Quadratic spatial solitons

George I. Stegeman

doi:10.1016/j.crhy.2006.02.008

Quadratic spatial solitons
[Solitons spatiaux quadratiques]

George I. Stegeman ¹

¹ College of Optics and Photonics/CREOL, University of Central Florida, 4000 Central Florida Boulevard, Orlando, FL 32816-2700, USA

Comptes Rendus. Physique, Volume 8 (2007) no. 2, pp. 221-233.

Résumé
Abstract

Les solitons spatiaux quadratiques, rayons qui se propagent à forme et amplitude constantes, sont gouvernés par les non-linéarités optiques du deuxième ordre et peuvent, dans des conditions appropriées, se produire dans tous les processus de mélange d'ondes. Ils sont multi-composantes, constitués de toutes les composantes fréquentielles qui sont couplées par une interaction non linéaire du deuxième ordre au voisinage d'une condition d'accord de phase. Ils ont été observés dans un certain nombre de milieux cristallins en volume, de guides d'ondes planaires en LiNbO₃ et sur des ensembles de guides d'ondes canaux en LiNbO₃, parallèles et faiblement couplés. Cet article fait le point sur les propriétés des solitons et leur processus d'excitation.

Quadratic spatial solitons, beams that propagate unchanged in shape and magnitude, are supported by second order optical nonlinearities and can occur in all wave mixing processes under appropriate conditions. They are multi-component, consisting of all the frequency components that are coupled by a second order nonlinear interaction near a phase-matching condition. They have been observed in a number of bulk crystalline media, in LiNbO₃ slab waveguides and in arrays of parallel, weakly coupled, LiNbO₃ channel waveguides. The properties of the solitons and their excitation will be reviewed.

Publié le : 2006-08-07

DOI : 10.1016/j.crhy.2006.02.008

Keywords: Soliton, Quadratic spatial solitons
Mot clés : Soliton, Solitons spatiaux quadratiques

Affiliations des auteurs :

George I. Stegeman ¹

¹ College of Optics and Photonics/CREOL, University of Central Florida, 4000 Central Florida Boulevard, Orlando, FL 32816-2700, USA

@article{CRPHYS_2007__8_2_221_0,
     author = {George I. Stegeman},
     title = {Quadratic spatial solitons},
     journal = {Comptes Rendus. Physique},
     pages = {221--233},
     publisher = {Elsevier},
     volume = {8},
     number = {2},
     year = {2007},
     doi = {10.1016/j.crhy.2006.02.008},
     language = {en},
}

TY  - JOUR
AU  - George I. Stegeman
TI  - Quadratic spatial solitons
JO  - Comptes Rendus. Physique
PY  - 2007
SP  - 221
EP  - 233
VL  - 8
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crhy.2006.02.008
LA  - en
ID  - CRPHYS_2007__8_2_221_0
ER  -

%0 Journal Article
%A George I. Stegeman
%T Quadratic spatial solitons
%J Comptes Rendus. Physique
%D 2007
%P 221-233
%V 8
%N 2
%I Elsevier
%R 10.1016/j.crhy.2006.02.008
%G en
%F CRPHYS_2007__8_2_221_0

George I. Stegeman. Quadratic spatial solitons. Comptes Rendus. Physique, Volume 8 (2007) no. 2, pp. 221-233. doi : 10.1016/j.crhy.2006.02.008. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2006.02.008/

Bibliographie
Cité par

[1] P.A. Franken; A.E. Hill; C.W. Peters; G. Weinreich Generation of optical harmonics, Phys. Rev. Lett. (1961), pp. 118-120

[2] N. Bloembergen; Y.R. Shen; F.A. Hopf; G.I. Stegeman; R.W. Boyd Nonlinear Optics, The Principles of Nonlinear OpticsApplied Classical Electrodynamics, vol. 2: Nonlinear OpticsNonlinear Optics, Benjamen, Reading, MA, 1965

[3] E. Infeld; G. Rowlands; N.N. Akhmediev; A. Ankiewicz Nonlinear Waves, Solitons and Chaos, Solitons, Nonlinear Pulses and Beams, Cambridge Univ. Press, Cambridge, 1990

[4] A. Barthelemy; S. Maneuf; C. Froehly Propagation soliton et auto-confinement de faisceaux laser par non linearité optique de Kerr, Opt. Comm., Volume 55 (1985), pp. 201-206

