Structured light entities, chaos and nonlocal maps
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866914116589846528 |
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| author | Okulov, A. Yu. |
| author_facet | Okulov, A. Yu. |
| contents | Spatial chaos as a phenomenon of ultimate complexity requires the efficient numerical algorithms. For this purpose iterative low-dimensional maps have demonstrated high efficiency. Natural generalization of Feigenbaum and Ikeda maps may include convolution integrals with kernel in a form of Green function of a relevant linear physical system. It is shown that such iterative $nonlocal$ $nonlinear$ $maps$ are equivalent to ubiquitous class of nonlinear partial differential equations of Ginzburg-Landau type. With a Green functions relevant to generic optical resonators these $nonlocal$ $maps$ emulate the basic spatiotemporal phenomena as spatial solitons, vortex eigenmodes breathing via relaxation oscillations mediated by noise, vortex-vortex and vortex-antivortex lattices with periodic location of vortex cores. The smooth multimode noise addition facilitates the selection of stable entities and elimination of numerical artifacts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_09274 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Structured light entities, chaos and nonlocal maps Okulov, A. Yu. Optics Pattern Formation and Solitons Quantum Physics Spatial chaos as a phenomenon of ultimate complexity requires the efficient numerical algorithms. For this purpose iterative low-dimensional maps have demonstrated high efficiency. Natural generalization of Feigenbaum and Ikeda maps may include convolution integrals with kernel in a form of Green function of a relevant linear physical system. It is shown that such iterative $nonlocal$ $nonlinear$ $maps$ are equivalent to ubiquitous class of nonlinear partial differential equations of Ginzburg-Landau type. With a Green functions relevant to generic optical resonators these $nonlocal$ $maps$ emulate the basic spatiotemporal phenomena as spatial solitons, vortex eigenmodes breathing via relaxation oscillations mediated by noise, vortex-vortex and vortex-antivortex lattices with periodic location of vortex cores. The smooth multimode noise addition facilitates the selection of stable entities and elimination of numerical artifacts. |
| title | Structured light entities, chaos and nonlocal maps |
| topic | Optics Pattern Formation and Solitons Quantum Physics |
| url | https://arxiv.org/abs/1901.09274 |