Multidimensional solitons in quadratic nonlinear media

Hayata, Kazuya; Koshiba, Masanori

doi:10.1103/physrevlett.71.3275

Cited by 186 publications

(74 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The self-focusing action of the nonlinearity compensated by diffraction results in self-sustained bright spatial solitons [12], which can exist as isolated states or form complex ensembles, sometimes interacting in a particle-like fashion [169][170][171][172][173][174][175]. Also, dark solitons [176][177][178][179][180][181][182][183][184] and optical vortices [185][186][187][188][189][190][191][192][193][194][195][196] have been described and experimentally observed.…”

Section: Mirrorless Configurationmentioning

confidence: 99%

Transverse Patterns in Nonlinear Optical Resonators

Staliūnas

Sánchez‐Morcillo

2003

Springer Tracts in Modern Physics

176

156

View full text Add to dashboard Cite

This book is devoted to the formation and dynamics of localized structures (vortices, solitons) and of extended patterns (stripes, hexagons, tilted waves) in nonlinear optical resonators such as lasers, optical parametric oscillators, and photorefractive oscillators. Theoretical analysis is performed by deriving order parameter equations, and also through numerical integration of microscopic models of the systems under investigation. Experimental observations, and possible technological implementations of transverse optical patterns are also discussed. A comparison with patterns found in other nonlinear systems, i.e. chemical, biological, and hydrodynamical systems, is given.

show abstract

Section: Mirrorless Configurationmentioning

confidence: 99%

Transverse Patterns in Nonlinear Optical Resonators

Staliūnas

Sánchez‐Morcillo

2003

Springer Tracts in Modern Physics

176

156

View full text Add to dashboard Cite

show abstract

“…They are ubiquitous objects in optical media [1] [3,7], quadratically nonlinear (χ (2) ) [2,8], and graded-index Kerr media [9]. While a fully localized STS in three dimensions (3D) has not yet been found in an experiment, 2D ones were observed in a bulk χ (2) medium [10].…”

mentioning

confidence: 99%

“…Spatiotemporal solitons (STS) [2], alias superspikes [3,4] or light bullets [5], were found in many works [2] - [9]. Although they cannot be stable in the uniform Kerr (χ (3) ) medium [6], stability can be achieved in saturable [3,7], quadratically nonlinear (χ (2) ) [2,8], and graded-index Kerr media [9]. While a fully localized STS in three dimensions (3D) has not yet been found in an experiment, 2D ones were observed in a bulk χ (2) medium [10].…”

mentioning

confidence: 99%

Stable Spinning Optical Solitons in Three Dimensions

et al. 2002

View full text Add to dashboard Cite

We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schrödinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.Optical solitons (spatial, temporal, or spatiotemporal) are self-trapped light beams or pulses that are supported by a balance between diffraction and/or dispersion and various nonlinearities. They are ubiquitous objects in optical media [1] [3,7], quadratically nonlinear (χ (2) ) [2,8], and graded-index Kerr media [9]. While a fully localized STS in three dimensions (3D) has not yet been found in an experiment, 2D ones were observed in a bulk χ (2) medium [10]. The interplay of spatio-temporal coupling and nonlinearity may also play an important role in self-defocusing media [11].Spinning (vortex) solitons are also possible in optical media. Starting with the works [12], both delocalized ("dark") and localized ("bright") optical vortices in 2D were investigated [13,14,15]. In the 3D case they take the shape of a torus ("doughnut") [16,17]. However, the only previously known physical model which could support stable 3D vortex solitons is the Skyrme model [18], which has recently found a new important application to Bose-Einstein condensates (BEC) [19]. Our objective in this paper is to identify fundamental models of the nonlinear-Schrödinger (NLS) type in 3D that give rise to stable spinning solitons, as NLS models are much simpler and closer to more experimental situations, having applications to optics, BEC, plasmas, etc. (see below).For bright vortex solitons stability is a major issue as, unlike their zero-spin counterparts, the spinning solitons are prone to destabilization by azimuthal perturbations. In 2D models with χ (2) and saturable nonlinearities an azimuthal instability was revealed by simulations [14] and observed experimentally [15]. As a result, a soliton with spin 1 splits into two or three fragments, each being a moving zero-spin soliton. Simulations of the 3D spinning STS in the χ (2) model also demonstrates its instability-induced splitting into separating zero-spin solitons [17]. Nevertheless, the χ (2) nonlinearity acting in combination with the self-defocusing Kerr (χ (3) ) nonlinearity, gives rise to the first examples of stable spinning (ring-shaped) 2D solitons with spin s = 1 and 2 [20]. It should be stressed that all the 2D spinning solitons actually represent static spatial beams; on the contrary, 3D solitons are moving spatiotemporal ones, which are localized not only in the transverse plane, but also in the propagation coordinate, see below.A model which may support stable spinning solitons in 3D is the one with a cubic-quintic (CQ) nonlinearity, which (in terms of optics) assumes a nonlinear correction to the medium's refractive index in the form δn = n 2 I − n 4 I 2 , I being the lig...

