Generation Of Hermite Research Articles

Generation of Hermite – Gaussian modes of high-power femtosecond laser radiation using binary-phase diffractive optical elements

We present the results of experiments on generation of Hermite – Gaussian modes up to the third order inclusive using binary-phase diffractive optical elements (DOEs) illuminated by subterawatt femtosecond laser pulses. We perform a compariosn of the mode formation using DOEs designed by the kinoform method and the fractional coding technique, when the DOEs are illuminated by both femtosecond radiation and cw laser radiation at close wavelengths.

The role of Jacobi polynomials in the theory of Hermite and Laguerre 2D polynomials

Using an alternative definition of usual Hermite polynomials, two problems in the theory of general Hermite and Laguerre 2D polynomials can be separated with advantage for the further treatment: the introduction of a general 2D matrix in the linear transformation of powers of the components of a 2D vector and the generation of Hermite (or Laguerre) polynomials by applying an integral operator to these powers. The Jacobi polynomials appear in the finite-dimensional irreducible representations of the two-dimensional general linear group GL(2,C).