Harmonic generation (HG, also called multiple harmonic generation) is a nonlinear optical process in which photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with times the energy of the initial photons (equivalently, times the frequency and the wavelength divided by ). General process In a medium having a substantial nonlinear susceptibility, harmonic generation is possible. Note that for even orders (), the medium must have no center of symmetry (non-centrosymmetrical). Because the process requires that many photons are present at the same time and at the same place, the generation process has a low probability to occur, and this probability decreases with the order . To generate efficiently, the symmetry of the medium must allow the signal to be amplified (through phase matching, for instance), and the light source must be intense and well-controlled spatially (with a collimated laser) and temporally (more signal if the laser has short pulses). Sum-frequency generation (SFG) A special case in which the number of photons in the interaction is , but with two different photons at frequencies and . Second-harmonic generation (SHG) A special case in which the number of photons in the interaction is . Also a special case of sum-frequency generation in which both photons are at the same frequency . Third-harmonic generation (THG) A special case in which the number of photons in the interaction is , if all the photons have the same frequency . If they have different frequency, the general term of four-wave mixing is preferred. This process involves the 3rd order nonlinear susceptibility . Unlike SHG, it is a volumetric process and has been shown in liquids. However, it is enhanced at interfaces. Materials used for THG Nonlinear crystals such as BBO (β-BaB2O4) or LBO can convert THG, otherwise THG can be generated from membranes in microscopy. Fourth-harmonic generation (FHG or 4HG) A special case in which the number of photons in interaction is . Reported around the year 2000, powerful lasers now enable efficient FHG. This process involves the 4th order nonlinear susceptibility . Materials used for FHG Some BBO (β-BaB2O4) are used for FHG. Harmonic generation for Harmonic generation for (5HG) or more is theoretically possible, but the interaction requires a very high number of photons to interact and has therefore a low probability to happen: the signal at higher harmonics will be very low, and