show abstract

“…For a second-harmonic generating medium, the existence of stable two-and threedimensional (2D and 3D) solitons was predicted as early as in 1981 [2], followed by studies of their propagation and stability against collapse [3][4][5][6], and of analogous 3D quantum solitons [7]. In a nonlinear Schrödinger model both stable and unstable LBs were found [8] and it was suggested that various models describing fluid flows yield stable 2D spatio-temporal solitons [9].…”

mentioning

confidence: 99%

Spatiotemporally Localized Multidimensional Solitons in Self-Induced Transparency Media

2000

View full text Add to dashboard Cite

"Light bullets" are multi-dimensional solitons which are localized in both space and time. We show that such solitons exist in two-and three-dimensional self-induced-transparency media and that they are fully stable. Our approximate analytical calculation, backed and verified by direct numerical simulations, yields the multi-dimensional generalization of the one-dimensional Sine-Gordon soliton. The concept of multi-dimensional solitons that are localized in both space and time, alias "light bullets" (LBs), was pioneered by Silberberg [1], and has since then been investigated in various nonlinear optical media, with particular emphasis on the question of whether these solitons are stable or not. For a second-harmonic generating medium, the existence of stable two-and threedimensional (2D and 3D) solitons was predicted as early as in 1981 [2], followed by studies of their propagation and stability against collapse [3][4][5][6], and of analogous 3D quantum solitons [7]. In a nonlinear Schrödinger model both stable and unstable LBs were found [8] and it was suggested that various models describing fluid flows yield stable 2D spatio-temporal solitons [9]. Recently, the first experimental observation of a quasi-2D "bullet" in a 3D sample was reported in Ref. [10].In this letter we predict a new, hitherto unexplored type of LBs, obtainable by 2D or 3D self-induced transparency (SIT). SIT involves the solitary propagation of an electromagnetic pulse in a near-resonant medium, irrespective of the carrier-frequency detuning from resonance [11,12]. The SIT soliton in 1D near-resonant media [13] is exponentially localized and stable. In order to investigate the existence of "light bullets" in SIT, i.e. solitons that are localized in both space and time, one has to consider a 2D or 3D near-resonant medium. Here we present an approximate analytical solution of this problem, which is checked by and in very good agreement with direct numerical simulations.Our starting point are the two-dimensional SIT equations in dimensionless form [14] − iE xx + E z − P = 0 (1a)Here E and P denote the slowly-varying amplitudes of the electric field and polarization, respectively, W is the inversion, z and x are respectively the longitudinal and transverse coordinates (in units of the effective absorption length α eff ), and τ the retarded time (in units of the input pulse duration τ p ). The Fresnel number F (F > 0), which governs the transverse diffraction in 2D and 3D propagation, is incorporated in x and the detuning ∆Ω of the carrier frequency from the central atomic resonance frequency is absorbed in E and P [15]. We have neglected polarization dephasing and inversion decay, considering pulse durations that are much shorter than the corresponding relaxation times. Eqs. (1) are then compatible with the local constraint |P| 2 + W 2 = 1, which corresponds to conservation of the Bloch vector [14].The first nontrivial question is to find a Lagrangian representation for these 2D equations, which is necessary for adequate understanding of the d...

show abstract

Multidimensional solitons in quadratic nonlinear media

Cited by 186 publications

References 13 publications

Transverse Patterns in Nonlinear Optical Resonators

Transverse Patterns in Nonlinear Optical Resonators

Stable Spinning Optical Solitons in Three Dimensions

Spatiotemporally Localized Multidimensional Solitons in Self-Induced Transparency Media

Contact Info

Product

Resources

About