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Birefringent Phase Matching

Definition: a technique of phase matching based on the birefringence of a crystal material

German: Phasenanpassung durch Doppelbrechung

Cite the article using its DOI: https://doi.org/10.61835/unq

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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.

birefringent phase matching in LBO — 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.

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.

Questions and Comments from Users

2021-08-06

In an OPO, the ordinary-polarized pump can have the same refractive index as an extraordinary-polarized signal or idler because the refractive index is polarization-sensitive in a birefringent crystal. However, how can the signal and idler experience the same refractive index, given that they are at different wavelengths but both polarized the same way?

The author's answer:

Signal and idler generally do not have the same refractive index, and they don't need to have that for phase matching. Phase matching in an OPO does not require that all involved phase velocities are equal. Instead, the sum of wavenumbers of signal and idler must match the wavenumber of the pump in the case of a collinear interaction.

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