Creation of Bessel–Gaussian Beams from Necklace Beams via Second-Harmonic Generation

The interest in (quasi-)nondiffracting beams is rooted in applications spanning from secure sharing cryptographic keys real-world free-space optical communications and high-order harmonic generation to high-aspect-ratio nanochannel machining, photopolymerization, and nanopatterning, just to mention a few. In this work, we explore the robustness of the approach for generating Bessel–Gaussian beams by Fourier transforming ring-shaped beams and push the limits further. Here, instead of ring-shaped beams, we use strongly azimuthally modulated necklace beams. Necklace structures are generated by interference of OV beams that carry equal topological charges of opposite signs. In order to effectively account for the azimuthal $\pi$-phase jumps in the necklace beams, we first generate their second harmonic, thereafter focusing (i.e., Fourier transforming) them with a thin lens. In this way, we successfully create Bessel–Gaussian beams in the second harmonic of a pump beam with strong azimuthal modulation. The experimental data presented are in good agreement with the developed analytical model.