Frequency offsets in frequency-locked semiconductor lasers

A commonly used technique for frequency locking a laser is dithering the laser frequency and monitoring the first derivative of the laser transmission through an absolute reference. In semiconductor lasers, this frequency dithering can be obtained easily by dithering the injection current. However, this dithering also modulates the laser output power. Here we show that this modulation of the laser output power results in an offset of the locked laser frequency from the reference frequency. We derive analytical expressions for these frequency offsets for semiconductor lasers frequency-locked to a Fabry-Perot transmission peak, a Gaussian absorption line, and a Lorentzian absorption line.