Particlelike nature of colliding three-dimensional optical solitons

Edmundson, D.; Enns, Richard H.

doi:10.1103/physreva.51.2491

Cited by 63 publications

(37 citation statements)

References 10 publications

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“…The two models produce essentially different results when the expansion is not valid. Critical conditions for the formation of 2D solitons in these systems were found numerically by QuirogaTeixeiro et al [29] (2D), and by Edmundson et al [27] and McLeod et al [28] for the 3D solitons. From those results, we can estimate the necessary experimental parameters for both the 2D and 3D case by the transformation to physical units.…”

Section: Theoretical Analysis Of Necessary Conditions For the Eximentioning

confidence: 71%

“…Evolution of the amplitude E of the electromagnetic wave in a lossless Kerr-like medium with anomalous GVD obeys the well-known scaled equation [24,26,27,28] …”

Section: Theoretical Analysis Of Necessary Conditions For the Eximentioning

confidence: 92%

“…It was shown that both rational [24,25,26,27,28] and cubic-quintic (CQ) [29,30,31] variants of the saturation readily support stable twodimensional (2D) and three-dimensional (3D) solitons. A difference between them is that the former cannot stabilize "spinning" solitons with an intrinsic vorticity, but the CQ nonlinearity makes it possible, in the 2D [32,33,34] and even 3D [35] cases.…”

Section: Introductionmentioning

confidence: 99%

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Criteria for the experimental observation of multidimensional optical solitons in saturable media

et al. 2004

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Criteria for experimental observation of multi-dimensional optical solitons in media with saturable refractive nonlinearities are developed. The criteria are applied to actual material parameters (characterizing the cubic self-focusing and quintic self-defocusing nonlinearities, two-photon loss, and optical-damage threshold) for various glasses. This way, we identify operation windows for soliton formation in these glasses. It is found that two-photon absorption sets stringent limits on the windows. We conclude that, while a well-defined window of parameters exists for two-dimensional solitons (spatial or spatiotemporal), for their three-dimensional spatiotemporal counterparts such a window does not exist, due to the nonlinear loss in glasses.

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Section: Theoretical Analysis Of Necessary Conditions For the Eximentioning

confidence: 71%

“…Evolution of the amplitude E of the electromagnetic wave in a lossless Kerr-like medium with anomalous GVD obeys the well-known scaled equation [24,26,27,28] …”

Section: Theoretical Analysis Of Necessary Conditions For the Eximentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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Criteria for the experimental observation of multidimensional optical solitons in saturable media

et al. 2004

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“…A cubic-quintic medium that features strong saturation of the Kerr effect could avoid collapse and provide confinement in several dimensions. [4][5][6][7] However, such a medium is difficult to find in practice. Photorefractive materials possess strongly saturating nonlinearity but their slow response restrict their use to the formation of spatial solitons.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal optical solitons in nonlinear dissipative media: From stationary light bullets to pulsating complexes

Akhmediev

Soto-Crespo

Grelu

2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Nonlinear dissipative systems display the full ͑3+1͒D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic GinzburgLandau equation model. Numerical simulations reveal the existence of stationary bell-shaped ͑3+1͒D solitons for both anomalous and normal chromatic dispersion regimes, as well as the formation of double soliton complexes. We provide additional insight concerning the possible dynamics of these soliton complexes, consider collision cases between two solitons, and discuss the ways nonstationary evolution can lead to optical pattern formation. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2746830͔The subject of dissipative solitons has emerged recently, driving an impressive number of studies in many areas of nonlinear science. Previous studies of purely temporal dissipative solitons have been highly useful, for both fundamental science and the development of high bit-rate optical telecommunications and passively mode-locked lasers. Now, it is the time for generalizations to "3+1…-D domain. An appropriate term to describe the new structures is "dissipative optical bullets." Spatiotemporal optical dissipative solitons are localized formations in systems with gain, loss, spectral filtering, dispersion, diffraction, and nonlinearity. The combined interplay between these physical effects creates an optical field confined in both temporal and transverse coordinates. The confinement occurs mainly due to the nonlinear gain balanced with a nonlinear loss in the system. The balance between nonlinearity and dispersion/diffraction, which was the main reason for the existence of conservative solitons, can be weakened or even lifted. Consequently, dissipative optical bullets can exist in media with either anomalous or normal dispersion. Optical bullets have extended regions of stability, which allow experimental observation and potential use of these objects. We present here a review of the latest numerical results concerning dissipative spatiotemporal optical solitons and their complexes. The interaction between stable dissipative light bullets reveals the importance of the phase difference between them. Controlling this parameter can lead to fusion, erasure of one of the solitons or to the formation of soliton complexes, or bound states. Collisions of solitons with nonzero velocities can also create these bound states. The bound states in turn can exhibit a wide range of dynamics, such as rotation and vibration, making them akin to atomic molecules. Among other interesting dynamical aspects of dissipative optical bullets presented in this work is a transverse pattern formation out of the light bullets that lack stability.

