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 (${\mathrm{LG}}_{01}$) into the 45\ifmmode^\circ\else\textdegree\fi{} rotated Hermite-Gauss (``pringle'') mode (${\mathrm{HG}}_{11}$), 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.