Vectorial Diffraction Model for Focusing a Gaussian Laser Beam by a Parabolic Metallic Mirror
Abstract
Vectorial Diffraction Model for Focusing a Gaussian Laser Beam by a Parabolic Metallic Mirror
Incoming article date: 13.11.2025A vectorial diffraction model is presented for the focusing of a Gaussian laser beam with a wavelength of 800 nm by a parabolic metallic mirror with a diameter of 15 mm and a focal length of 150 mm. The model is based on a rigorous calculation of the reflected electromagnetic field using s- and p-polarization basis functions, complex Fresnel coefficients, and the Kirchhoff–Rayleigh surface integral. The reflective coating is characterized by a complex refractive index n = 0.145 + 4.5i, corresponding to silver in the near-infrared spectral range. The incident beam has a waist radius of 3 mm at the mirror’s vertex plane. The field distribution in the focal plane is numerically computed on a 300×300 grid over a ±30 μm region. Focus quality is evaluated using three criteria: total intensity, radial intensity distribution, and the full width at half maximum (FWHM) of the focal spot. A focal spot with FWHM ≈ 8.56 μm is obtained, in close agreement with the theoretical diffraction-limited estimate. The results demonstrate that accounting for the vectorial nature of the field and the dissipative properties of the metal enables accurate prediction of polarization distortions and energy losses in practical mirror-based focusing systems.
Keywords: vectorial diffraction model, parabolic metallic mirror, Gaussian laser beam, Fresnel coefficients, complex refractive index