Abstract
The chapter presents a new scalar model of optical beam propagation in nonlinear media, as it is developed in [1–4]. The model addresses narrow beams and stresses on nonlinearly induced diffraction, an effect of medium inhomogeneity introduced by the spatial variation of the nonlinear polarization. Strarting from the vector nonparaxial model of beam propagation in nonlinear media, it is shown that not the vectorial nature of the carrier wave field, but a scalar effect which comes out from the (div/E)-term in the wave equation and has the meaning of nonlinear diffraction, controls predominating over the nonparaxiality, the balance between diffraction and nonlinearity in the formation of the spatial solitons. The conclusion is based on analytical and numerical solutiuons of the nonlinear equations for the beam envelopes and on analysis of the wave power conservation laws derived. Both third (Kerr-type)- and second- order nonlinearities are treated as well as both planar waveguides and bulk media are covered. Single beam propagation and beam interaction and coupling are described. New solitary-wave solutions are presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Boardman, A.D., Marinov, K., Pushkarov, D.I. and Shivarova, A. (2000) Influence of nonlinearly induced diffraction on spatial solitary waves, Opt. Quant. Electr. 32, 49–62.
Marinov, K, Pushkarov, D.I. and Shivarova, A. (2000) Beam propagation in Kerr-type nonlinear waveguides, PhysicaScripta T84, 197–199.
Boardman, A.D., Marinov, K., Pushkarov, D.I. and Shivarova, A. (2000) Wave-beam coupling in quadratic nonlinear optical waveguides: Effects of nonlinearly induced diffraction, Phys. Rev. E 62, 2871–2877.
Malomed, B.A., Marinov, K, Pushkarov, D.I. and Shivarova, A. (2000) Stability of narrow beams in bulk Kerrtype nonlinear media, Phys. Rev. A, submitted.
Shen, Y.R. (1975) Self-focusing: Experimental, Prog. Quant. Electr. 291, 1–34.
Marburger, J.H. (1975) Self-focusing: Theory, Prog. Quant. Electr. 4, 35–110.
De la Fuente, R., Varela, O. and Michinel, H. (2000) Fourier analysis of non-paraxial self-focusing, Opt. Commun. 173, 403–411.
Granot, E., Sternklar, Sh., Isbi, Yu., Malomed, B. and Lewis, A. (2000) On the existence of subwavelength spatial solitons, Opt. Commun. 178, 431435.
Ciattoni, A, Di Porto, P., Crosignani, B. and Yariv, A (2000) Vectorial nonparaxial propagation equation in the presence of a tensorial refractive-index perturbation, J. Opt. Soc. Am. B 17, 809–819.
Blair, S. (2000) Nonparaxial one-dimensional spatial solitons, Chaos 10, 570–583.
Askar’yan, G. A, (1962) Effect of the gradient of a strong electromagnetic ray on electrons and atoms, ZhETF 42, 1567–1570.
Chiao, R.Y., Garmire, E. and Townes, C.H. (1964) Self-trapping of optical beams, Phys. Rev. Lett. 13, 479–482.
Talanov, V.I. (1964) On the self-focusing of electromagnetic waves in nonlinear media, Izv. VUZ-Radiofizika 7, 564–565.
Kelley, P.L. (1965) Self-focusing of optical beams, Phys. Rev. Lett. 15, 1005–1008.
Abakarov, D.I., Akopyan, A A and Pekar, S.I. (1967) To the theory of self-focusing in nonlinearly polarizing media, ZhETF 52, 463–466.
Vlasov, S.N., Petrishtev, V.A and Talanov, V.I. (1971) Averaged description of wave beams in linear and nonlinear media (momentum theory), Izv. VUZ-Radiofizika 14, 1353–1363.
Karlsson, M. (1992) Optical beams in saturable self-focusing media, Phys. Rev. A 46, 2726–2734.
Manassah, J. and Gross, B. (1992) Comparison of the paraxial-ray approximation and the variational method solutions to the numerical results for a beam propagation in a self-docusing Kerr medium, Opt. Lett. 17, 976–978.
Fibich, G.(1996) Adiabatic law for self-focusing of optical beams, Opt. Lett. 21, 1735–1737.
