Focusing properties and focal shift of a vortex cosine-hyperbolic Gaussian beam

In this paper, we investigate the focusing properties of a vortex-cosh-Gaussian (vChG) beam passing through a converging thin lens. Based on the Huygens-Fresnel diffraction integral, we derived the analytical propagation equation as well as the beam width expression of a focused vChGB. It is shown that the focusing properties including the focal shift of the focused vChGB are crucially dependent on the incident beam parameters namely the decentered parameter and the topological charge in addition to the Gaussian Fresnel number\({N_F}\). From typical numerical examples, it is found that the focused vChGB is transformed into a multi-lobes structure shape at the real focus plane, and the principal maximum intensity of the beam is located away from the axis. The amount of focal shift, which is determined from the minimum spot size criterion, is strongly dependent on the Fresnel number, the decentered parameter and the vortex charge m. The obtained results may be useful for the applications of the vChGBs in beam shaping and beam focusing.

Focusing properties and focal shift of vortex Hermite-cosh- Gaussian beams

In this work, we investigate the focusing properties of a vortex Hermite-cosh-Gaussian beam (vHChGB) passing through a converging lens system. The analytical propagation equation as well as the beam width expression of a focused vHChGB is derived based on the Huygens-Fresnel diffraction principle. From the obtained formulae, the effects of the Gaussian Fresnel number NF and the beam parameters on the structure of the light intensity distribution and the beam spot size in the focal region are analyzed numerically. It is shown that the focal shift, which is determined from the minimum beam spot width criterion, is affected strongly by the change of the Fresnel number, the parameter b, and it is slightly altered by the vortex charge M and nearly insensitive to the beam order n. For a fixed value of NF, the focal shift is smaller when the parameter b or the vortex charge M is larger. The focal shift decreases monotonously with the increase of Fresnel number until it vanishes asymptotically for large NF. The obtained results may be useful for the applications of the vHChGBs in beam shaping and beam focusing.

INTRACAVITY LARGE-SCALE HETEROGENEITY AND THEIR INFLUENCE ON RADIATION PARAMETERS OF POWERFUL LASERS

Large‑scale inhomogeneities occur in the optical resonator of a high‑power laser due to uneven redistribution of heat and errors in the alignment of the circuit. Such inhomogeneities can significantly affect the characteristics of laser radiation. The paper analyzes the effect of large‑scale phase inhomogeneities associated with the separation and thermal deformation of unstable resonator mirrors on the parameters of the laser radiation – the power and angular divergence. The numerical simulation of the unstable resonator in the di‑fractional approximation is carried out, on the basis of which the quantitative effect of phase aberrations such as optical wedge (separation) and spherical lens (thermodeformation) on the power and divergence of laser radiation depending on the main characteristics of the unstable resonator‑the Fresnel number and the magnification coefficient is determined. The results of experimental studies of the effect of separation on the radiation parameters of a 100‑kilowatt CO2 gas‑dynamic laser are presented. The results of the work should be taken into account in the structural‑parametric optimization of the resonator.

Numerical investigation of the influence of wavefront distortion on the laser near-field characteristics

The effect of the initial phase distortion of the laser on near-field transmission characteristics in free space is investigated both numerically and theoretically. It is demonstrated and proposed that the near-field modulation and fluence contrast of the output laser beam are changing with the increase of both spatial low- and high-frequency wavefront distortion. The simulation results show that in order to ensure the beam quality in propagation, the Fresnel number should be controlled not <50 generally and the wavefront distortion should also be minimized by controlling both low- and high-frequency phase coefficient not larger than 0.6.

Changes in the Beam Parameters of Partially Coherent Sinh-Gaussian Beams after Passage through an Astigmatic Lens

Based on the propagation law of partially coherent beams, the analytical expression of the beam width, waist positions and the far-field divergence angle of partially coherent sinh-Gaussian (ShG) beams through an astigmatic lens were derived. The effect of astigmatism and spatial coherence parameter on the beam parameters was mainly analyzed. It is found that the beam width depends on the astigmatic coefficient, spatial coherence parameter, decentered parameter, fresnel number and propagation distance in general. The astigmatism results in a difference between the beam widths, waist positions and far-field divergence angles in thexandydirections.