We developed a singly-resonant optical parametric oscillator (SRO) based on a nonlinear crystal of 5%-ppMgCLN congruent lithium niobate chip and pumped at 1064 nm by an extended cavity diode laser widely tuneable from 1050 to 1070 nm injecting a 10 W Yb-fiber amplifier. It generates an idler wave between 3 and 4 µm and a signal wave between 1450 and 1650 nm. The SRO cavity is stabilized to the top of a Fabry-Perot transmission fringe. We then demonstrated a mode-hop-free idler tuning range of 500 GHz. This broad continuous tunability could be used for multi-species high resolution spectroscopy in the mid-infrared. Moreover, we have revisited the plane waves SRO theory, whose analytical solutions were given for the first time in 1969 by Kreuzer in the form of a transcendental equation, using a very powerful perturbative method which takes into account the depletion of the pump. We were able to determine the input-output relations of SRO in the form of very simple explicit relationships, showing that the output powers are proportional to the cubic root of the pump power.
