Twisting of three-dimensional Hermite—Gaussian beams

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

“…'y is related with the focal length of the optical elements of the transformation optics (sec. [4][5].…”

“…It was recently shown that for angle of rotations differing from 45° or input beams with different Rayleigh lengths in both transverse directions the output field distribution in the plane of the waist is characterized by the product of a Hermite-polynomial with a complex argument and a gaussian distribution. 4 In this paper the propagation behavior of the complex Hermite-Gaussian beams is investigated which in general differs from the propagation of standard Hermite-Gaussian beams. Beside the transverse scaling the structure of the intensity profiles changes with the Additionally to this propagation behavior of complex (separable) HermiteGaussian modes the beams generated by the mode converter for input beams with different Rayleigh lengths in the transverse directions or input beams with a tilt relative to the axis of the mode converter differing from 45° show a coupling of the transverse directions.…”

Tailored UV-laser source for fluorescence spectroscopy of biomolecules

“…Thus the total length, L, is then twisted Hermite-Gaussian beam with complex arguments [15]. The nearly symmetric beam was focused with a lens, f 1 , to a beam radius of 1 mm (e À2 intensity) inside the laser medium.…”

“…In optical beam analysis of laser resonators the Hermite-Gaussian mode functions are commonly used to describe propagation through the optical system, since in real lasers the beam is usually distorted by optical elements in the cavity, and a rectangular coordinate system is preferred because of its ability to describe both astigmatic and stigmatic beams [13]. It has been proven, both theoretically and experimentally, that astigmatic beams mathematically described by Hermite-Gaussian mode functions, such as the output from a broad-strip diode-laser, can be transformed into Laguerre-Gaussian beams by using two cylindrical lenses with the same focal length [14,15]. This, however, can only be achieved when predefined conditions are met.…”

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.…”