[5] S. Maneuf; F. Reynaud Quasi-steady state self-trapping of first, second and third order sub-nanosecond soliton beams, Opt. Commun., Volume 66 (1988), pp. 325-329

[6] J.S. Aitchison; A.M. Weiner; Y. Silberberg; M.K. Oliver; J.L. Jackel; D.E. Leaird; E.M. Vogel; P.W. Smith Observation of spatial optical solitons in a nonlinear glass waveguide, Opt. Lett., Volume 15 (1990), pp. 471-473

[7] J.S. Aitchison; K. Al-Hemyari; C.N. Ironside; R.S. Grant; W. Sibbett Observation of spatial solitons in AlGaAs waveguides, Electron. Lett., Volume 28 (1992), pp. 1879-1880

[8] P.L. Kelley Self-focusing of optical beams, Phys. Rev. Lett., Volume 15 (1965), pp. 1005-1008

[9] J.E. Bjorkholm; A. Ashkin cw self-focusing and self-trapping of light in sodium vapor, Phys. Rev. Lett., Volume 32 (1974), pp. 129-132

[10] G. Duree; J.L. Shultz; G. Salamo; M. Segev; A. Yariv; B. Crosignani; P. DiPorto; E. Sharp; R.R. Neurgaonkar Observation of self-trapping of an optical beam due to the photorefractive effect, Phys. Rev. Lett., Volume 71 (1993), pp. 533-536

[11] M. Shih; M. Segev; G.C. Valley; G. Salamo; B. Crosignani; P. DiPorto Observation of two-dimensional steady-state photorefractive screening solitons, Electron. Lett., Volume 31 (1995), pp. 826-827

[12] M. Peccianti; A. De Rossiu; G. Assanto; A. De Luca; C. Umeton; I.C. Khoo Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells, Appl. Phys. Let., Volume 77 (2000), pp. 7-9

[13] E.A. Ultanir; G.I. Stegeman; D. Michaelis; F. Lederer; Ch. Lange Stable dissipative spatial solitons in semiconductor optical amplifiers, Phys. Rev. Lett., Volume 90 (2003), pp. 3903-3906

[14] Y.N. Karamzin; A.P. Sukhorukov; Yu.N. Karamzin; A.P. Sukhorukov Mutual focusing of high-power light beams in media with quadratic nonlinearity, Sov. Phys. JETP, Volume 20 (1974), pp. 339-342

[15] L.A. Ostrovskii; G.I. Stegeman; D.J. Hagan; L. Torner Self-action of light in crystals, JETP Lett., Volume 5 (1867), pp. 272-275 Reviewed in $χ^{(2)}$ cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons J. Opt. Quant. Electron., 28, 1996, pp. 1691-1740

[16] R. Schiek; Y. Baek; G.I. Stegeman One-dimensional spatial solitons due to cascaded second-order nonlinearities in planar waveguides, Phys. Rev. E, Volume 53 (1996), pp. 1138-1141

[17] R. Schiek; R. Iwanow; G.I. Stegeman; G. Schreiber; W. Sohler One-dimensional spatial soliton families in optimally engineered QPM lithium niobate waveguides, Opt. Lett., Volume 29 (2004), pp. 596-598

[18] W.E. Torruellas; Z. Wang; D.J. Hagan; E.W. VanStryland; G.I. Stegeman; L. Torner; C.R. Menyuk Observation of two-dimensional spatial solitary waves in a quadratic medium, Phys. Rev. Lett., Volume 74 (1995), pp. 5036-5039

[19] P. Di Trapani; G. Valiulis; W. Chianglia; A. Adreoni Two-dimensional spatial solitary waves from traveling wave parametric amplification of the quantum noise, Phys. Rev. Lett., Volume 80 (1998), pp. 265-269

[20] B. Bourliaguet; V. Couderc; A. Barthelemy; G.W. Ross; P.G.R. Smith; D.C. Hanna; C. De Angelis Observation of quadratic spatial solitons in periodically poled lithium niobate, Opt. Lett., Volume 24 (1999), pp. 1410-1412

[21] X. Liu; L.J. Qian; F.W. Wise Generation of optical spatiotemporal solitons, Phys. Rev. Lett., Volume 82 (1999), pp. 4631-4634

[22] R. Malendevich; L. Jankovic; S. Polyakov; R. Fuerst; G.I. Stegeman; Ch. Bosshard; P. Gunter Two-dimensional Type I quadratic spatial solitons in KNbO₃ near non-critical phase-matching, Opt. Lett., Volume 27 (2002), pp. 631-633

