Many applications, e.g., within biomedicine stand to benefit greatly from the development of diode laser-based multi- Watt efficient compact green laser sources. The low power of existing diode lasers in the green area (about 100 mW) means that the most promising approach remains nonlinear frequency conversion of infrared tapered diode lasers. Here, we describe the generation of 3.5 W of diffraction-limited green light from SHG of a single tapered diode laser, itself yielding 10 W at 1063 nm. This SHG is performed in single pass through a cascade of two PPMgO:LN crystals with re-focusing and dispersion compensating optics between the two nonlinear crystals. In the low-power limit, such a cascade of two crystals has the theoretical potential for generation of four times as much power as a single crystal without adding significantly to the complexity of the system. The experimentally achieved power of 3.5 W corresponds to a power enhancement greater than 2 compared to SHG in each of the crystals individually and is the highest visible output power generated by frequency conversion of a single diode laser. Such laser sources provide the necessary pump power for biophotonics applications, such as optical coherence tomography or multimodal imaging devices, e.g., FTCARS-OCT, based on a strongly pumped ultrafast Ti:Sapphire laser.