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Continuous-wave (cw) singly-resonant optical parametric oscillators (SROs) represent versatile sources of widely tunable, high-power, single-frequency radiation in spectral regions inaccessible to lasers. Pumped at 1.064 mum, PPLN cw SROs can cover the 1-5 mum spectral range, but access to wavelengths <1mum is precluded by photorefractive damage in PPLN. Due to its large photorefractive damage threshold at and relatively high nonlinearity, MgO:sPPLT is an attractive alternative for frequency conversion below 1 mum. Operation of these cw SROs was made possible only by deploying commercial, high-power, high-cost, frequency-doubled cw Nd:YVO4 laser (Coherent, Verdi-10). Here, we demonstrate operation of such green-pumped cw SROs using a fiber-based laser pump source. The key to the successful realization of such a cw SRO is efficient generation of high-power cw radiation in the green using simple single-pass second harmonic generation (SHG) of an infrared fiber laser in a suitable nonlinear crystal to provide the pump radiation. A 30-W, cw Yb fiber laser at 1.064 mum is frequency-doubled in a 30-mm MgO:sPPLT crystal (HC Photonics) with a single grating (Lambda=7.97 mum) to provide up to 9.64 W of single-frequency green power at 532 nm.