  7. Sibbett W, Lagatsky A.A, Brown CTA. The development and application of femtosecond laser systems. Opt Express 2010; 20(7): 6989-7001.
  8. Burdin VA, Bourdine AV. Dispersion characteristics of step index single mode optical fiber with Kerr nonlinearity. Proc SPIE 2017; 10342: 103420N.
  9. Burdin VA, Bourdine AV, Andreev VA, Yablochkin K.A. Spectral characteristics of step index single mode optical fiber with Kerr nonlinearity. Proc SPIE 2018; 10774: 107740L.
  10. Snyder AW. Understanding monomode optical fibers. Proc IEEE 1981; 69(1): 6-13.
  11. Love JD, Hussey CD. Variational approximations for higher-order modes of weakly-guiding fibers. Opt Quantum Electron 1984; 16(1): 41-48.
  12. Snyder АW, Love JD. Optical waveguide theory. London, New York: Chapman & Hall; 1983.
  13. Burdin VA, Bourdine AV. Solution for arbitrary order guided mode propagating over optical circle fi-ber based on Gaussian approximation. Physics of wave processes and radio engineering systems 2011; 14(2): 65-72.
  14. Burdin VA, Bourdine AV, Volkov KA. Spectral characteristics of LP11 mode of step index optical fiber with Kerr nonlinearity. Proc SPIE 2018; 10774: 107740N.
  15. Bourdine AV, Burdin VA, Sultanov AH, Delmuchametov OR. Algorithm for optical fiber chromatic dispersion calculation based on full-vector mixed finite element method [In Russian]. Infokommunikacionnye Tehnologii 2009; 7(2): 13-20.
  16. Agrawal G. Nonlinear fiber optics. London, San Diego: Academic Press; 2007.
  17. Petermann K. Fundamental mode microbending loss in graded-index and W fibers. Opt Quantum Electron 1977; 9: 167-175.
  18. Burdin VA, Bourdine AV. A System of nonlinear characteristic equations for two-mode propagation in step-index optical fiber. Proc OWTNM Workshop 2018: 31.
  19. Kelley C. Numerical methods for nonlinear equations. ActaNumerica 2018; 27: 207-287.
  20. Corning SMF-28 Optical Fiber. Product Information. Corning PI1036 2002: 4.
  21. Garcia H, Johnson AM, Oguama FA, Trivedi S. New approach to the measurement of the nonlinear refractive index of short (< 25 m) lengths of silica and erbium-doped fibers. Opt Lett 2003; 28(19): 1796-1978.
  22. Traore A, Lalanne E, Johnson AM. Determination of the nonlinear refractive index of multimode silica fiber with a dual-line ultra-short pulse laser source by using the induced grating autocorrelation technique. Opt Express 2015; 23(13): 17127-17137.
  23. Burdin V. Algorithm for estimation of material dispersion of fused silica glass optical fibers. Proc SPIE 2015; 9533: 95330J.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: ko@smr.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20