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Time Evolution of SU(1,1) Coherent States

100%
Zaleśny J.
Acta Physica Polonica A
|
2000
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vol. 98
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issue 1-2
11-22
EN
Mathematical aspects of the SU(1,1) group parameter ξ dynamics governed by Hamiltonians exhibiting some special types of time dependence was presented on an elementary level from the point of view of the Möbius transformation of complex plane. The trajectories of ξ in continuous and mappings in discrete dynamics are considered. Some simple examples were examined. Analytical considerations and numerical results were given.
2
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Optical Kerr Type Nonlinearity

100%
Zaleśny J.
Acta Physica Polonica A
|
2001
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vol. 99
|
issue 1
191-124
EN
The origin of the Kerr type nonlinearity of the medium as a result of the interaction between photons via the Dirac delta-potential is presented in the formalism adopted from the photon wave function approach. In the view of the result the optical soliton may be treated as a bound state (cluster) of many photons.
3
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Stationary Solutions of the Electromagnetic TE Waves Propagating Along a Single Interface Between the Two Kerr-Type Nonlinear Media

63%
Wabia M., Zaleśny J.
Acta Physica Polonica A
|
1999
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vol. 95
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issue 5
801-812
EN
Propagation of the TE electromagnetic waves in self-focusing medium is governed by the nonlinear Schrödinger equation. In this paper the stationary solutions of this equation have been systematically presented. The phase-plane method, qualitative analysis, and mechanical interpretation of the differential equations are widely used. It is well known that TE waves can be guided by a single interface between two semi-infinite media, providing that one of the media has a self-focusing (Kerr-type) nonlinearity. This special solution is called a spatial soliton. In this paper our interests are not restricted to the soliton solutions. In the context of the nonlinear substrate and cladding we have found solutions which could be useful to describe also the incident light in a nonlinear medium. This result is the main point of the paper. Some of the presented stationary solutions were already used in a similar optical context in the literature but we show a little wider class of solutions. In the last section we review and illustrate some results concerning the spatial soliton solution.
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