Electromagnetic Waveguides

  • Sergey LebleEmail author
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 109)


We start out from the development of the general theory, giving details of modifications to the results in the book [1, Sect. 3.4]. Let a slab of a dielectric span the interval \(z\in [-h,h]\). We shall call this a planar waveguide, in accordance with most publications (e.g., [3]). In this section we shall mainly follow [4], a continuation of [1]. Assume the linear isotropic (averaged) part of a dielectric constant is \(\varepsilon \) inside the interval and unity outside.


  1. 1.
    S. Leble, Nonlinear Waves in Waveguides with Stratification (Springer, Berlin, 1991), p. 164CrossRefGoogle Scholar
  2. 2.
  3. 3.
    J.U. Kang, G.I. Stegeman, J.S. Aitchison, N. Akhmediev, PRL 76, 3699–3702 (1996)ADSCrossRefGoogle Scholar
  4. 4.
    S. Leble, Nonlinear waves in optical waveguides and soliton theory applications, Optical Solitons, Theoretical and Experimental Challenges (Springer, Berlin, 2003), pp. 71–104Google Scholar
  5. 5.
    I. Yu. Popov, Zero-range potentials model for planar waveguide in photonic crystal. Techn. Phys. Lett. 25(16), 45–49 (1999)Google Scholar
  6. 6.
    C.R. Menyuk, Nonlinear pulse propagation in birefringent optical fibers. IEEE J. Quantum Electron 23(2), 174–176 (1987)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    H. Ono, J. Phys. Soc. Jpn. 39, 1082–1091 (1975)ADSCrossRefGoogle Scholar
  8. 8.
    R.J. Joseph, J. Phys. A 10, 1225–1227 (1977)ADSCrossRefGoogle Scholar
  9. 9.
    S.B. Leble, Izv. Akad. Nauk SSSR, Fiz. Atm. Okean 20, 1199–1204 (1984)Google Scholar
  10. 10.
    J.U. Kang, G.I. Stegeman, J.S. Atchison, Opt. Lett. 21, 189 (1996)ADSCrossRefGoogle Scholar
  11. 11.
    M.N. Islam, Opt. Lett. 15, 417 (1990)ADSCrossRefGoogle Scholar
  12. 12.
    S.V. Manakov, JETP 65, 505 (1973)Google Scholar
  13. 13.
    V.E. Zakharov, A.B. Shabat, Sov. Phys. JETP 34, 62 (1972)Google Scholar
  14. 14.
    M. Bertolotti, A. D’Andrea, E. Fazio et al., Opt. Commun. 168, 399 (1999)ADSCrossRefGoogle Scholar
  15. 15.
    S.A. Khan, C.-M. Chang, Z. Zaidi, W. Shin, Y. Shi, A.K. Ellerbee Bowdena, O. Solgaarda, Metal–insulator–metal waveguides for particle trapping and separation. Lab on a Chip, Issue 12 (2016)Google Scholar
  16. 16.
    M. Chbat, C. Menyuk, I. Glesk, P. Prucnal, Opt. Lett. 20, 258 (1995)ADSCrossRefGoogle Scholar
  17. 17.
    S.T. Cundiff, B.C. Collings, N.N. Achmediev, J.M. Soto-Crespo, K. Bergman, W.H. Knox, Phys. Rev. Lett. 2, 3988 (1999)ADSCrossRefGoogle Scholar
  18. 18.
    C. Anastassiu, M. Segev, K. Steiglitz et al., PRL 83, 2332 (1999)ADSCrossRefGoogle Scholar
  19. 19.
    H.G. Winful, Opt. Lett. 11, 33 (1986)ADSCrossRefGoogle Scholar
  20. 20.
    K.J. Blow, N.J. Doran, D. Wood, Opt. Lett. 12, 202 (1987)ADSCrossRefGoogle Scholar
  21. 21.
    K.J. Blow, N.J. Doran, D. Wood, J. Opt. Soc. Am. B 5, 381 (1988)ADSCrossRefGoogle Scholar
  22. 22.
    E. Feigenbaum, M. Orenstein. Plasmon–Soliton.
  23. 23.
