Английская Википедия:Harmonic generation
Harmonic generation (HG, also called multiple harmonic generation) is a nonlinear optical process in which <math>n</math> photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with <math>n</math> times the energy of the initial photons (equivalently, <math>n</math> times the frequency and the wavelength divided by <math>n</math>).
General process
In a medium having a substantial nonlinear susceptibility, harmonic generation is possible. Note that for even orders (<math>n = 2,4,\dots</math>), the medium must have no center of symmetry (non-centrosymmetrical).[1]
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 <math>n</math>. 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).[2]
Sum-frequency generation (SFG)
Шаблон:Main A special case in which the number of photons in the interaction is <math>n = 2</math>, but with two different photons at frequencies <math>\omega_1</math> and <math>\omega_2</math>.
Second-harmonic generation (SHG)
Шаблон:Main A special case in which the number of photons in the interaction is <math>n = 2</math>. Also a special case of sum-frequency generation in which both photons are at the same frequency <math>\omega</math>.
Third-harmonic generation (THG)
A special case in which the number of photons in the interaction is <math>n = 3</math>, if all the photons have the same frequency <math>\omega</math>. If they have different frequency, the general term of four-wave mixing is preferred. This process involves the 3rd order nonlinear susceptibility <math>\chi^{(3)}</math>.[3]
Unlike SHG, it is a volumetric process[4] and has been shown in liquids.[5] However, it is enhanced at interfaces.[6]
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.[7]
Fourth-harmonic generation (FHG or 4HG)
A special case in which the number of photons in interaction is <math>n = 4</math>. Reported around the year 2000,[8] powerful lasers now enable efficient FHG. This process involves the 4th order nonlinear susceptibility <math>\chi^{(4)}</math>.
Materials used for FHG
Some BBO (β-BaB2O4) are used for FHG.[9]
Harmonic generation for <math>n > 4</math>
Harmonic generation for <math>n = 5</math> (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 requires very intense lasers to be generated. To generate high harmonics (like <math>n = 30</math> and so on), the substantially different process of high harmonic generation can be used.
Sources
See also
References
