Birefringent Phase Matching
Author: the photonics expert Dr. Rüdiger Paschotta (RP)
Definition: a technique of phase matching based on the birefringence of a crystal material
More general term: phase matching
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DOI: 10.61835/unq Cite the article: BibTex plain textHTML Link to this page! LinkedIn
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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Suppliers
The RP Photonics Buyer's Guide contains 26 suppliers for birefringent materials. Among them:
Artifex Engineering
We offer a wide range of polarizers and polarization optics for many different uses. Choosing the right polarization optic for your application can be a bewildering task, as we offer a wide range for many different uses.
A brief tutorial is available on our website.
Feel free to contact us for assistance. Our experienced staff is only too pleased to help you with the decision process.
EKSMA OPTICS
EKSMA Optics has various kinds of birefringent crystal materials including various nonlinear crystals, some of our laser crystals and Raman crystals and polarizing optics crystals.
Shalom EO
Shalom EO offers various birefringent materials, including: MgF2 crystals, LiNbO3 and alpha-BBO crystals, quartz crystals, calcite crystals, and YVO4 crystals. The crystals exhibit excellent properties when used to make waveplates, Glan and Thompson polarizers, and other optical components. Crystal ingots, blanks, and polished and coated optical elements made of birefringent crystals are offered according to your request.
Shalom EO also offers other optical crystal materials, including: nonlinear crystals, laser crystals, and electric-optical and acousto-optic crystals.
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.