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Second-harmonic generation
Second harmonic generation (also called frequency doubling or abbreviated SHG) is a nonlinear optical process, in which photons with the same frequency interacting with a nonlinear material are effectively "combined" to generate new photons with twice the energy, and therefore twice the frequency and half the wavelength of the initial photons. Second harmonic generation, as an even-order nonlinear optical effect, is only allowed in mediums without inversion symmetry. It is a special case of sum frequency generation.
Second harmonic generation was first demonstrated by Peter 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 coherent 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. The formulation of SHG was initially described by N. Bloembergen and P. S. Pershan at Harvard in 1962.〔Bloembergen, N., and P. S. Pershan. "Light Waves at Boundary of Nonlinear Media." Physical Review 128.2 (1962): 606-&. (doi:10.1103/PhysRev.128.606 )〕 In their extensive evaluation of Maxwell's equations at the planar interface between a linear and nonlinear medium, several rules for the interaction of light in non-linear mediums were elucidated.
Generating the second harmonic, often called frequency doubling, is also a process in radio communication; it was developed early in the 20th century, and has been used with frequencies in the megahertz range. It is a special case of frequency multiplication.
==Types of SHG in crystals==
Second harmonic generation occurs in three types, denoted 0, I and II. In ''Type 0 SHG'' two photons having extraordinary polarization with respect to the crystal will combine to form a single photon with double the frequency/energy and extraordinary polarization. In ''Type I SHG'' two photons having ordinary polarization with respect to the crystal will combine to form one photon with double the frequency and extraordinary polarization. In ''Type II SHG'', two photons having orthogonal polarizations will combine to form one photon with double the frequency and extraordinary polarization. For a given crystal orientation, only one of these types of SHG occurs. In general to utilise ''Type 0'' interactions a quasi-phase-matching crystal type will be required, for example periodically poled lithium niobate (PPLN).
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