[23] H. Kim; L. Jankovic; G.I. Stegeman; S. Carrasco; L. Torner; D. Eger; M. Katz Quadratic spatial solitons in periodically poled KTiOPO₄, Opt. Lett., Volume 28 (2003), pp. 640-642

[24] R. Iwanow; R. Schiek; G.I. Stegeman; T. Pertsch; F. Lederer; Y. Min; W. Sohler Observation of discrete quadratic solitons, Phys. Rev. Lett. (2004), p. 113902

[25] R. Iwanow; G.I. Stegeman; R. Schiek; T. Pertsch; F. Lederer; Y. Min; W. Sohler Highly localized discrete quadratic solitons in periodically poled lithium niobate waveguide arrays, Opt. Lett., Volume 30 (2005), pp. 1033-1035

[26] A.V. Buryak; P. DiTrapani; D. Skryabin; S. Trillo Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications, Phys. Rep., Volume 370 (2002), pp. 63-235

[27] R. Schiek; Y. Baek; G.I. Stegeman Second harmonic generation and cascading nonlinearity in titanium-indiffused lithium niobate channel waveguides, J. Opt. Soc. Am. B, Volume 15 (1998), pp. 2255-2268

[28] A.V. Buryak; Y.S. Kivshar; A.V. Buryak; Y.S. Kivshar; A.V. Buryak; Y.S. Kivshar Solitons due to second harmonic generation, Phys. Lett. A, Volume 19 (1994), pp. 1612-1614 (Erratum)

[29] C.R. Menyuk; R. Schiek; L. Torner Solitary waves due to $χ^{(2)} : χ^{(2)}$ cascading, J. Opt. Soc. Am. B, Volume 11 (1994), pp. 2434-2443

[30] A.E. Kaplan Eigenmodes of $χ^{(2)}$ wave mixings: cross-induced second-order nonlinear refraction, Opt. Lett., Volume 18 (1993), pp. 1223-1225

[31] G. Assanto; G.I. Stegeman The simple physics of quadratic spatial solitons, Opt. Express, Volume 10 (2002), pp. 388-396

[32] L. Torner Stationary solitary waves with second-order nonlinearities, Opt. Commun., Volume 114 (1995), pp. 136-140

[33] L. Torner; C.R. Menyuk; G.I. Stegeman; L. Torner; C.R. Menyuk; G.I. Stegeman Solitons with second-order nonlinearities, J. Opt. Soc. Am. B, Volume 19 (1994), pp. 1615-1617

[34] L. Torner; E.M. Wright Soliton excitation and mutual locking of light beams in bulk quadratic nonlinear crystals, J. Opt. Soc. Am. B, Volume 13 (1996), pp. 864-875

[35] R. Schiek; Y. Baek; G.I. Stegeman; I. Baumann; W. Sohler One-dimensional quadratic walking solitons, Opt. Lett., Volume 24 (1999), pp. 83-85

[36] S. Trillo; P. Ferro; S. Trillo; P. Ferro Periodical waves, domain walls, and modulational instability in dispersive quadratic nonlinear media, Phys. Rev. E, Volume 20 (1995), pp. 438-440

[37] G.I. Stegeman; R. Schiek; H. Fang; R. Malendevich; L. Jankovic; L. Torner; W. Sohler; G. Schreiber Beam evolution in quadratically nonlinear 1-dimensional media: LiNbO₃ slab waveguides, Laser Phys., Volume 13 (2003), pp. 137-147

[38] H. Fang; R. Malendevich; R. Schiek; G.I. Stegeman Spatial modulational instability in one-dimensional LiNbO₃ slab waveguides, Opt. Lett., Volume 25 (2000), pp. 1786-1788

[39] A.I. D'yachenko; V.E. Zakharov; A.N. Pushkarev; V.E. Shvets; V.V. Yan'kov Solitonic turbulence in nonintegrable wave systems, Sov. Phys. JETP, Volume 96 (1989), pp. 2026-2048

[40] L. Torner; D. Mihalache; D. Mazilu; E.M. Wright; W.E. Torruellas; G.I. Stegeman Stationary trapping of light beams in bulk second-order nonlinear media, Opt. Commun., Volume 121 (1995), pp. 149-155