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“…STS i n vari ous typ es of no nl i near opti cal envi ro nm ents ha ve attra cted a great deal of i nterest [22{ 42]. However, col l apse do es not ta ke pl ace, m aki ng sta bl e LB possibl e, i n medi a wi th satura bl e [25,26,31], qua dra ti c [35,39], and cubi c-qui nti c [43,44] nonl ineari ti es, i n o˜-resona nce two -level system s [41] as wel l as i n self -i nduced-tra nsparency m edi a [40]. R ecentl y i n Ref.…”

mentioning

confidence: 99%

Spinning Optical Spatiotemporal Solitons in Quadratic Media

Mihalache

2001

Acta Phys. Pol. A

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T he uni que features of the families of bri ght spinning spatiotemp oral solitons (doughnuts or vortex light bullets ) in disp ersive quadratic media, includi ng their stabili ty , are presented. Both analyti cal results, obtained by means of a simple variational approximation, and numerical simulations are presented and compared. I t w as found that though the variational approximation is not very accurate, it correctly describ es the qualitati ve features of the spinni ng spatiotemp ora l solitons. T he spinni ng light bullets are subj ect to a strong azimuthal instabil ity , which leads to the brea k-up of the spinni ng soliton into a set of fragments, each b eing a s t a b l e nonspinn in g spatiotemp oral soliton.PAC S numb ers: 42.65.T g, 42. 65. Sf 1. I n t r o d u ct io n Sol i ton s i n opti cal m edi a wi t h qua dra ti c nonl ineari ti esexhi bi t uni que dyna mi cal b ehavi ors a nd ha ve a p otenti al for appl i cati ons to pho to ni c devi ces [1{ 20]. One of the funda menta ll y i m po rta n t pro p erti es i s the fact tha t , unl ike the Kerr no nl i neari ty [21], the qua dra ti c nonl i neari ty do esno t l ead to wa ve col l apsei n any physi cal di mension [3 ], and thus i t op ens a way to generate sta bl e spati otem p ora l sol i tons (S TS), or \ l i ght bul l ets" (L B) [21], i .e., ful l y l ocal i zed spati otem p ora l ob j ects tha t resul t fro m the simul taneous bal ance of di˜ra cti on and di spersion by no nl i near pha se-m odul ati on. STS i n vari ous typ es of no nl i near opti cal envi ro nm ents ha ve attra cted a great deal of i nterest [22{ 42]. However, col l apse do es not ta ke pl ace, m aki ng sta bl e LB possibl e, i n medi a wi th satura bl e [25,26,31], qua dra ti c [35,39], and cubi c-qui nti c [43,44] nonl ineari ti es, i n o˜-resona nce two -level system s [41] as wel l as i n self -i nduced-tra nsparency m edi a [40]. R ecentl y i n Ref.[41] the pro pagati on of 2D f emto second opti cal pul ses i n an o˜-resona nce tw o-level m edium was addressed. W i thi n the qua siadi aba ti ng fol l owi ng appro ach, the evol uti on of the pul se i s governed by a general i zed Ka dom tsev{ Petvi ashvil i equati on wi th coupl i ng (4 7)

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Particlelike nature of colliding three-dimensional optical solitons

Cited by 63 publications

References 10 publications

Criteria for the experimental observation of multidimensional optical solitons in saturable media

Criteria for the experimental observation of multidimensional optical solitons in saturable media

Spatiotemporal optical solitons in nonlinear dissipative media: From stationary light bullets to pulsating complexes

Spinning Optical Spatiotemporal Solitons in Quadratic Media

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