Lens optics as an optical computer for group contractions

Download

index.pdf

Date

2003-05-01

Author

Baskal, S
Kim, YS

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

128
views

46
downloads

It is shown that the one-lens system in para-axial optics can serve as an optical computer for contraction of Wigner's little groups and an analog computer that transforms analytically computations on a spherical surface to those on a hyperbolic surface. It is shown possible to construct a set of Lorentz transformations which leads to a 2x2 matrix whose expression is the same as those in the para-axial lens optics. It is shown that the lens focal condition corresponds to the contraction of the O(3)-like little group for a massive particle to the E(2)-like little group for a massless particle, and also to the contraction of the O(2,1)-like little group for a spacelike particle to the same E(2)-like little group. The lens-focusing transformations presented in this paper allow us to continue analytically the spherical O(3) world to the hyperbolic O(2,1) world, and vice versa. Since the traditional role of Wigner's little groups has been to dictate the internal space-time symmetries of massive, massless, and imaginary-mass particles, the one-lens system provides a unification of those symmetries.

Subject Keywords

Wigner

URI

https://hdl.handle.net/11511/64793

Journal

PHYSICAL REVIEW E

DOI

https://doi.org/10.1103/physreve.67.056601

Collections

Department of Physics, Article

Suggestions

OpenMETU
Core

Exciton related nonlinear optical properties of a spherical quantum dot Aksahin, E.; Unal, V. Ustoglu; Tomak, Mehmet (2015-11-01) The nonlinear optical properties of an exciton in a spherical quantum dot (QD) is studied analytically. The nonlinear optical coefficients are calculated within the density matrix formalism. The electronic problem is solved within the effective mass approximation. The contributions from the competing effects of the confinement, the Coulomb interaction, and the applied electric field are calculated and compared with each other. We have made no assumptions about the strength of the confinement. We concentrate...
Nonlinear optical properties of a Poschl-Teller quantum well under electric and magnetic fields AYTEKİN, ÖZLEM; Turgut, Sadi; Tomak, Mehmet (2012-04-01) The nonlinear optical properties of a Poschl-Teller Quantum well (PTQW) under electric and magnetic fields are studied. The salient feature of this potential is its flexibility. It can be made asymmetrical by a proper choice of its two parameters. Optical rectification, second and third-harmonic generation susceptibilities are calculated using the density matrix formalism. We study the effects of quantum confinement, electric and magnetic fields on all of these optical coefficients.
Excitonic effects on the nonlinear optical properties of small quantum dots KARABULUT, İBRAHİM; Safak, H.; Tomak, Mehmet (IOP Publishing, 2008-08-07) The excitonic effects on the nonlinear optical properties of small quantum dots with a semiparabolic confining potential are studied under the density matrix formalism. First, within the framework of the strong confinement approximation, we present the excitonic states and then calculate the excitonic effects on the nonlinear optical properties, such as second harmonic generation, third harmonic generation, nonlinear absorption coefficient and refractive index changes. We find the explicit analytical expres...
Nonlinear optical properties of a Woods-Saxon quantum dot under an electric field AYTEKİN, ÖZLEM; Turgut, Sadi; Unal, V. Ustoglu; Aksahin, E.; Tomak, Mehmet (Elsevier BV, 2013-12-01) A theoretical study of the effect of the confining potential on the nonlinear optical properties of two dimensional quantum dots is performed. A three-parameter Woods-Saxon potential is used within the density matrix formalism. The control of confinement by three parameters and an applied electric field gives one quite an advantage in studying their effects on the nonlinear properties. The coefficients investigated include the optical rectification, second and third-harmonic generation and the change in the...
OPTICAL SYSTEM DESIGN, INTEGRATION AND TESTING OF A 2D SCANNING LIDAR Cerit, Kübra; Bek, Alpan; Department of Physics (2022-1-20) In this thesis, optical system design, integration and testing of a compact LIDAR system with 270 degree field-of-view that based on time of flight principle is developed by Rekrom Optoelectronics. This system can identify objects and measure distances up to 100 m away. LIDAR has become a much needed and used technology in various fields. The most important of these areas are robotic systems, autonomous vehicles and unmanned aerial, land and sea platforms navigation and environmental awareness. The main r...

Citation Formats

S. Baskal and Y. Kim, “Lens optics as an optical computer for group contractions,” PHYSICAL REVIEW E, pp. 0–0, 2003, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64793.