On-axis Gaussian Beam Research Articles

梯度折射率球对在轴高斯波束散射的几何光学近似

梯度折射率球对在轴高斯波束散射的几何光学近似

Gaussian beam diffraction in inhomogeneous and nonlinear media: analytical and numerical solutions by complex geometrical optics

Abstract The method of paraxial complex geometrical optics (CGO) is presented, which describes Gaussian beam diffraction in arbitrary smoothly inhomogeneous media, including lens-like waveguides. By way of an example, the known analytical solution for Gaussian beam diffraction in free space is presented. Paraxial CGO reduces the problem of Gaussian beam diffraction in inhomogeneous media to the system of the first order ordinary differential equations, which can be readily solved numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous media as compared to the numerical methods of wave optics. For the paraxial on-axis Gaussian beam propagation in lens-like waveguide, we compare CGO solutions with numerical results for finite differences beam propagation method (FD-BPM). The CGO method is shown to provide 50-times higher rate of calculation then FD-BPM at comparable accuracy. Besides, paraxial eikonal-based complex geometrical optics is generalized for nonlinear Kerr type medium. This paper presents CGO analytical solutions for cylindrically symmetric Gaussian beam in Kerr type nonlinear medium and effective numerical solutions for the self-focusing effect of Gaussian beam with elliptic cross section. Both analytical and numerical solutions are shown to be in a good agreement with previous results, obtained by other methods.

Electromagnetic scattering by multi-layered spheres in a 2-D Gaussian beam

Based on formula of vector wave functions in spherical and cylindrical coordinates and their transformation relations，a new method to solve beam coefficients of a two dimensions (2-D) on-axis Gaussian beam is provided. An analyzical expansion of beam coefficients is obtained. With the help of generalized Lorentz Mie theory，electromagnetic scattering by multi-layered spheres in a 2-D Gaussian beam is deduced. Distribution of scattering intensity changing with scattering angle are simulated. A comparison of scattering intensity with results of incident plane wave is given.

Paraxial propagation of Gaussian beam through curved transverse parabolic graded-index waveguides

Based on the unitary transformation and the Lie algebra decomposition technology widely used in quantum mechanics, we obtain the analytical propagation kernel of a light field through curved transverse parabolic graded-index (GRIN) waveguides. The results show that, unlike in a straight parabolic graded-index waveguide, the curve of a transverse parabolic GRIN waveguide can result in two new effects during a Gaussian beam propagation: one is a phase shift including a global one and a local one, which result in the direction change of the light beam propagating through such a curved transverse parabolic GRIN waveguide. The other is to transform an on-axis Gaussian beam into a off-axis Gaussian one. In addition, the deviation of the Gaussian beam distribution center from the center of the curved transverse parabolic GRIN waveguide is also calculated.

Scattering of a spheroidal particle illuminated by a Gaussian beam

An approach to expanding a Gaussian beam in terms of the spheroidal wave functions in spheroidal coordinates is presented. The beam-shape coefficients of the Gaussian beam in spheroidal coordinates can be computed conveniently by use of the known expression for beam-shape coefficients, g(n), in spherical coordinates. The unknown expansion coefficients of scattered and internal electromagnetic fields are determined by a system of equations derived from the boundary conditions for continuity of the tangential components of the electric and magnetic vectors across the surface of the spheroid. A solution to the problem of scattering of a Gaussian beam by a homogeneous prolate (or oblate) spheroidal particle is obtained. The numerical values of the expansion coefficients and the scattered intensity distribution for incidence of an on-axis Gaussian beam are given.

Coherent laser addition using binary phase gratings

Binary phase diffraction gratings are shown to couple light coherently from a laser array into a single on-axis beam. The diffraction grating, designed to split a single beam into a specific number of equal intensity diffraction orders, is placed inside the cavity formed by the laser array and a common output mirror. The grating superimposes the light beams from the lasers in the array and produces a far-field pattern with the same divergence as that of a single laser. Six GaAlAs lasers from an antireflection-coated linear array were combined with a coupling efficiency of 68.4%. The far field of the combined GaAlAs lasers consisted of a single on-axis Gaussian beam.