Characterizing output beams for lasers that use high-magnification unstable resonators

Abstract

Laser beams generated from high-magnification on-axis unstable resonators by use of hard-edged optics typically have a doughnut-shaped distribution in the near field (i.e., a flat-top profile with a hole in the middle for an axially coupled beam). We derive analytical expressions describing this distribution by using the flattened Gaussian beams concept. The superposition of two flattened Gaussian beams whose flatness and steepness of edges are controlled by defined parameters (i.e., the beam width and the order) is used to analyze the output beam intensity along the propagation axis. Finally, experimental measurements of beam propagation from a copper-vapor laser fitted with a high-magnification unstable resonator show excellent agreement with theoretical predictions.

Beam propagation analysis in unstable laser resonators (ULR): low to high magnification

“…[l]. The superposition ofa standard FGB model, as described by Eq.l, with an additional FGB (called the constructed FGB), creates a central shadow and gives an expression for a Flattened Gaussian Beam with a Hole in the Middle (FGBHM) [2]. In the near-field when z=0, the constructed FGB for which the amplitude distribution and steepness can be varied from that of Eq.1, is written as:…”

“…where M, the beam order ofthe constructed FGB, controls the steepness ofthe shoulders ofthe hole, and i is a variable constant which enables various spatial intensity distributions to be achieved [2].…”

“…al. [2]. By changing a variable constant called ii, various beam profiles can be developed and by using the propagating formula, at different transverse planes, the intensity profile at any arbitrary plane can be predicted.…”

Fractional Fourier transform for annular flat-topped beams

“…One of the most typical examples is that the copper-vapor lasers output intensity profile is a flat-topped distribution with an axial shadow, when the onaxis unstable resonators and injection-seeded copper-vapor laser oscillators are used [13] . To model the beam with a doughnut-shaped profile in the near field, Saghafi et al [14] proposed an analytical expression for it in the cylindrical coordinate system, which was expressed as a superposition of two flattopped Gaussian beams and was extremely in good agreement with the experimental result.In this paper, following Tovar's [15] research, where a multiGaussian beam shape was proposed as a model for laser beam profile that has a nearly flat top, we develop an analytical expression in the cylindrical coordinate system to describe the beam with a nearly flat-topped profile and an on-axial shadow simultaneously, namely, the annular flat-topped beam. The FRFT for an annular flat-topped beam is studied.…”

“…One of the most typical examples is that the copper-vapor lasers output intensity profile is a flat-topped distribution with an axial shadow, when the onaxis unstable resonators and injection-seeded copper-vapor laser oscillators are used [13] . To model the beam with a doughnut-shaped profile in the near field, Saghafi et al [14] proposed an analytical expression for it in the cylindrical coordinate system, which was expressed as a superposition of two flattopped Gaussian beams and was extremely in good agreement with the experimental result.…”