Decoupling of coherent Gaussian beams with general astigmatism

Twisted elliptical multi-Gaussian Schell-model beams and their propagation properties: comment

The inadequacy of using beam propagation factors Mx2, My2 for general astigmatic beams as those analyzed in the paper J. Opt. Soc. Am. A37, 89 (2020)JOAOD60740-323210.1364/JOSAA.37.000089 is discussed, and the appropriate beam invariants to be considered are presented.

Conservation of extremal ellipticity and analytical expressions for astigmatism and asymmetry in Gaussian beam transformations

A Gaussian beam with initial astigmatism, waist, and M² asymmetry propagates through a simple optical system consisting of a single thin, aberration-free lens. We derive simple analytical expressions for the asymmetry, astigmatism, and ellipticity of the beam after the lens, and show that the maximal ellipticity of the beam is a conserved quantity that is solely dependent on these input parameters. This appears to still hold for general astigmatic Gaussian beams. Our simple, analytical results conveniently determine the trade-off between astigmatism and asymmetry of a laser for a given output maximum ellipticity requirement pre- or post-lenses.

Modeling of the general astigmatic Gaussian beam and its propagation through 3D optical systems

The paper introduces the complete model of the general astigmatic Gaussian beam as the most general case of the Gaussian beam in the fundamental mode. This includes the laws of propagation, reflection, and refraction as well as the equations for extracting from the complex-valued beam description its real-valued parameters, such as the beam spot radii and the radii of curvature of the wavefront. The suggested model is applicable to the case of an oblique incidence of the beam at any 3D surface that can be approximated by the second-order equation at the point of incidence. Thus it can be used in simulations of a large variety of 3D optical systems. The provided experimental validation of the model shows good agreement with simulations.

Optical phase space, Wigner representation, and invariant quality parameters

Wigner's quasi probability and related functional and operator methods of quantum mechanics have recently played an important role in optics. We present an account of some of these developments. The symmetry structures underlying the ray and wave approaches to paraxial optics are explored in some detail, and the manner in which the Wigner phase-space representation captures the merits of both approaches is brought out. A fairly self-contained analysis of the second or intensity moments of general astigmatic partially coherent beams and of their behavior under transmission through astigmatic first-order optical systems is presented. Geometric representations of the intensity moments that render the quality parameters or polynomial invariants manifest are discussed, and the role of the optical uncertainty principle in assigning unbeatable physical bounds for these invariants is stressed. Measurement of the ten intensity moments of an astigmatic partially coherent beam is considered.

Beam propagation (m(2)) measurement made as easy as it gets: the four-cuts method

Tolerance analysis shows that an efficient M(2) measurement plan is a first cut (beam diameter measurement) at 0.5-2.0 Rayleigh ranges to one side of the waist, which is matched by interpolation between second and third cuts to the opposite side. The waist is measured by a fourth cut halfway between the matched diameters, yielding an easy two-parameter curve fit for M(2).

Mode characteristics of twisted resonators composed of two cylindrical mirrors

We examine the optical resonator composed of two astigmatic elements, in a twisted configuration. These cavities have mode cross-sections with principal axes that rotate on propagation. Explicit cavity mode equations are derived for the case of identical mirrors. Such a resonator is appropriate for a solid-state laser that is end-pumped with the output of a laser-diode array brought to a line focus. We present a simple analysis of the significance of rotational misalignment, which effects the pump-to-mode power coupling, beam quality, and cavity stability.