Lallemand, P. and Bloembergen, N. (1965) Self-focusing of laser beams and stimulated Raman gain in liquids, Phys. Rev. Lett. 15, 1010–1012.
Dawes, E.L. and Marburger, J.H. (1969) Computer studies in self-focusing, Phys. Rev. 179, 862–868.
Yablonovich, E. and Bloembergen, N. (1972) Avalanche ionization and the limiting diameter of filaments induced by light pulses in transparent media, Phys. Rev. Lett. 29, 907–910.
Suter, D. and Blasberg, T. (1993) Stabilization of transverse solitary waves by a nonlocal response of the medium, Phys. Rev. A 48, 4583–4587.
La Fontaine, B., Vidal, F., Jiang, Z., Chien, C.Y., Comtois, D., Desparois, A, Johnston, T.W., Kieffer, J.-C. and Pepin, H. (1999) Filamentation of ultrashort pulse laser beams resulting from their propagation over long distance in air, Phys. Plasmas 6, 1615–1621.
Mlejnek, M., Wright E.M. and Moloney, J.V. (1999) Power dependence of dynamic spatial replenishment of femtosecond pulses propagating in air, Opt. Express 4, 223–228.
Pohl, D. (1970) Vectorial theory of self-trapped light beams, Opt. Commun. 2, 305–308.
Feit, M.D. and Fleck, J.A., Jr. (1988) Beam nonparaxiality, filament formation and beam breakup in the self-focusing of optical beams, J. Opt. Soc. Am. B 5 633–640.
Akhmediev, N., Ankiewicz, A and Soto-Crespo, J.M. (1993) Does the nonlinear Schrödinger equation correctly describe beam propagation?, Opt. Lett. 18, 411–413.
Soto-Crespo, J.M. and Akhmediev, N. (1993) Description of the self-focusing and collapse effects by a modified nonlinear Schrödinger equation, Opt. Commun. 101, 223–230.
Chi, S. and Guo, Qi. (1995) Vector theory of self-focusing of an optical beam in Kerr-media, Opt. Lett. 20, 1598–1600.
Fibich, G. (1996) Small beam nonparaxiality arests self-focusing of optical beams, Phys. Rev. Lett 76, 4356–4359.
Crosignani, B., Di Porto, P. and Yariv, A(1997) Nonparaxial equation for linear and nonlinear optical propagation, Opt. Lett. 22, 778–780.
Granot, E., Sternklar, Sh., Isbi, Yu., Malomed, B. and Lewis, A(1997) Subwavelength spatial solitons, Opt. Lett. 22, 1290–1292.
Sheppard, AP. and Haelterman, M. (1998) Nonparaxiality stabilizes three-dimensional soliton beams in Kerr-media, Opt. Lett. 23, 1820–1822.
Blair, S. and Wagner, K. (1998) (2+1)-D propagatioan of spatio-temporal solitary waves including higher-order corrections, Opt. Quant. Electr, 30, 697–737.
Granot, E., Sternklar, Sh., Isbi, Yu., Malomed, B. and Lewis, A (1999) Subwavelength non-local spatial solitons, Opt. Commun. 166, 121–126.
Eisenberg, H.S. and Silberberg, Y. (1999) Phase defects in self-focusing of ultrashort pulses, Phys. Rev. Lett. 83, 540–543.
Pushkarov, Kh. I., Pushkarov, D.I. and Tomov, I.V. (1979) Self-action of light beams in nonlinear media: soliton solutions, Opt. Quant. Electr. 11, 471–478.
Marinov, K, Pushkarov, D.I. and Shivarova, A (2001) Bright solitary-wave beams in bulk Kerr-type nonlinear media, in: AD. Boardman (ed.) Soliton Driven Photonics, Kluwer Academic Publishers, Dordrecht
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Marinov, K., Pushkarov, D.I., Shivarova, A. (2001). Effects of Nonlinearly Induced Inhomogeneity on Solitary Wave Formation. In: Boardman, A.D., Sukhorukov, A.P. (eds) Soliton-driven Photonics. NATO Science Series, vol 31. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0682-8_31
Download citation
DOI: https://doi.org/10.1007/978-94-010-0682-8_31
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-7131-1
Online ISBN: 978-94-010-0682-8
eBook Packages: Springer Book Archive