arXiv subjects

Jaroslaw Zalesny

Publications and source records attributed to Jaroslaw Zalesny.

5 recordsLinked to original sources

arXiv2008

The simple complex numbers

A new simple geometrical interpretation of complex numbers is presented. It differs from their usual interpretation as points in the complex plane. From the new point of view the complex numbers are rather operations on vectors than points. Moreover, in this approach the real, imaginary and complex numbers have similar interpretation. They are simply some operations on vectors. The presented interpretation is simpler, more natural, and better adjusted to possible applications in geometry and physics than the usual one, especially for describing rotations in a plane. The relation of the new approach to the usual interpretation and especially to the notion of complex plane is also clarified in the paper. The new interpretation of complex numbers gives new insight into their applications in physics, which is demonstrated by some elementary examples in mechanics and optics

physics.ed-ph↗

arXiv2002

Stationary Solutions of the Electromagnetic TE Waves Propagating along a Single Interface between the Two Kerr-Type Nonlinear Media

Propagation of the TE electromagnetic waves in self-focusing medium is governed by the nonlinear Schroedinger 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 the 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 nonlinear medium. This result is the main point of the paper. Some of the presented stationary solutions were already used in similar optical context in 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.

physics.optics↗

arXiv2002

Time Evolution of SU(1,1) coherent states

Mathematical aspects of the SU(1,1) group parameter x dynamics governed by Hamiltonians exhibiting some special types of time dependence has been presented on an elementary level from the point of view of Moebius transformation of complex plane. The trajectories of x in continuous and mappings in discrete dynamics are considered. Some simple examples have been examined. Analytical considerations and numerical results have been given.

physics.optics↗

arXiv2002

Propagation of photons in resting and moving media

The propagation of photon in a dielectric may be described with the help of the scalar and vector potentials of the medium. The main novelty of the paper is that the concept of the vector potential (which is connected with the velocity of the medium) can be extended to relativistic velocities of the medium. The position-dependent photon wave function was used to describe the propagation of the photon. The new concepts of the velocity of photon as particle and the photon mass in the dielectric medium were proposed.

physics.optics↗

arXiv2002

Optical Kerr type nonlinearity

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.

physics.optics↗