A practical guide to feedback control for Pound–Drever–Hall laser linewidth narrowing

Abstract

The Pound–Drever–Hall (PDH) technique for laser linewidth narrowing is widely used by AMO experimentalists. However, achieving a high-performance PDH locking requires substantial engineering experience, which is scattered across literature and often lacks a cohesive control-theory perspective. Excellent pedagogical papers exist on the theory of the PDH error signal (Black in Am J Phys 69:79, 2000; Day et al. in IEEE J Quantum Electron 28:1106, 1992; Thorpe et al. in Opt Express 16:15980, 2008; Reinhardt et al. in Opt Express 25:1582, 2017), but they rarely cover feedback control. General-purpose control theory literature (Bechhoefer in Rev Mod Phys 77:783, 2005; Ogata in Modern control engineering. Pearson Education, London, 2010) seldom discusses PDH laser locking specifically. Although excellent PDH review articles (Hall et al. in Handbook of optics. McGraw-Hill Professional, New York, 1999; Fox et al. in Stabilizing diode lasers to high-finesse cavities. National Institute of Standards and Technology, Boulder 2003; Nagourney in Quantum electronics for atomic physics and telecommunication. Oxford University Press, Oxford 2014) provide thorough knowledge and practice on both aspects, they are not novice-friendly. We extend prior works (Hall et al. 1999; Fox et al. 2003; Nagourney 2014) by addressing component choice and loop tuning using modern tools like a vector network analyzer. We organize multifaceted engineering considerations systematically, grounded in feedback control principles. Our target reader is researchers setting up a PDH laser lock for the first time; we eschew advanced topics like minimizing residual amplitude modulation (RAM). Our guidance is illustrated by step-by-step optimization of the lock for a 1650 nm ECDL.