Second harmonic generation
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Second harmonic generation (SHG, also called frequency doubling) is a nonlinear optical process, in which photons interacting with a nonlinear material are effectively "combined" to form new photons with twice the energy, and therefore twice the frequency and half the wavelength of the initial photons.
Only under special circumstances is the rate of conversion of photons to the higher-energy photons significant. The two fundamental requirements for efficient nonlinear power conversion are that the pump intensity is high over a certain propagation length, and that the involved beams preserve a certain phase relationship over that length. Under properly optimized conditions, it is common to obtain 20-50% conversion efficiency by focussing an intense laser beam into a suitable nonlinear crystal. This is widely used, for example to generate green light at 532 nm from the near infrared output of a at 1064 nm.
Some common materials used for second harmonic generation are potassium titanyl phosphate (KTP), lithium triborate (LBO), cesium lithium borate (CLBO), lithium tantalate, and lithium niobate.
As mentioned above, a high conversion efficiency requires that the input light and the second harmonic light are kept in phase. This is not the case without special measures, because the speed of light in a material generally varies with wavelength due to dispersion of the index of refraction. In some nonlinear crystals, a particular combination of crystal orientation and crystal temperature can be found where, due to birefringence, the fundamental and second harmonic light see the same index of refraction, and so remain in phase as they propagate. In other nonlinear materials, where this is not possible, periodic poling is used to keep the waves approximately in phase. This technique, called quasi-phase matching, is commonly used for lithium niobate and lithium tantalate, and greatly expands the options for efficient frequency doubling at various wavelengths and temperatures. Quasi-phasematching in optical waveguides has be used to demonstrate 99% conversion efficency (see Fejer below).
Second harmonic generation crystals are used in some commercially available green laser pointers.
Second harmonic generation was first demonstrated by P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich at the University of Michigan, Ann Arbor, in 1961. The demonstration was made possible by the invention of the laser, which created the required high intensity monochromatic light. They focused a ruby laser with a wavelength of 694 nm into a quartz sample. They sent the output light through a spectrometer, recording the spectrum on photographic paper, which indicated the production of light at 347 nm. Famously, when published in the journal Physical Review Letters, the copy-editor mistook the dim spot (at 347 nm) on the photographic paper as a speck of dirt and removed it from the publication.
References
- P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7, p. 118–119 (1961). http://link.aps.org/abstract/PRL/v7/p118 DOI: 10.1103/PhysRevLett.7.118
- K. R. Parameswaran, J. R. Kurz, R. V. Roussev, M. M. Fejer, "Observation of 99% pump depletion in single-pass second-harmonic generation in a periodically poled lithium niobate waveguide", Optics Letters, 27, p. 43-45 (January 2002).
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