Sensing Optical Cavity Mismatch with a Mode-Converter and Quadrant Photodiode
Fabian Maga\~na-Sandoval, Thomas Vo, Daniel Vander-Hyde, J. R., Sanders, Stefan W. Ballmer

TL;DR
This paper introduces a novel optical cavity mismatch sensing technique using a cylindrical lens mode converter, RF quadrant photodiodes, and heterodyne detection, enabling precise alignment and mode mismatch measurements.
Contribution
It demonstrates an innovative optical mode conversion method combined with RF detection for improved cavity mismatch sensing.
Findings
Successful conversion of LG01 to HG11 mode
Effective measurement of mode mismatch signals
Generation of a feedback error signal via heterodyne detection
Abstract
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.
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