Focusing of Radially Polarized Bessel-Gauss Beams

Radially polarized Bessel-Gauss beams exhibit significant application value in optical micromanipulation, laser processing, and high-resolution imaging due to their unique focusing properties. By combining radial polarization states with Bessel-Gauss mode characteristics, these beams generate distinctive intensity distributions and electric field components in the focal region. Code implementation typically involves calculating vectorial diffraction integrals using Fourier optics methods, where MATLAB's fft2 function can efficiently handle the propagation calculations.

To achieve efficient focusing, binary optical elements (such as phase plates) are commonly employed to manipulate wavefront phase, combined with high numerical aperture (NA) objectives to enhance focusing capability. High-NA objectives significantly reduce focal spot size, while binary optical elements precisely control phase distribution to optimize the focal field. Algorithm design often incorporates Zernike polynomial expansions for phase profile generation, with ring width and phase step parameters programmable via phase retrieval optimization routines.

The electric field of radially polarized light develops strong longitudinal components near the focal point, making it excellent for nanoscale light-matter interactions. The non-diffracting property of Bessel-Gauss beams helps maintain beam shape during propagation, further improving focusing stability and controllability. Numerical simulations typically utilize Richards-Wolf vectorial diffraction theory, implemented through Hankel transform algorithms that maintain computational efficiency while handling azimuthal symmetry.

By optimizing design parameters of binary phase elements, such as zone width and phase steps, focal spot size and energy distribution can be tailored to meet various application requirements. This technology opens new possibilities for precision optical systems, particularly in applications requiring subwavelength-scale control. Parameter optimization often employs genetic algorithms or gradient descent methods, with performance metrics including Strehl ratio and focal depth evaluation through computational electromagnetic solvers.