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| {{for|a description of experimental techniques using sum-frequency generation|Sum frequency generation spectroscopy}}
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| '''Sum-frequency generation''' ('''SFG''') is a [[non-linear optics|non-linear optical]] process. This phenomenon is based on the annihilation of two input photons at [[angular frequency|angular frequencies]] <math>\omega_1</math> and <math>\omega_2</math> while, simultaneously, one photon at frequency <math>\omega_3</math> is generated. As with any phenomenon in [[nonlinear optics]], this can only occur under conditions where: | |
| *The light is interacting with matter;
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| *The light has a very high intensity (typically from a [[pulsed laser]]).
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| Sum-frequency generation is a "parametric process",<ref>[http://books.google.com/books?id=uoRUi1Yb7ooC&lpg=PP1&dq=nonlinear%20optics&pg=PA14 Boyd, ''Nonlinear Optics'', page 14]</ref> meaning that the photons satisfy energy conservation, leaving the matter unchanged:
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| :<math>\hbar\omega_3 = \hbar\omega_1 + \hbar\omega_2 </math>
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| A special case of sum-frequency generation is [[second-harmonic generation]], in which ω<sub>1</sub>=ω<sub>2</sub>=1/2ω<sub>3</sub>. In fact, in experimental physics, this is the most common type of sum-frequency generation. This is because in second-harmonic generation, only one input light beam is required, but if ω<sub>1</sub>≠ω<sub>2</sub>, 2 simultaneous beams are required, which can be more difficult to arrange. In practice, the term "sum-frequency generation" usually refers to the less common case where ω<sub>1</sub>≠ω<sub>2</sub>.
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| For sum-frequency generation to occur efficiently, a condition called [[nonlinear optics|phase-matching]] must be satisfied:<ref>[http://books.google.com/books?id=uoRUi1Yb7ooC&pg=PA79 Boyd, ''Nonlinear optics'', page 79]</ref>
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| :<math>\hbar k_3 \approx \hbar k_1 + \hbar k_2 </math>
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| where <math>k_1,k_2,k_3</math> are the [[angular wavenumber]]s of the three waves as they travel through the medium. (Note that the equation resembles the equation for [[conservation of momentum]].) As this condition is satisfied more and more accurately, the sum-frequency generation becomes more and more efficient. Also, as sum-frequency generation occurs over a longer and longer length, the phase-matching must become more and more accurate.
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| Some common SFG applications are described in the article [[sum frequency generation spectroscopy]].
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| ==References==
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| {{reflist}}
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| {{optics-stub}}
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| [[Category:2nd-harmonic generation]]
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| [[Category:Nonlinear optics]]
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