[41] L. Torner; D. Mazilu; D. Mihalache Walking solitons in quadratic nonlinear media, Phys. Rev. Lett., Volume 77 (1996), pp. 2455-2458

[42] S.V. Polyakov; G.I. Stegeman Existence and properties of quadratic solitons in anisotropic media: variational approach, Phys. Rev. E, Volume 66 (2002), p. 046622

[43] S. Polyakov; R. Malendevich; L. Jankovic; G.I. Stegeman; Ch. Bosshard; P. Gunter Effects of anisotropic diffraction on quadratic multi soliton excitation in non-critically phase-matched crystal, Opt. Lett., Volume 27 (2002), pp. 1049-1051

[44] H. Kim; L. Jankovic; G.I. Stegeman; S. Carrasco; L. Torner; M. Katz; D. Eger Second harmonic generation, beam dynamics and spatial soliton generation in periodically poled KTiOPO₄ (PPKTP), Acta Phys. Polon., Volume 103 (2003), pp. 107-120

[45] S. Carrasco; S. Polyakov; H. Kim; L. Jankovic; G.I. Stegeman; J.P. Torres; L. Torner; M. Katz Observation of multiple soliton generation mediated by amplification of asymmetries, Phys. Rev. E, Volume 67 (2003) (046616-1)

[46] S. Polyakov; L. Jankovic; H. Kim; G.I. Stegeman; S. Carrasco; L. Torner; M. Katz Properties of quadratic multi-soliton generation near phase-match in periodically poled potassium titanyl phosphate, Opt. Express, Volume 11 (2003), pp. 1328-1337

[47] L. Jankovic; S. Polyakov; G. Stegeman; S. Carrasco; L. Torner; Ch. Bosshard; P. Gunter Complex soliton-like pattern generation in Potassium Niobate due to noisy, high intensity, input beams, Opt. Express, Volume 11 (2003), pp. 2206-2210

[48] M. Ohkawa; R.A. Fuerst; G.I. Stegeman Characteristics of second harmonic generation with quadratic soliton generation versus conventional methods, J. Opt. Soc. Am. B, Volume 15 (1998), pp. 2769-2773

[49] D.N. Christodoulides; F. Lederer; Y. Silberberg Discretizing light behavior in linear and nonlinear waveguide lattices, Nature, Volume 424 (2003), pp. 817-823

[50] H.S. Eisenberg; Y. Silberberg; R. Morandotti; A.R. Boyd; J.S. Aitchison Discrete spatial optical solitons in waveguide arrays, Phys. Rev. Lett., Volume 81 (1998), pp. 3383-3386

[51] J.W. Fleischer; M. Segev; N.K. Efremidis; D.N. Christodoulides Observation of two-dimensional discrete solitons in optically-induced nonlinear photonic lattices, Nature, Volume 422 (2003), pp. 147-151

[52] A. Fratalocchi; G. Assanto; K.A. Brzdakiewicz; M.A. Karpierz Discrete propagation and spatial solitons in nematic liquid crystals, Opt. Lett., Volume 29 (2004), pp. 1530-1532

[53] R. Iwanow; R. Schiek; G.I. Stegeman; T. Pertsch; F. Lederer; Y. Min; W. Sohler Arrays of weakly coupled, periodically poled lithium niobate waveguide arrays: beam propagation and discrete spatial quadratic solitons, J. Optoelectron. Rev., Volume 13 (2005), pp. 113-121

[54] T. Peschel; U. Peschel; F. Lederer Discrete bright solitary waves in quadratically nonlinear media, Phys. Rev. E, Volume 57 (1998), pp. 1127-1133

[55] S. Darmanyan; A. Kobyakov; F. Lederer; S. Darmanyan; A. Kamchatnov; F. Lederer Optical shock waves in media with quadratic nonlinearity, Phys. Rev. E, Volume 57 (1998), pp. 2344-2349 (R4120-3)

[56] R. Iwanow; R. Schiek; G.I. Stegeman; Y. Min; W. Sohler Discrete modulational instability in periodically poled lithium niobate waveguide arrays, Opt. Express, Volume 13 (2005), pp. 7794-7799

[57] S. Suntsov; K.G. Makris; D.N. Christodoulides; G.I. Stegeman; A. Haché; R. Morandotti; H. Yang; G. Salamo; M. Sorel Observation of surface discrete solitons, Phys. Rev. Lett., Volume 96 (2006) no. 6, p. 063901

Cité par Sources :

Commentaires - Politique