Interaction of coupled-vector optical vortices

Andersen, David R.; Kovachev, Lubomir M.

doi:10.1364/josab.19.000376

Cited by 7 publications

(11 citation statements)

References 10 publications

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“…Corresponding solutions were found by Andersen and Kovachev [2002]; Kovachev [2004a] for nonlinear Maxwell equations and by Kovachev [2004b] for MaxwellDirac equations. The internal structure of the three-dimensional vector vortices with radially symmetric total intensity is described in this case by spherical harmonics.…”

Section: Multi-component Vortex Solitonsmentioning

confidence: 90%

Optical vortices and vortex solitons

2005

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Optical vortices are phase singularities nested in electromagnetic waves that constitute a fascinating source of phenomena in the physics of light and display deep similarities to their close relatives, quantized vortices in superfluids and Bose-Einstein condensates. We present a brief overview of the major advances in the study of optical vortices in different types of nonlinear media, with emphasis on the properties of vortex solitons. Self-focusing nonlinearity leads, in general, to the azimuthal instability of a vortex-carrying beam, but it can also support novel types of stable or meta-stable self-trapped beams carrying nonzero angular momentum, such as ring-like solitons, necklace beams, and soliton clusters. We describe vortex solitons created by multi-component beams, by parametrically coupled beams in quadratic nonlinear media, and in partially incoherent light, as well as discrete vortex solitons in periodic photonic lattices.

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Section: Multi-component Vortex Solitonsmentioning

confidence: 90%

Optical vortices and vortex solitons

2005

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“…In [2], we find that the constraint given in (4.3) corresponds to the next two experimental situations:…”

Section: Experimental Conditionsmentioning

confidence: 88%

“…Some of the experimental possibilities for this small term to become important were discussed in [21]. In [2] it was shown that this second derivative in the direction of propagation term is in the same order and with the same sign as the others only in some special cases: optical pulses near the Langmuir frequency or near some of the electronic resonances. In these regions, the sign of the dispersion is negative and the scalar 2D+1 NLS becomes a 3D+1 NLS one.…”

Section: Introductionmentioning

confidence: 99%

Optical vortices in dispersive nonlinear Kerr‐type media

Kovachev

2004

International Journal of Mathematics and Mathematical Sciences

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The applied method of slowly varying amplitudes gives us the possibility to reduce the nonlinear vector integrodifferential wave equation of the electrical and magnetic vector fields to the amplitude vector nonlinear differential equations. Using this approximation, different orders of dispersion of the linear and nonlinear susceptibility can be estimated. Critical values of parameters to observe different linear and nonlinear effects are determined. The obtained amplitude equations are a vector version of 3D + 1 nonlinear Schrödinger equation (VNSE) describing the evolution of slowly varying amplitudes of electrical and magnetic fields in dispersive nonlinear Kerr-type media. We show that VNSE admits exact vortex solutions with classical orbital momentum = 1 and finite energy. Dispersion region and medium parameters necessary for experimental observation of these vortices are determined.2000 Mathematics Subject Classification: 35Q55, 45G15, 90C30. Introduction.At the present time, there are no difficulties for experimentalist in laser physics and nonlinear optics to obtain picosecond or femtosecond optical pulses with equal durations in x, y, and z directions. The problems with the so-generated light bullets arise in the process of their propagation in a nonlinear media with dispersion. In the transparency region of a dispersive Kerr-type media, as it was established in [6,14], the scalar paraxial approximation (no dispersion in the direction of propagation) is in a very good accordance with the experimental results. The paraxial approximation, used in the derivation of the scalar 2D + 1 nonlinear Schrödinger equation (NLS), does not include (in first-or second-order of magnitude) a small second derivative of the amplitude function in the direction of propagation. The inclusion of this term does not change the main result dramatically in the case of a linear propagation (pulses with small intensity), as generated optical bullets at short distance are transformed in optical disks, with large transverse and small lengthwise dimension. Some of the experimental possibilities for this small term to become important were discussed in [21]. In [2] it was shown that this second derivative in the direction of propagation term is in the same order and with the same sign as the others only in some special cases: optical pulses near the Langmuir frequency or near some of the electronic resonances. In these regions, the sign of the dispersion is negative and the scalar 2D+1 NLS becomes a 3D+1 NLS one. Propagation of optical bullets under the dynamics of 2D+1 and 3D+1 NLS is investigated also in relation to different kinds of nonlinearity [9,10,19,23,24]. A generation of a new kind of 2D and 3D optical pulses, the so-called optical vortices, has recently become a topic of considerable interest. Generally, the optical vortices

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“…For all cited theories, no exact solutions have been found, but numerical and energy momentum techniques are used. The existence of exact stable vortex solutions of these types of nonlinear equations was finally discovered with the vector generalization of the 3D + 1 NSE [2]. It has also been shown numerically that these vortices are stable at distances comparable to those where localized solutions of the one-component scalar equation are self-focusing rapidly.…”

Section: Introductionmentioning

confidence: 93%

“…There are some differences between the nonlinear conditions for localized solutions of the vector nonlinear Schrodinger equation (VNLS) and the localized conditions for the nonlinear Maxwell equations (NMEs). The nonlinear parameter for the VNLS is written [2] as…”

Section: Experimental Conditionsmentioning

confidence: 99%

Optical leptons

Kovachev

2004

International Journal of Mathematics and Mathematical Sciences

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We obtain optical vortices with classical orbital momentum Ã¢Â„Â“=1 and spin j=Ã‚Â±1/2 as exact solutions of a system of nonlinear Maxwell equations (NMEs). Two kinds of Kerr-type media, namely, those with and without linear dispersion of the electric and the magnet susceptibility, are investigated. The electric and magnetic fields are represented as sums of circular and linear components. This allows us to reduce the NME to a set of nonlinear Dirac equations (NDEs). The vortex solutions in the case of media with dispersion admit finite energy, while the solutions in case of media without dispersion admit infinite energy. The amplitude equations are obtained from equations of nonstationary optical and magnetic response (dispersion). This includes also the optical pulses with time duration of order of and less than the time of relaxation of the media (femtosecond pulses). The possible generalization of NME to a higher number of optical components and a higher number of Ã¢Â„Â“ and j is discussed

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Interaction of coupled-vector optical vortices

Cited by 7 publications

References 10 publications

Optical vortices and vortex solitons

Optical vortices and vortex solitons

Optical vortices in dispersive nonlinear Kerr‐type media

Optical leptons

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