Definition: a technique of phase matching based on the birefringence of a crystal material
Birefringent phase matching is a technique for achieving phase matching of a nonlinear process by exploiting the birefringence of a nonlinear crystal. For example, the process of frequency doubling of a 1064-nm beam in a lithium niobate (LiNbO3) crystal can be phase-matched by using the ordinary polarization for the pump beam and the extraordinary polarization for the second-harmonic beam. When the appropriate crystal temperature is set, the birefringence just cancels the chromatic dispersion. The dispersion alone would normally lead to the higher refractive index for the second-harmonic light, so that phase matching would not be possible.
Figure 1: Birefringent noncritical phase matching of frequency doubling in LBO with a pump wavelength of 1064 nm. The beams propagate in the X direction, the pump wave is polarized in the Z direction, and the second-harmonic wave in the Y direction. At 149 °C, the birefringence compensates the effect of chromatic dispersion, so that the refractive indices for both waves are equal.
The common forms of birefringent phase matching are
noncritical phase matching with beam propagation along an axis of the index ellipsoid (see Figure 1), and
critical phase matching where the angle dependence of the extraordinary refractive index is exploited.
Another distinction refers to the involved polarization states:
For type-I phase matching, signal and idler (or the two input waves for frequency doubling or sum frequency generation) have the same polarization.
For type-II phase matching, these waves have orthogonal polarization states.
(In the literature, some other definitions occur occasionally.)
A common alternative to birefringent phase matching is quasi-phase matching (QPM), where all involved waves can have the same polarization direction so that birefringence is not relevant.
For more details, see the article on phase matching.
