Combined laser variosystems paraxial design for longitudinal movement of a Gaussian beam waist

Abstract

Optical variosystems that form the required diameter of the Gaussian beam waist and perform its smooth longitudinal movement with a constant diameter for laser technologies, processing materials, moving microobjects, etc., are considered. A combined method based on a movable tunable-focus lens for changing the optical characteristics of laser variosystems is proposed. The features and fundamental differences between the laws of transformation of Gaussian beams by optical systems of different structures for the dimensional synthesis of laser variosystems are discussed. Based on these laws and the theory of laser optics, a method for the dimensional synthesis of one- and two-component laser variosystems is developed, an algorithm for their automated synthesis, and an example of calculation are given.

Reconstructing the Spatial Parameters of a Laser Beam Using the Transport-of-Intensity Equation

“…The dependences of the laser beam radius w(z) and the radius of curvature of its wavefront R(z) on the longitudinal coordinate z are described by the following equations [22]:…”

The optical refractometry using transport-of-intensity equation

“…Then, at the second stage, the wavefront radius of curvature R (z 2 ) is calculated by approximating the obtained phase values ϕ (z 2 ) of the laser beam with a hyperbolic dependence according to the following equations [18,19]: where z R is a Rayleigh length, w (z) is the laser beam radius at the level 1/e 2 and w 0 denotes the beam waist radius. At the final stage, based on the reconstructed spatial characteristics of the laser beam that passed through the optical lens, the refractive index of the lens is determined.…”

“…Consider a plano-convex lens with a known radius of curvature R l and an unknown focal length f ′ as an example. According to [19], there is a one-to-one relationship between the spatial parameters of the laser beam and the focal length of the plano-convex lens:…”