Transformation of Hermite-Gaussian beams into complex Hermite-Gaussian and Laguerre-Gaussian beams

Abstract

Hermite-Gaussian, Laguerre-Gaussian and complex Hermite-Gaussian modes are solutions of the paraxial wave equation. Using an astigmatic optical system each type of beams can be transformed into the others. This allows a generation of complex ilermite-Gaussian modes with twist whose propagation behaviour is investigated in detail.

Matrix factorization of the mode converter

“…Eppich and Laabs et al showed [1,2] that any three-dimensional astigmatic Hermite-Gaussian beam can be transformed into a symmetric Lagueree-Gaussian beam with twist by using a mode converter consisting of three cylindrical lenses. The theoretical predication was confirmed by the experiments of TEM m0 -mode Nd:YAG lasers and diode laser stacks [1][2][3][4]. It was also found [4] that the threecylindrical-lens mode converter is equivalent to a two lens optics, or a single thick cylindrical lens.…”

“…The theoretical predication was confirmed by the experiments of TEM m0 -mode Nd:YAG lasers and diode laser stacks [1][2][3][4]. It was also found [4] that the threecylindrical-lens mode converter is equivalent to a two lens optics, or a single thick cylindrical lens. Therefore, an interesting question arises: Can the transfer matrix of the mode converter be factorized according to a certain rule?…”

Reshaping a multimode laser beam into a constructed Gaussian beam for generating a thin light sheet

“…where r and η are the cylindrical coordinates in the near and far field and the rest of the functions and parameters are as described before. Furthermore, mode converters can act like a bridge between standard higher order modes and twisted modes with a complex argument . For many laser applications, a beam with a uniform intensity profile (ie, uniform energy density over a defined cross section) is crucial.…”

Tailored UV-laser source for fluorescence spectroscopy of biomolecules

“…In our set-up, instead of using two cylindrical lenses a thick cylindrical lens is used as a mode converter. The extension between the two cylindrical surfaces (called the center plate) is determined by [16] t ¼ 2r…”