Sensing Optical Cavity Mismatch with a Mode-Converter and Quadrant Photodiode

We present a new technique for sensing optical cavity mode mismatch and alignment by using a cylindrical lens mode converting telescope, radio-frequency quadrant photodiodes, and a heterodyne detection scheme. The telescope allows the conversion of the Laguerre-Gauss bullseye mode (LG01) into the 45deg rotated Hermite-Gauss ("pringle") mode (HG11), which can be easily measured with quadrant photodiodes. We show that we can convert to the HG basis optically, measure mode mismatched and alignment signals using widely produced radio-frequency quadrant photodiodes, and obtain a feedback error signal with heterodyne detection.