General Astigmatic Beam Research Articles

Quasi-optical design and analysis of a remote steering launcher for CFETR ECRH system

In order to optimize the operational safety and reliability of the upper launcher for the CFETR ECRH system, a design of the launcher for NTM control based on the remote steering concept is currently being carried out for comparison with the front steering equivalent. This paper presents the layout design and analysis of the quasi-optical system in the remote steering launcher. A 3D visual quasi-optical design tool has been developed for the quasi-optical system, which can parameterize modeling, perform general astigmatic beam calculation and show the accurate beam propagation path in the upper port. Three identical sets of quasi-optical modules are arranged in the launcher, and each one consists of two fixed double-curvature focusing mirrors, which focus and reflect the steering beams (−12°–12°) from two square corrugated waveguides. The beam characteristics at the resonance layer are described, and the average beam radius is < 100 mm. The peak head loads on the surfaces of the two fixed mirrors are 1.63 MW/m2 and 1.52 MW/m2. The position and size of the beam channel in the blanket are obtained, and the opening apertures on the launcher-facing and plasma-facing sides of the blanket module are 0.54 m2 and 0.4 m2, respectively.

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.

S-shaped non-paraxial corrections to general astigmatic beams.

Non-paraxial perturbation wave equations are solved for general astigmatic Gaussian beams for the first time, to the best of our knowledge, in the angular spectrum representation by taking into account generic boundary conditions. Expressions for second-order corrections are derived and exemplified with an optical cavity made of two cylindrical mirrors. Non-paraxial corrections can lead, depending on the choice of boundary conditions, to a transverse S-shaped beam mode, which has been qualitatively been observed in a highly divergent non-planar four-mirror cavity.

Measurement of the M2 beam propagation factor using a focus-tunable liquid lens

We demonstrate motion-free beam quality M² measurements of stigmatic, simple astigmatic, and general astigmatic (twisted) beams using only a focus-tunable liquid lens and a CCD camera. We extend the variable-focus technique to the characterization of general astigmatic beams by measuring the 10 second-order moments of the power density distribution for the twisted beam produced by passage through multimode optical fiber. Our method measures the same M² values as the traditional variable-distance method for a wide range of laser beam sources, including nearly TEM(00) (M²≈1) and general astigmatic multimode beams (M²≈8). The method is simple and compact, with no moving parts or complex apparatus and measurement precision comparable to the standard variable-distance method.

General Astigmatic Beam Propagation in Complex Quasi-Optical Launchers: Application to the ITER ECRH Remote Steering Upper Launcher

Launching systems that use in sequence more than one mirror to direct and focus electron cyclotron (EC) waves with a sufficient steering capability in relevant absorption regions of fusion plasmas may produce general astigmatic beams. The double curvature of a generic reflecting surface, even induced by deformation effects in quasi-optical systems that handle high power, is an additional source of general astigmatism. Describing the propagation of general astigmatic Gaussian beams is a necessary step in the optimization phase of a complex EC resonance heating (ECRH) launcher, since simple astigmatism treatment does not reproduce the main feature of these beams, whose spot and phase ellipse orientation changes with propagation even in free space. The correct orientation for both spot ellipse and phase ellipse is one of the input key parameters to perform realistic calculations with beam-tracing codes, which aim to characterize a launching system in terms of localized heating and current drive efficiency. In this work we describe the influence of double-curvature effects and deformations on beam propagation in terms of beam dimensions and directions. In particular, we present an application of the theory of general astigmatic Gaussian beam propagation in vacuum to the case of the remote steering option for the ITER ECRH upper launcher. In this option beams are found to be strongly astigmatic, with a major/minor axis ratio in relevant absorption regions ranging from 2.3 to 4.4 in the cases examined. Furthermore, the major axis of the resulting spot ellipses presents an orientation angle variation (from the last mirror to the expected absorption regions) ranging from 9.1 to 22.8 deg in the cases investigated. The final orientation is close to a vertical direction with respect to the equatorial plane of ITER.

Twisting of three-dimensional Hermite—Gaussian beams

The mode converter first applied by Tamm and Weiss and generalized by Allen and co-workers can be used to transform any general astigmatic beam into a stigmatic beam with twist. For the special case of three dimensional Hermite—Gaussian beams the transformed beams are twisted Hermite—Gaussian beams with complex arguments. Only if a set of conditions is fulfilled are the transformed beams Laguerre—Gaussian beams. The influence of the input beam parameters on the output beam is discussed.

Determination of the ten second order intensity moments

The general astigmatic beam can be characterized by its ten second order moments in first order approach. Most intensity moments, except the beam twist, can be determined by measuring the intensity in a reasonable number of positions around the waist of the beam. The beam twist is determined by applying a rotated cylindrical lens. The ten intensity moments of two kinds of astigmatic beam were determined: a simple astigmatic TEM 8,0 Hermite–Gaussian beam and a twisted beam generated from the TEM 8,0 mode. The experimental results were compared with the theoretical calculations and demonstrate that the ten second order moments of a beam can be determined in a rather simple way.

Measurement of all ten second-order moments of an astigmatic beam by the use of rotating simple astigmatic (anamorphic) optics

The propagation of any general astigmatic laser beam through any paraxial optical system can be characterized to second order by a 4 × 4 matrix of second moments in the transverse spatial and angular coordinates, with this matrix having at most ten independent elements. We show how to interpret the two existing beam invariants that contain these elements in terms of an overall beam quality factor Meff4 and an intrinsic antigmatism factor a. We describe a general procedure for determining all ten parameters for any arbitrary beam by measuring only second-order moments of the beam irradiance in a single transversal plane after the beam has passed through at most four simple astigmatic optical systems. A number of such systems containing, in particular, only one or two rotating cylindrical lenses and a CCD camera are proposed and analyzed in more detail.

Invariance properties of general astigmatic beams through first-order optical systems

With a new mathematical formulation expressed in terms of the direct product of matrices, the propagation laws for the first-, second-, third-, and fourth-order moments of a general astigmatic beam are derived. It is emphasized that the possibility of finding invariants for propagation through linear optical systems results from the symplectic structure of optical phase space. Invariant quantities for the propagation of general astigmatic beams are defined.

Gaussian Light Beams with General Astigmatism

This paper considers the propagation and diffraction of coherent light beams through nonorthogonal optical systems such as sequences of astigmatic lenses oriented at oblique angles to each other. The fundamental (gaussian) mode has elliptical light spots in each beam cross section and ellipsoidal (or hyperboloidal) wavefronts near the axis. It is found that the orientation of the light spot differs from that of the wavefront, and changes continuously by as much as pi radians as the beam propagates through free space. A theory of these general astigmatic beams is given and simple experimental observations are described. The coupling factor between two such beams is also given.