Optical vortices in dispersive nonlinear Kerr-type media
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...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204301018 |
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| _version_ | 1832563624461205504 |
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| author | Lubomir M. Kovachev |
| author_facet | Lubomir M. Kovachev |
| author_sort | Lubomir M. Kovachev |
| collection | DOAJ |
| description | 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 ℓ=1 and finite energy. Dispersion
region and medium parameters necessary for experimental
observation of these vortices are determined. |
| format | Article |
| id | doaj-art-2b021b5df16843bf9675cf963de68e7d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2b021b5df16843bf9675cf963de68e7d2025-02-03T01:12:55ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-0120041894996710.1155/S0161171204301018Optical vortices in dispersive nonlinear Kerr-type mediaLubomir M. Kovachev0Institute of Electronics, Bulgarian Academy of Sciences, Tsarigradsko, Chaussee 72, Sofia 1784, BulgariaThe 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 ℓ=1 and finite energy. Dispersion region and medium parameters necessary for experimental observation of these vortices are determined.http://dx.doi.org/10.1155/S0161171204301018 |
| spellingShingle | Lubomir M. Kovachev Optical vortices in dispersive nonlinear Kerr-type media International Journal of Mathematics and Mathematical Sciences |
| title | Optical vortices in dispersive nonlinear Kerr-type media |
| title_full | Optical vortices in dispersive nonlinear Kerr-type media |
| title_fullStr | Optical vortices in dispersive nonlinear Kerr-type media |
| title_full_unstemmed | Optical vortices in dispersive nonlinear Kerr-type media |
| title_short | Optical vortices in dispersive nonlinear Kerr-type media |
| title_sort | optical vortices in dispersive nonlinear kerr type media |
| url | http://dx.doi.org/10.1155/S0161171204301018 |
| work_keys_str_mv | AT lubomirmkovachev opticalvorticesindispersivenonlinearkerrtypemedia |