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

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 but they rarely cover feedback control. General-purpose control theory literature seldom discuss PDH laser locking specifically. Although excellent PDH review articles provide thorough knowledge and practice on both aspects but they are not reader-friendly. We extend prior works 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.