dorsal/arxiv
View SchemaStandard and Embedded Solitons in Nematic Optical Fibers
| Authors | R. F. Rodriguez, J. A. Reyes, A. Espinosa-Ceron J. Fujioka, B. A. Malomed |
|---|---|
| Categories | |
| ArXiv ID | physics/0306189 |
| URL | https://arxiv.org/abs/physics/0306189 |
| DOI | 10.1103/PhysRevE.68.036606 |
Abstract
A model for a non-Kerr cylindrical nematic fiber is presented. We use the multiple scales method to show the possibility of constructing different kinds of wavepackets of transverse magnetic (TM) modes propagating through the fiber. This procedure allows us to generate different hierarchies of nonlinear partial differential equations (PDEs) which describe the propagation of optical pulses along the fiber. We go beyond the usual weakly nonlinear limit of a Kerr medium and derive an extended Nonlinear Schrodinger equation (eNLS) with a third order derivative nonlinearity, governing the dynamics for the amplitude of the wavepacket. In this derivation the dispersion, self-focussing and diffraction in the nematic are taken into account. Although the resulting nonlinear $PDE$ may be reduced to the modified Korteweg de Vries equation (mKdV), it also has additional complex solutions which include two-parameter families of bright and dark complex solitons. We show analytically that under certain conditions, the bright solitons are actually double embedded solitons. We explain why these solitons do not radiate at all, even though their wavenumbers are contained in the linear spectrum of the system. Finally, we close the paper by making comments on the advantages as well as the limitations of our approach, and on further generalizations of the model and method presented.
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"abstract": "A model for a non-Kerr cylindrical nematic fiber is presented. We use the\nmultiple scales method to show the possibility of constructing different kinds\nof wavepackets of transverse magnetic (TM) modes propagating through the fiber.\nThis procedure allows us to generate different hierarchies of nonlinear partial\ndifferential equations (PDEs) which describe the propagation of optical pulses\nalong the fiber. We go beyond the usual weakly nonlinear limit of a Kerr medium\nand derive an extended Nonlinear Schrodinger equation (eNLS) with a third order\nderivative nonlinearity, governing the dynamics for the amplitude of the\nwavepacket. In this derivation the dispersion, self-focussing and diffraction\nin the nematic are taken into account. Although the resulting nonlinear $PDE$\nmay be reduced to the modified Korteweg de Vries equation (mKdV), it also has\nadditional complex solutions which include two-parameter families of bright and\ndark complex solitons. We show analytically that under certain conditions, the\nbright solitons are actually double embedded solitons. We explain why these\nsolitons do not radiate at all, even though their wavenumbers are contained in\nthe linear spectrum of the system. Finally, we close the paper by making\ncomments on the advantages as well as the limitations of our approach, and on\nfurther generalizations of the model and method presented.",
"arxiv_id": "physics/0306189",
"authors": [
"R. F. Rodriguez",
"J. A. Reyes",
"A. Espinosa-Ceron J. Fujioka",
"B. A. Malomed"
],
"categories": [
"physics.optics"
],
"doi": "10.1103/PhysRevE.68.036606",
"title": "Standard and Embedded Solitons in Nematic Optical Fibers",
"url": "https://arxiv.org/abs/physics/0306189"
},
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