---

Investigation of the Transverse mode of a laser with variation of the Hermite and Laguerre polynomia

Corresponding Author : R. A. Jewel (rausanatik@live.com)

Authors : R. A. Jewel (rausanatik@live.com), Y. Haque (yasmeen@sust.edu), S. K. Das (skdas-phy@sust.edu)

Keywords : Gaussian beam, Cartesian symmetry, Transverse mode

Abstract :

This paper aims at explaining the operation of Hermite and Laguerre polynomials on the Gaussian beam in the case of higher order laser modes. The parameters of Hermite polynomial explain the Hermite–Gaussian laser beam in the Cartesian symmetry and that of Laguerre polynomial explains Laguerre–Gaussian laser beam in the cylindrical symmetry. In this paper it is shown that the Gaussian beam changes its shape as the parameters of the polynomials are changed and the change is explained. There is derivation of the two types of beam mode equations but how the beams develop as they propagate is illustrated in this paper. It gives the calculation of the energy and intensity of the laser just viewing the type of mode on the screen.  

Published on June 30th, 2010 in Volume 12, Issue1, Applied Sciences and Technology