    S. Leble, A. Perelomova, The Dynamical Projectors Method: Hydro and Electrodynamics, vol. 29 (Taylor and Francis, Abingdon, 2018)Google Scholar
  24. 24.
    G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, Cambridge, 1997)Google Scholar
  25. 25.
    Y. Kodama, A. Hasegawa, Theoretical foundation of optical-soliton concept in fibers. Prog. Opt. 30, 205–259 (1992)CrossRefGoogle Scholar
  26. 26.
    J.D. Jackson: Wiley India Pvt. Limited (2007)Google Scholar
  27. 27.
  28. 28.
    R.W. Boyd, Nonlinear Optics (Academic Press, Boston, 1992)Google Scholar
  29. 29.
    V.M. Galitskii, V.M. Ermachenko, Macroscopic Electrodynamics, Moscow High School (1988)Google Scholar
  30. 30.
    C. Montes et al., Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics (Springer, Berlin, 2013)Google Scholar
  31. 31.
    S.B. Leble, B. Reichel, Mode interaction in multi-mode optical fibers with Kerr effect (2005), arxiv:physics/0502122
  32. 32.
    D. Hondros, P. Debye, Elektromagnetische wellen an dielektrischen drähten. Ann. Phys. 32, 465 (1910)CrossRefGoogle Scholar
  33. 33.
    H. Zahn, Über den nachweis elektromagnetischer wellen an dielektrischen drähten. Ann. Phys. 49, 907 (1916)CrossRefGoogle Scholar
  34. 34.
    K. Iizuka, Engineering Optics, vol. 35, 2nd edn., Springer Series in Optical Sciences (Springer, New York, 1985)CrossRefGoogle Scholar
  35. 35.
    A. Hasegawa, M. Matsumoto, Optical Solitons in Fibers, Springer Series in Photonics (Springer, Berlin, 2003)CrossRefGoogle Scholar
  36. 36.
    V.E. Zakharov, A.B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional modulation of waves in nonlinear media, Zhurn. Eksp. Teor. Fiz. 61, 118–134 (1971) [Sov. Phys. JETP 34, 62–69 (1972)]Google Scholar
  37. 37.
    S.K. Turitsyn, B.G. Balea, M.P. Fedoruk, Dispersion-managed solitons in fibre systems and lasers. Phys. Rep. 521(4), 135–203 (2012). DecemberADSCrossRefGoogle Scholar
  38. 38.
    V. Cautaerts, Y. Kodama, A. Maruta, H. Sugavara, Nonlinear Pulses in Ultra-Fast Communications. Les Houches Lectures, Lecture 9 (Springer, Berlin 1999) p. 147Google Scholar
  39. 39.
    E. Seve, G. Millot S. Trillo: Phys. Rev. E 61, 3139–3150 (2000)ADSCrossRefGoogle Scholar
  40. 40.
    E. Doktorov S.B. Leble, Dressing Method in Mathematical Physics (Springer, Berlin, 2007). ISBN 83-88007-03-3Google Scholar
  41. 41.
    T. Schäfer, C.E. Wayne, Propagation of ultra-short optical pulses in cubic nonlinear media. Phys. D 196, 90–105 (2004)MathSciNetCrossRefGoogle Scholar
  42. 42.
    S. Buch, G.P. Agrawal, Soliton stability and trapping in multimode fibers. Opt. Lett. 40(2), 225–228 (2015)ADSCrossRefGoogle Scholar
  43. 43.
    S.B. Leble, B. Reichel, Mode interaction in few-mode optical fibres with Kerr effect. J. of Modern Optics 55, 1–11 (2007)ADSCrossRefGoogle Scholar
  44. 44.
    S.B. Leble, B. Reichel, The equations for interaction of polarization modes in optical fibres including the Kerr effect (2008). Scholar
  45. 45.
    S.B. Leble, B. Reichel, On convergence and stability of a numerical scheme of coupled nonlinear Schrödinger equations. Comput. Math. Appl. 55, 745–759 (2008)MathSciNetCrossRefGoogle Scholar
  46. 46.
