Lasers which emit light in the short wavelength spectral range are expensive and not sufficiently reliable for many applications. A more economically way to generate such radiation is achieved by frequency doubling. Especially the generation of green laser radiation is an important requirement of the lithographic industry. At present the argon ion laser is being displaced more and more by frequency doubled diode pumped Nd:YAG lasers which deliver tens of watt in TEMoo and are the first choice for pumping the Titanium Sapphire which is of high importance and frequently used in research labs. In biophotonics the green radiation serves as "optical tweezers" and the analysis of living cells. The principles of the generation of frequency doubled light will be explained and simultaneously the possibilities of non linear optics learnt in this experiment. The understanding of non linear optical effects is very important for laser technology, since the processes of generation of short pulses are also based on non linear effects. Within the experiment the phase matching condition will be presented and analysed. The efficiency of frequency doubling will be determined and hints for an optimized conversion rate will be evaluated in the experiment. For the first time the frequency doubling can be followed up in an impressive manner by a practical experiment. The fundamental wave is generated by a diode laser pumped Nd:YAG laser with an open resonator structure. The non - linear crystal is placed simply into the resonator and suddenly green light appears. Furthermore also the mode structure of the Nd:YAG laser becomes visible and shows a great variety of transverse modes. By introducing an adjustable iris into the cavity the number and kind of modes can be controlled and reduced down to TEMoo. By using the "Red 660 nm" option the Nd:YAG laser is operated at 1.3 µm and a special cut KTP crystal allows the frequency doubling into the red part of the spectrum.