Birefringent Phase Matching
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.
Note that the coupling between fundamental and second-harmonic light, for example, can be described with a nonlinear tensor, which can be such that waves of different polarization directions can be coupled.
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.
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