    S. Leble, B. Reichel, Coupled nonlinear Schrödinger equations in optical fibers theory: from general to solitonic aspects. Eur. Phys. J. Spec. Topics 173(1), 5–55 (2009)ADSCrossRefGoogle Scholar
  47. 47.
    M. Kuszner, S. Leble, B. Reichel, Multimode systems of nonlinear equations: derivation, integrability, and numerical solutions. Theor. Math. Phys. 168(1), 977 (2011)MathSciNetCrossRefGoogle Scholar
  48. 48.
    M. Kuszner, S. Leble,Waveguide Electromagnetic Pulse Dynamics: Projecting Operators Method. In: Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications, ed. by K. Porsezian, R. Ganapathy, 24 November 2015. (CRC Press Reference, 2015)Google Scholar
  49. 49.
    D. Gacemi, J. Mangeney, R. Colombelli, A. Degiron, Subwavelength metallic waveguides as a tool for extreme confinement of THz surface waves. Sci. Rep. 3, Article number 1369 (2013)Google Scholar
  50. 50.
    A.P. Prudnikov, YuA Brychkov, O.I. Marichev, Integrals and Series: Special Functions (Publ, Gordon and Breach Sci, 1998)zbMATHGoogle Scholar
  51. 51.
    C.R. Menyuk, IEEE J. Quant. Elect. 253, 2674 (1989)ADSCrossRefGoogle Scholar
  52. 52.
    A. Hasegawa, M. Matsunoto, Optical Solitons in Fibers (Springer, Berlin, 2003)Google Scholar
  53. 53.
    L.F. Mollenauer, R.H. Stolen, J.P. Gordon, Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers. Phys. Rev. Lett. 45, 1095 (1980)ADSCrossRefGoogle Scholar
  54. 54.
    A.D. Boardman, A. Shivarova, S. Tanev, D. Zyapkov, Nonlinear coefficients and the effective area of cross-phase modulation coupling of lp01 optical fibre modes. J. Mod. Opt. 42, 2361 (1995)ADSCrossRefGoogle Scholar
  55. 55.
    K.T. McDonald, Axicon Gaussian laser beams. Joseph Henry Laboratories, (Princeton, 2000), arxiv:physics/0003056
  56. 56.
    M. Artiglia, P. Di Vita G. Coppa, M. Potenza, A. Sharma, Mode field diameter measurements in single-mode optical fibers. J. Lightwave Tech. 7, 1139 (1989)ADSCrossRefGoogle Scholar
  57. 57.
    IYu. Popov, A.I. Trifanov, E.S. Trifanova, Dielectric waveguides with photonic crystal properties. Comput. Math. Math. Phys. 50(11), 1830–1836 (2010)MathSciNetCrossRefGoogle Scholar
  58. 58.
    V.V. Kozlov, Quantum electrodynamics of optical solitons for communication technologies. IEEE J. QE 9, 1468 (2003)Google Scholar
  59. 59.
    C.R. Menyuk, J. Opt. Soc. Am. B 5, 392 (1988)ADSCrossRefGoogle Scholar
  60. 60.
    S.J. Garth, C. Pask, Nonlinear effects in elliptical-core few-mode optical fibers. J. Opt. Soc. Am. B: Opt. Phys. 9, 243–250 (1992). Scholar
  61. 61.
    C.R. Menyuk, J. Eng. Math. 36, 113 (1999)MathSciNetCrossRefGoogle Scholar
  62. 62.
    V. Malyshev, E.C. Jarque, Optical hysteresis and instabilities inside the polariton band gap. J. Opt. Soc. Am. B 12, 1868 (1995); 14, 1167 (1997)ADSCrossRefGoogle Scholar
  63. 63.
    P.V. Mamyshev, S.V. Chemikov, E.M. Dianov, Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines. IEEE J. QE 27, 2347 (1991)CrossRefGoogle Scholar
  64. 64.
    K. Porsezian, Soliton models in resonant and nonresonant optical fibers. Pramana J. Phys. 57, 1003 (2001)ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Immanuel Kant Baltic Federal UniversityKaliningradRussia

Personalised recommendations