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Optical Cavities: Free-Space Laser Resonators
Published in Chunlei Guo, Subhash Chandra Singh, Handbook of Laser Technology and Applications, 2021
The next section of this chapter reviews the optics of Gaussian light beams. These beams are solutions of the wave equation for propagation in a homogeneous, isotropic medium and are the fundamental modes of geometrically stable open resonators. The diffraction of Gaussian beams can be treated directly with analytical methods, simplifying calculations of laser-beam propagation and mode-matching between resonators. The minimum diffraction of a Gaussian beam is used to define the diffraction-limited beam quality factor M2 of one. The fundamental mode of a stable two-mirror cavity can be determined by matching the Gaussian-beam wavefront radii to the mirror radii. More complicated cavities are typically analysed with ABCD or ray-transfer-matrix techniques. Such analysis and application of the ray transfer matrices to the propagation of Gaussian beams are discussed here. A description of higher-order transverse modes of stable resonators follows and is used for a further description of beam quality.
Diffraction of Gaussian Beams
Published in Glen D. Gillen, Katharina Gillen, Shekhar Guha, Light Propagation in Linear Optical Media, 2017
Glen D. Gillen, Katharina Gillen, Shekhar Guha
Figures 10.9 and 10.10, and Eqs. (10.28) and (10.29), can be used to predict the theoretical maximum intensity and theoretical minimum beam waist for a clipped focused Gaussian beam. For example, if an unperturbed Gaussian beam having a wavelength of 780 nm and a minimum spot size of 5µm passes through an aperture located 1 cm before the focal spot with a diameter of 1 mm (a/ωa = 1), then the new theoretical maximum intensity would be 40% of that of a diffraction-limited Gaussian beam, and the new theoretical beam waist would be 46% wider than that of an unperturbed beam. If the aperture diameter is increased to 1.5 mm, then the theoretical maximum intensity would double to 80%, and the minimum beam waist would shrink to only 12.4% wider than that of a diffraction-limited beam.
Light Sources
Published in Toru Yoshizawa, Handbook of Optical Metrology, 2015
At z = zR, Equation 1.71 yields w(z)=2w0. Hence, the Rayleigh range is the distance at which the cross-sectional area of the Gaussian beam doubles. In addition, the Rayleigh range is the distance at which the curvature of the beam wavefront is minimum. As the beam propagates along z, the curvature of the beam wavefront varies with z according to R(z)=z+zR2z
Analysis of the influence of atmospheric turbulence on modulating retro-reflector optical communication
Published in Journal of Modern Optics, 2022
Mengtong Xie, Jingyuan Wang, Jianhua Li, Zhiyong Xu, Zhang Li, Jiyong Zhao, Yang Su, Zhou Hua, Ailin Qi, Huiping Shen
The first step is to model the optical source. The gaussian beam is a relatively common model which presents a Gaussian distribution in a plane perpendicular to the direction of propagation. The distribution of Gaussian beam in uniform media can be expressed as [15] where where is the lateral displacement from the transmitter and retro-reflector axis, is the phase difference, is the wave number, is the beam radius, is the beam waist radius, is the radius of curvature, and is the refractive index of the medium (Figure 2).
M2 factor of conically refracted Gaussian beams
Published in Journal of Modern Optics, 2022
Erko Jalviste, Viktor Palm, Viktor Peet
Since the pioneering proposal by A. E. Siegman [1,2], the factor or the beam propagation factor has become a widely used practical parameter characterizing the quality of laser beams [3–5]. This factor is defined as the product of the waist radius and the divergence angle of a beam divided by the analogous product for an ideal Gaussian beam. Accordingly, an ideal Gaussian beam has and the least possible divergence angle for a given waist size. The ISO standard 11146 describes the recommended procedure for calculation the second-moment radii and the value [6].