Quadratic Solitons: Past, Present, and Future

Kivshar, Yuri S.

doi:10.1007/978-94-007-0850-1_42

Cited by 9 publications

(5 citation statements)

References 81 publications

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“…(3)], E = 12000. We see that, with the increase of the mismatch β, the energy of the FF component of the spinning soliton increases, similar to the case of nonspinning solitons in pure χ (2) media [42,45,46,47].…”

Section: The Model and Spinning Solitonssupporting

confidence: 58%

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

et al. 2002

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We show that the quadratic interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-defocusing cubic nonlinearity, give rise to completely localized spatiotemporal solitons (vortex tori) with vorticity s = 1. There is no threshold necessary for the existence of these solitons. They are found to be stable if their energy exceeds a certain critical value, so that the stability domain occupies about 10 % of the existence region of the solitons. On the contrary to spatial vortex solitons in the same model, the spatiotemporal ones with s = 2 are never stable. These results might open the way for experimental observation of spinning three-dimensional solitons in optical media.

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Section: The Model and Spinning Solitonssupporting

confidence: 58%

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

et al. 2002

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“…However, parametric interactions can strongly modify the dynamics of spatial beams or temporal pulses. The parametrically coupled waves in a medium with quadratic nonlinearity may experience mutual spatial focusing or temporal compression and lock together into a stationary state, quadratic soliton (see Sukhorukov [1988]; Torner [1998]; Kivshar [1997]; Etrich, Lederer, Malomed, Peschel, and Peschel [2000]; Torruellas, Kivshar, and Stegeman [2001]; Boardman and Sukhorukov [2001]; Buryak, Di Trapani, Skryabin, and Trillo [2002], and references therein).…”

Section: Wave Interchange and Signal Deflectionmentioning

confidence: 99%

“…Respectively, the first sub-process is responsible for the generation of the SH field, with the most efficient conversion observed at ∆k = 0, while the second sub-process, also called cascading, can be associated with an effective intensity-dependent change of the phase of the fundamental harmonic (∼ d 2 /∆k), which is similar to that of the cubic nonlinearity (DeSalvo, Hagan, Sheik-Bahae, Stegeman, Vanstryland, and Vanherzeele [1992]; Stegeman, Hagan, and Torner [1996]; Assanto, Stegeman, Sheik-Bahae, and Vanstryland [1995]). This latter effect is responsible for the generation of the so-called quadratic solitons, two-wave parametric soliton composed of the mutually coupled fundamental and second-harmonic components (Sukhorukov [1988]; Torner [1998]; Kivshar [1997]; Etrich, Lederer, Malomed, Peschel, and Peschel [2000]; Torruellas, Kivshar, and Stegeman [2001]; Boardman and Sukhorukov [2001]; Buryak, Di Trapani, Skryabin, and Trillo [2002], and references therein).…”

mentioning

confidence: 99%

Multistep parametric processes in nonlinear optics

2005

Self Cite

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We present a comprehensive overview of different types of parametric interactions in nonlinear optics which are associated with simultaneous phase-matching of several optical processes in quadratic nonlinear media, the so-called multistep parametric interactions. We discuss a number of possibilities of double and multiple phase-matching in engineered structures with the sign-varying second-order nonlinear susceptibility, including (i) uniform and non-uniform quasi-phase-matched (QPM) periodic optical superlattices, (ii) phase-reversed and periodically chirped QPM structures, and (iii) uniform QPM structures in non-collinear geometry, including recently fabricated two-dimensional nonlinear quadratic photonic crystals. We also summarize the most important experimental results on the multi-frequency generation due to multistep parametric processes, and overview the physics and basic properties of multi-color optical parametric solitons generated by these parametric interactions.

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“…This follows from the two i n tegral relations which c a n be obtained from the variational principle (13) and directly from the stationary equations (11,12) after multiplying the rst equation by 1 , the second one by 2 2 , with summation of the obtained results, followed by their integration over x (for details, see 11]). In the case when the operators are negative de nite, the following conditions must be ful lled: (15) has to be a positive q u a n tity. As a result, the last inequality (16) reads as…”

Section: Basic Equationsmentioning

confidence: 99%

The two-parameter soliton family for the interaction of a fundamental and its second harmonic

Grimshaw¹,

Кузнецов²,

Shapiro³

2001

Physica D: Nonlinear Phenomena

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Additional Information:• This is a pre-print. The definitive version: GRIMSHAW, KUZNETSOV and SHAPIRO, 2001. The two-parameter soliton family for the interaction of a fundamental and its second harmonic. Physica D, 152, Metadata Record: https://dspace.lboro.ac.uk/2134/766Please cite the published version.The two-parameter soliton family for the interaction of a fundamental and its second harmonic For a system of interacting fundamental and second harmonics the soliton family is characterized by t wo independent parameters, a soliton potential and a soliton velocity. It is shown that this system, in the general situation, is not Galilean invariant. As a result, the family of movable solitons cannot be obtained from the rest soliton solution by applying the corresponding Galilean transformation. The region of soliton parameters is found analytically and con rmed by n umerical integration of the steady equations. On the boundary of the region the solitons bifurcate. For this system there exist two kinds of bifurcation: supercritical and subcritical. In the rst case the soliton amplitudes vanish smoothly as the boundary is approached. Near the bifurcation point the soliton form is universal, determined from the nonlinear Schrodinger equation. For the second type of bifurcations the wave amplitudes remain nite at the boundary. In this case the Manley-Rowe i n tegral increases inde nitely as the boundary is approached, and therefore according to the VK-type stability criterion, the solitons are unstable.

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Quadratic Solitons: Past, Present, and Future

Cited by 9 publications

References 81 publications

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

Multistep parametric processes in nonlinear optics

The two-parameter soliton family for the interaction of a fundamental and its second harmonic

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