Second-harmonic generation of perfect vortex beams and their transformation characteristics during propagation

The systematic and comprehensive research on the single-pass second harmonic generation (SHG) of the perfect vortex beam (PVB) under low fundamental wave depletion is reported. Based on Fourier transformation of the Bessel-Gaussian vortex beam (BGVB) generated through the combination of the spiral phase plate and the axicon, the perfect vortex beam (PVB) at 1064 nm with topological charge (TC) up to 6 is created. By single-pass SHG of these PVBs through the MgO-doped, periodically poled congruent LiNbO3 crystal, PVBs at green wavelength (532 nm) with TCs up to 12 are generated. The TC of the PVB is identified by the interferogram between the PVB and the reference TEM00 Gaussian beam. The SH power (efficiency) of the PVB is measured to be independent of the TC. Furthermore, the impacts of beam parameters, including the ring radius (rho) and the ring half-width (Delta), on the SH efficiency of the PVB, are also investigated. The SH efficiency is inversely proportional to both the ring radius rho and ring half-width Delta. Experimental results agree well with those theoretical ones. The SH PVB transforms to the BGVB at the far-field. The paper also indicates that by transforming the Laguerre-Gaussian vortex beam (LGVB) into the PVB, the detrimental impact that the SH efficiency of LGVB decreases with the increase of TC value can be effectively mitigated, and high SH efficiency can be maintained even at high TC value.