Frequency-doubling of continuous laser light in Laguerre-Gaussian modes LG_0,0 and LG_3,3

For future generations of gravitational wave detectors, it is proposed to use the helical Laguerre-Gaussian LG_3,3 mode to reduce thermal noise, which limits the detector sensitivity. At the same time, this requires the efficient generation of squeezed vacuum states in the LG_3,3 mode for quantum noise reduction. Since this technique includes the process of second harmonic generation (SHG), we experimentally compare the conversion efficiency and harmonic output field of the LG_0,0 and LG_3,3 modes in a cavity-enhanced SHG using the same 7% doped MgO:LiNbO₃ crystal. Conversion efficiencies of 96% and 45% are achieved, respectively. The influence of mode mismatches and astigmatism is analyzed to estimate the ratio of the pump mode-dependent effective nonlinearities to be d_0,0/d_3,3∼5. Furthermore, we show that absorption loss in the crystal is more relevant for the LG_3,3 mode.