Vortex beams with orbital angular momentum (OAM) have many unique properties compared to other beams, and their spiral wavefront structure and phase changes open up new dimensions for applications such as lithography, optical communication, optical trapping, and quantum entanglement. In recent decades, researchers have been exploring the linear and nonlinear transmission of the Laguerre-Gaussian (LG) vortex beam in media, and the coverage has been continuously expanded, which lays a solid foundation for developing the optical vortex. Most relevant research focuses on analyzing the properties of vortex beams and their linear transmission and evolution. However, the ultrashort pulse vortex laser has become a research hotspot with extensive studies. Since the inclusion of nonlinear processes will greatly increase the complexity of vortex beam analysis, the study on transmission and evolution of ultrashort pulse vortex lasers in nonlinear media is still rare. Thus, we experimentally investigate the propagation of mid-infrared LG beams in organic crystal DSTMS due to the cubic-quintic nonlinear effect and analyze the differences in the effect of polarization of the incident vortex beam on the transverse light field distribution.

High power mid-infrared optical parametric amplifier (OPA) pulses with 1450 nm center wavelength, 60 fs pulse duration, and 1 kHz repetition rate serve as the pump of the system. After passing through a customized spiral phase plate (SPP), the mid-infrared laser light is modulated into vortex beams and incident perpendicularly onto the surface of an organic crystal with a 640 μm thickness. A 4f imaging system is constructed using two lenses to conduct imaging on the spot in either plane perpendicular to the light propagation direction within the crystal. The CCD camera moves back and forth in the horizontal direction to observe and record the spot evolution of the vortex beam during propagation, starting from the rear surface of the crystal.

In the experiment, the spot changes of mid-infrared vortex light before and after passing through the DSTMS crystal are found and compared with those of the BBO crystal to analyze the spot characteristics of the vortex beam after passing through different crystals. After passing through the BBO crystal, there is still only one bright ring in the spot, with the spot radius almost unchanged. However, after passing through the DSTMS crystal, the spot changes significantly from the original doughnut structure to three thin bright rings, and the number of rings increases. This is due to the nonlinear process of three-photon absorption of pump light by the DSTMS crystal. When the pump light polarization fulfills the optimal THz generation conditions, the nonlinear refractive index of DSTMS mainly originates from the quasi-χ(3) effect due to a combination of the cascaded 2^nd-order OR process and the linear EO effect. The contribution from the intrinsic χ(3) nonlinearity of DSTMS should be negligible. Its additional nonlinear refractive index causes the refractive index of the pump light to vary with light intensity, which in turn leads to spectrum broadening. For each spectral component generated after the spectrum broadening of the incident LG beam in the Kerr medium, its respective corresponding LG mode has the same topological charge and radial index. As the frequency value of each spectral component is different, the respective corresponding Rayleigh length and beam waist position are different to bring various light field expressions for the LG vortex beam corresponding to each spectral component. Therefore, the corresponding brightest rings have different radii, and each bright ring generally does not coincide with each other in the observation plane, resulting in a weak spot intensity in most regions of the observation plane. To verify the above optical spot evolution process, we can simulate the light field distribution of the LG beam before and after passing through the DSTMS medium with a Kerr-like effect by MATLAB simulation analysis based on the generalized Gaussian beam decomposition method, with the simulation results shown in Fig. 3. Fig. 3(c) reveals that the effect of the Kerr medium on the incident LG beam is to produce LG beams with different radial modes. Meanwhile, the effect of the polarization of the incident vortex light on the spot of the outgoing light from the rear surface of the crystal is further investigated experimentally, and the experimental results illustrate that the incident light with different polarization produces vortex beams with different light intensity distributions.

We research the evolutionary mechanism of vortex beams in nonlinear organic crystal DSTMS initially, showing that the nonlinear transmission effect can change the light intensity distribution of vortex beams to a large extent. The generalized Gaussian beam decomposition method is utilized to simulate and analyze the light intensity distribution of the LG beam before and after passing through the medium with a Kerr-like effect, which indicates that the Kerr medium affects the incident LG beam by producing LG beams with different radial modes. Additionally, the effect of different polarization of the incident vortex light on vortex mid-infrared laser transmission in DSTMS is studied to demonstrate the effect of nonlinear transmission on the LG beam.