Sum frequency generation

Illustration of the effect. are the frequencies of light, is the susceptibility. ${\displaystyle \omega _{1,2,3}}$ ${\displaystyle \chi ^{(2)}}$

The sum frequency generation is in the physics of the non-linear optics , an effect in which two light beams of different frequency through a propagation medium having an electric susceptibility , generates a third light beam having the second order, the frequency of which corresponds to the sum of the two original light beams. Since high intensities are necessary for this , this effect is mainly used with lasers . Closely related to this effect are the difference frequency generation, where the difference between the light frequencies is generated, and the frequency doubling, where a frequency is doubled.

In the case of the sum frequency generation, energy conservation must

${\displaystyle \hbar \omega _{3}=\hbar \omega _{1}+\hbar \omega _{2}}$

as well as conservation of momentum

${\displaystyle \hbar {\vec {k}}_{3}\approx \hbar {\vec {k}}_{1}+\hbar {\vec {k}}_{2}}$

be given. Here are the reduced Planckian quantum of action , the circular frequencies and the wave vectors of the two incoming or "added" light waves. The conservation of momentum only has to be approximately fulfilled for the effect to occur in principle, however, the most exact fulfillment possible maximizes the intensity of the added wave or too high a deviation from equality very quickly leads to an almost complete suppression of the effect. This results from the phase matching condition : Since the different frequencies (and thus different wavelengths ) lead to a different refractive index due to dispersion , each of the light waves has a different speed, which ultimately leads to destructive interference . The only efficient way to solve this problem is with birefringent crystals . A commonly used crystal is beta barium borate (BBO). ${\displaystyle \hbar }$ ${\displaystyle \omega _{1,2,3}}$ ${\displaystyle {\vec {k}}_{1,2,3}}$

Further information

• Sum and Difference Frequency Generation in the Encyclopedia of Laser Physics and Technology (Engl.)
• Robert W. Boyd: Nonlinear Optics . 3. Edition. Academic Press, New York 2008, ISBN 978-0-12-369470-6 .