Phase Matching

In order to obtain high conversion efficiency, the phase vectors of input beams and generated beams have to be matched: 

Dk = k3 - k2 - k1 = 2pn3/l3 - 2pn2/l2 - 2pn1/l1 = 0 (for sum frequency generation)


Where:Dk is phase mismatching, kis phase vector at li and ni is refractive index at liIn low power case, the relationship between conversion efficiency and phase mismatching is:


It is clear that the conversion efficiency will drop dramatically if Dk increases.


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Critical Phase Matching

The phase-matching can be obtained by angle tilting, temperature tuning or other methods. The angle tilting is mostly used to obtain phase-matching as shown in the left figure. If the angle between optical axis and beam propagation (q) isn't equal to 90o or 0o, we call itcritical phase-matching (CPM). Otherwise, 90o non-critical phase-matching (NCPM) is for q=90o and 0oNCPM is for q=0o.

Two types of phase-matching are classified in consideration of polarization of lasers. If the polarizations of two input beams (for sum frequency) are parallel to each other, it is called type I phase-matching. If the polarizations are perpendicular to each other, it is called type II phase-matching

type I phase-matching type I phase-matching