Unrestricted Diffraction Characteristics Of Non-paraxial LG₀₀ Mode And LG₁₀ Mode Gaussian Beams

The analysis on the unrestricted diffraction of non-paraxial Gaussian beams will provide theoretical basis for the practical application.This paper analyzes the unrestricted diffraction characteristics of non-paraxial LGOO mode and LG10 mode Gaussian beams,including the following two aspects:Based on the first solution of scalar Rayleigh-Sommerfeld diffraction integral formula and the radial electric field of the non-paraxial LGOO mode and LG10 mode Gaussian beams in the waist,the azimuthal electric field amplitude distributions of the unrestricted diffraction far-field are given.The characteristics of the azimuthal electric field amplitude distributions of the unrestricted diffraction far-field of the non-paraxial LGOO mode and LG10 mode Gaussian beams in the waist and the azimuthal electric field amplitude distributions of the non-paraxial LG00 mode and LG10 mode Gaussian beams in the far-field are analyzed.According to the definition and formula of the power in the bucket,the power in the bucket of the azimuthal electric field amplitude distributions of the unrestricted diffraction far-field of the non-paraxial LG00 mode and LG10 mode Gaussian beams in the waist and the azimuthal electric field amplitude distributions of the non-paraxial LGOO mode and LG10 mode Gaussian beams in the far-field is calculated.The sine value of far-field divergence half-angle is calculated when the power in the bucket within it of the azimuthal electric field of the unrestricted diffraction far-field of the non-paraxial LGOO mode Gaussian beam in the waist and the azimuthal electric field of the non-paraxial LGOO mode Gaussian beam in the far-field is 86.47%.The sine value of far-field divergence half-angle is calculated when the power in the bucket within it of the azimuthal electric field of the unrestricted diffraction far-field of the non-paraxial LG10 mode Gaussian beam in the waist and the azimuthal electric field of the non-paraxial LG10 mode Gaussian beam in the far-field is 90.84%.Based on the scalar Debye diffraction integral formula and the azimuthal electric field of the non-paraxial LG00 mode and LG10 mode Gaussian beams in the far-field,the radial electric field amplitude distributions at the center of the wavefront curvature of the unrestricted diffraction are given.The similarities and differences between the radial electric field amplitude distributions at the center of the wavefront curvature of the unrestricted diffraction of the non-paraxial LG00 mode and LG10 mode Gaussian beams in the far-field and the radial electric field amplitude distributions of the non-paraxial LGOO mode and LG10 mode Gaussian beams in the waist are analyzed by relative errors.The spot radiu is calculated when the power in the bucket within it of the radial electric field at the center of the wavefront curvature of the unrestricted diffraction of the non-paraxial LGOO mode Gaussian beam in the far-field and the radial electric field of the non-paraxial LGOO mode Gaussian beam in the waist is 86.47%.The spot radiu is calculated when the power in the bucket within it of the radial electric field at the center of the wavefront curvature of the nrestricted diffraction of the non-paraxial LG10 mode Gaussian beam in the far-field and the radial electric field of the non-paraxial LG10 mode Gaussian beam in the waist is 90.84%.And the beam propagation factor of non-paraxial LG00 mode and LG10 mode Gaussian beams is calculated.