This study proposed a method for calculating any arbitrarily linear polarization paraxial optical field propagation in
Gradient-index (GRIN) lens. The proposed method uses multiple thin-phase sheets to approximate a GRIN lens. This
study also compares the proposed method with the other well-known method. That is, using a single lens equivalent
optical system of Fractional Fourier transform (FrFT) to simulate a GRIN lens. The evolution in GRIN lenses of many
special beams have been calculated by the FRFT-method. This study use both methods to calculate the Helmholtz-Gauss
beam evolution in GRIN lenses of a small and a high gradient constant, respectively. Numerical results shows that the
differences between two calculation methods appeared while the GRIN lens of a high gradient constant. This study
provides an alternative approach could calculate the linearly polarized field evolution in GRIN lenses with higher
precision, which will be useful to the optical design of GRIN lens systems.
This study drafts simulation code to model the optical filed oscillation of end-pumped solid-state lasers, and proposed a
kind of axicon-based stable laser resonator. Using numerical explorations, we find a systematic method to the selective
excitation of nearly non-diffraction Mathieu-Gauss beams in end-pumped solid-state lasers with the proposed resonator.