We present an all-solid-state laser source emitting up to 2.1 W of single-frequency light at 671 nm developed for laser cooling of lithium atoms. It is based on a diode-pumped, neodymium-doped orthovanadate (Nd:YVO$_4$) ring laser operating at 1342 nm. Optimization of the thermal management in the gain medium results in a maximum multi-frequency output power of 2.5 W at the fundamental wavelength. We develop a simple theory for the efficient implementation of intracavity second harmonic generation, and its application to our system allows us to obtain nonlinear conversion efficiencies of up to 88%. Single-mode operation and tuning is established by adding an etalon to the resonator. The second-harmonic wavelength can be tuned over 0.5 nm, and mode-hop-free scanning over more than 6 GHz is demonstrated, corresponding to around ten times the laser cavity free spectral range. The output frequency can be locked with respect to the lithium $D$-line transitions for atomic physics applications. Furthermore, we observe parametric Kerr-lens mode-locking when detuning the phase-matching temperature sufficiently far from the optimum value.
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