Diploma thesis

3 Theory
3.1 Three-wave mixing
Nonlinear optics is the science of light-matter and light-light interaction in nonlinear
materials. Effects are ”nonlinear” in the sense that the response of the material
depends nonlinearly upon the applied electric field. Interactions of this kind are
embedded in a wide range of phenomena, from the Kerr-effect to frequency mixing
processes. In this work, we focus solely on three-wave mixing processes.
3.1.1 Sum frequency generation
Since its discovery in 1961 by Franken et al. [13], second harmonic generation
(SHG) or sum frequency generation (SFG) became one of the most commonly used
nonlinear optical effects. Its use ranges from tiny green laser pointers to expensive
mode locked pulsed Nd:YAG laser systems. SFG describes the combination of two
photons to a third photon with higher energy, inside a nonlinear material, under
the restrictions of energy and momentum conservation. In the special case of two
identical photons merging, this process is called SHG (see Figure 3.1). The classical
Figure 3.1: Sum frequency generation, energy conservation and momentum
conservation
differential equation describing SFG is derived from the Maxwell equations assuming
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