Summary form only given. The linewidth enhancement factor, also referred to as Henry factor or α factor, quantifies the intrinsic phase-amplitude coupling in a laser gain medium. Very extensive literature exists on measurement methods for semiconductor lasers, including direct estimation of the gain asymmetry, pump induced phase modulation (“AM/FM” method) and optical injection. Unfortunately none of these methods is well-suited for solid-state lasers, which feature slower dynamics and small values of α. Few measures are available in the literature: a value of α = 0.25 ± 0.13 was found in a Nd:YVO 4 laser, using injection and AM/FM modulation methods [1], and a surprisingly large α ~ 1 was reported in Nd:YAG microchip lasers.Here, we propose a new "FM/AM" method based on the amplitude response of the laser to a phasemodulated injection. We show that for an injected laser, this response is minimal for a particular value Δm of the frequency detuning Δ between the injected field and the laser field, and that this value is directly related to a. Furthermore, unlike standard methods that often use pump modulation, we operate at a constant intracavity power, so the measurement is free from any thermal considerations [2]. Our method can greatly benefit of operating the laser in a dual frequency regime, that is, when the laser produces two orthogonal polarization modes with a tunable frequency difference. Indeed, this, combined with a frequency-shifted optical feedback, allow to avoid the critical need of an external stable master laser, as one mode of the laser can be used to inject the other one.