Laser linewidth optimization in a feedback loop

Many applications today require stable optical frequency references, such as fully-stabilized optical frequency combs (OFCs), continuous-wave (cw) lasers referenced to high-finesse optical resonators or to various types of atomic/molecular transitions. Feedback loops are used for this purpose, in particular phase-locked loops (PLL). For example, a cw laser diode can be phase-locked to an optical mode of an OFC, or to another stable laser, via feedback to its injection current. The purpose of a PLL is to reduce as much as possible the noise of the considered signal, which is realized in practice by adjusting the parameters of a servo-controller to minimize the error signal. However, some residual noise always remains, which is typically characterized by the residual integrated phase noise Δφ
rms
. Another parameter of high interest for laser experimentalists is the linewidth (full width at half maximum, FWHM) of the stabilized laser, which should be as narrow as possible, especially when phase-locking a “noisy” slave laser to a narrow-linewidth master laser. A narrow linewidth is of particular interest for high-resolution laser spectroscopy. A simple and widely used mean to determine the linewidth of a laser from its noise spectrum makes use of the β-separation line that we introduced a few years ago [1]. However, this gives only an approximate value of the linewidth. Recently, we introduced a more direct relationship between the phase noise power spectral density (PSD) S
φ
(f) and the power spectrum and the associated linewidth of the laser [2], based on the Middleton's expansion [3].