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The acceleration of electrons by using a Bessel-Gaussian (BG) beam in vacuum is studied. It is shown that the axial electric field of a linearly or circularly polarized BG beam of order n = 1 can be used to accelerate electrons. The general features of the acceleration of electrons by using a linearly or circularly polarized BG beam, such as the transversal and axial electric-field components, phase velocity, slippage distance, accelerating potential, and energy gain etc., are analyzed.

The focal switch of cosine-Gaussian (CsG) beams passing through a system with the aperture and lens separated is studied analytically and numerically. It is shown that the focal switch of CsG beams can appear not only for the apertured case, but also for the unapertured case. The necessary condition for the focal switch is that truncation parameter α > αc and the beam parameter β > βc, αc, βc being the corresponding critical values. There exists a maximum of the relative transition height Δzsw as α varies, and Δzsw increases with increasing β and decreasing Nw. The normalized axial intensity minimum Imin / Imax decreases with an increase of α and β, and Imin / Imax remains unchanged as Nw varies.

By using the second-order moment of the power density, the beam width, far-field divergence angle and M2 factor of nonparaxial truncated flattened Gaussian (FG) beams are derived analytically. It is shown that the M2 factor of nonparaxial truncated FG beams depends not only on the truncation parameter δ and beam order N, but also on the initial waist-width to wavelength ratio w0/λ. The far-field divergence angle approaches an asymptotic value of θmax=63.435° when the truncation parameter δ → 0. For the special cases of N = 0 and δ → ∞ our results reduce to those of nonparaxial truncated Gaussian beams and nonparaxial untruncated FG beams, respectively.

Based on the Rayleigh–Sommerfeld diffraction integral, the diffraction of converging spherical waves at a circular aperture is studied in a general case. The expression for the intensity near focus of strongly converging spherical diffracted waves is derived, which reduces to the well known result expressed in terms of Lommel functions for the case of weakly converging spherical diffracted waves. The intensity distributions at the geometrical focal plane and along the axis are given. Numerical comparative examples are presented to illustrate the more general applicability of our results.

By using the methods of the matrix decomposition and expansion of the hard-edged aperture function into a finite sum of complex Gaussian functions, the recurrence propagation expressions for a flattened Gaussian beam (FGB) through multi-apertured optical imaging systems of B = 0 are derived and illustrated with numerical examples. Comparisons with the straightforward numerical integration of the Collins formula and with the previous work are made. It is shown that the main advantages of our methods and results are the more accuracy and great reduction of computer time.

The propagation properties of decentered twisted Gaussian Schell-model (DTGSM) beams passing through a misaligned first-order optical system are studied. The explicit expressions for the cross-spectral density function and Wigner distribution function of the output beam are derived, which retain their form unchanged. It is shown that the DTGSM beams preserve their closed property. The second-order moments matrix and the Wigner distribution function evolve with the usual laws, whereas the first-order moments matrix varies, as if a ray passes through such system. The propagation of DTGSM beams through an aligned first-order optical system is treated as the limiting case that corresponds to the vanishing misalignment parameters.

By using the Rayleigh diffraction integral formula, a far-field asymptotic solution of the wave equation is found, which represents non-paraxial elliptical Gaussian beams. The basic properties of such beams are studied, and a comparison with the previous work is also made.

Based on the Collins formula and irradiance moments definition, the propagation of the kurtosis parameter of super-Gaussian beams through a spherically aberrated lens is studied. Detailed numerical results are given. It is shown that, as compared with aberration-free super-Gaussian beams, the profile of spherically aberrated super-Gaussian beams can be leptokurtic, mesokurtic or platykurtic, depending on the aberration and propagation distance. The results for the spherically aberrated Gaussian beams can be dealt with as a special case treated in this paper. Finally, the advantage of our method is pointed out.

By using the beam coherence-polarization (BCP) matrix approach, analytical propagation equations of partially polarized Gaussian Schell-model (PGSM) beams through an axis-unsymmetric paraxial optical ABCD system are derived, which enable us to study the propagation-induced polarization changes and irradiance distributions at any propagation distance of PGSM beams through axis-unsymmetric systems within the framework of the paraxial approximation. Detailed numerical results for a PGSM beam passing through a bifocal lens are presented to illustrate the propagation properties of PGSM beams. A comparison with the previous work is also made.

The explicit expressions for the beam propagation factor (M2 factor) and far-field distribution of Bessel-Modulated Gaussian beams with quadratic radial dependence are derived. The results are analyzed with numerical example.

The propagation behavior and M2-factor of truncated cosh-Gaussian (ChG) beams are studied by using the asymptotic approach. Detailed numerical results are given to illustrate the dependence of M2-factor on the beam decentered parameter β, truncation fraction p and power fraction f. Our results are self-consistent and reduce to those of Pare and Belanger [Opt. Commun.123, p. 679 (1996a); Proc. SPIE2870, p. 104 (1996b)]. The advantage of the approach is shown, and the problems introduced by the hard-aperture diffraction and the approach used are discussed.

The method of Gaussian beam ray-equivalent modelling, first proposed by Arnaud, is generalized to the case of general astigmatism. It has been shown that a generally astigmatic Gaussian beam can be properly represented by two complex rays, or equally by four real rays, which are treated by the well-known propagation equation and ray tracing method in geometric optics, and from which the beam parameters are easily obtained. Illustrative numerical examples are given. The equivalence between the complex-ray treatment and the generalized ABCD law is also shown.

Three-dimensional astigmatic resonators, typical examples of which are the resonators bounded by cylindrical-spherical mirrors and cylindrical-cylindrical mirrors oriented at an arbitrary crossed angle, are investigated in detail by using a complex curvature tensor concept and generalized tensor ABCD law. Computerized numerical calculations illustrate some interesting characteristics of these astigmatic resonators.