Nonlinear Crystal Materials

Author: the photonics expert Dr. Rüdiger Paschotta

Optical crystals can exhibit different kinds of optical nonlinearities, which can be utilized in various ways:

• Crystals with a not too high lattice symmetry exhibit a <$\chi^{(2)}$> nonlinearity. They are mainly used for parametric nonlinear frequency conversion (e.g. in frequency doublers and optical parametric oscillators), also for electro-optic modulators.
• Others only have <$\chi^{(3)}$> nonlinearities. Here, one may exploit the Kerr effect, e.g. for four-wave mixing. The delayed nonlinear response is the basis of Raman scattering and Brillouin scattering.

In essentially all cases, artificial (rather than naturally occurring) crystals are used.

Choice of Nonlinear Crystals

Many different properties of a nonlinear crystal can be important for an application e.g. in nonlinear frequency conversion:

• The magnitude of the effective nonlinear coefficient <$d_\rm{eff}$> depends on the nonlinear tensor components and on the utilized phase-matching configuration. A high nonlinearity is important particularly if the achievable optical intensities are low.
• The chromatic dispersion and birefringence properties determine the possibilities for phase matching and the phase-matching bandwidth, angular acceptance (for critical phase matching), etc.
• Normally, the crystal material should have a high optical transparency for all wavelengths involved – for example, for pump, signal and idler in an optical parametric amplifier.

Additional properties can be relevant for a comparison:

• the availability of crystals with consistently good quality, large size and a reasonable price
• the material's potential to be periodically poled to achieve quasi-phase matching
• linear absorption, which can cause heating at high optical power levels, so that the phase matching is disturbed, and thermal lensing may occur
• the ease of fabricating high-quality anti-reflection coatings on the crystals, which reliably adhere to the surfaces (even under conditions of substantial temperature changes, as sometimes required)
• the chemical durability; e.g., some crystal materials are hygroscopic, others undergo chemical changes when heated in a vacuum chamber for application of a dielectric coating
• the resistance against optical damage, gray tracking, photodarkening, green-induced infrared absorption, and the like
• the resistance against photorefractive effects (which are often called photorefractive damage, even though this is usually reversible)

The choice of the most suitable crystal material for a given application is often far from trivial; it should involve the consideration of many aspects. For example, a high nonlinearity for frequency conversion of ultrashort pulses does not help if the interaction length is strongly limited by a large group velocity mismatch and the low damage threshold limits the applicable optical intensities. Also, it can be highly desirable to use a crystal material which can be critically phase-matched at room temperature because noncritical phase matching often involves the operation of the crystal in a temperature-stabilized crystal oven. However, the feasibility of critical phase matching may be given only for sufficiently high peak powers.

Frequently Used <$\chi^{(2)}$> Nonlinear Crystal Materials

Lithium Niobate and Tantalate

Lithium niobate (LiNbO₃) and lithium tantalate (LiTaO₃) are materials with a relatively strong nonlinearity. They are often used for nonlinear frequency conversion and also for electro-optic modulators. Both materials are available in congruent and in stoichiometric form, with important differences concerning periodic poling and photorefractive effects (see below). Lithium niobate and tantalate are the most often used materials in the context of periodic poling; the resulting materials are called PPLN (periodically poled lithium niobate) and PPLT, respectively, or PPSLN and PPSLT for the stoichiometric versions. Both have a relatively low damage threshold, but do not need to be operated at high intensities due to their high nonlinearity. They have a tendency for photorefractive effects, which are detrimental for frequency conversion, but are used for, e.g., holographic data storage in Fe-doped LiNbO₃ crystals. The tendency for “photorefractive damage” depends strongly on the material composition; e.g. it can be reduced via MgO doping and by using a stoichiometric composition.

Potassium Niobate

Potassium niobate (KNbO₃) has a high nonlinearity. It is used for, e.g., frequency doubling to blue wavelengths and in piezoelectric applications.

KTP, KTA, RTP, RTA

Potassium titanyl phosphate (KTP, KTiOPO₄) may be flux-grown (cheaper) or hydrothermal (better for high powers, lower tendency for gray tracking → photodarkening). The “KTP family” of materials also includes KTA (KTiOAsO₄), RTP (RbTiOPO₄) and RTA (RbTiAsPO₄). These materials tend to have relatively high nonlinearities and are suitable for periodic poling.

KDP, KD^*P

Potassium dihydrogen phosphate (KDP, KH₂PO₄) and potassium dideuterium phosphate (KD^*}P or DKDP, KD₂PO₄, exhibiting extended infrared transmission), are available in large sizes at low price. They exhibit good homogeneity over large volumes and have a high damage threshold, but are hygroscopic and have a low nonlinearity.

Borate Crystals

There are a number of borates, the most important ones being lithium triborate (LiB₃O₅ = LBO), cesium lithium borate (CLBO, CsLiB₆O₁₀), β-barium borate (β-BaB₂O₄ = BBO, often used in Pockels cells), bismuth triborate (BiB₃O₆ = BIBO), and cesium borate (CSB₃O₅ = CBO). Borates are generally hygroscopic; that problem is severe e.g. for CLBO, also substantial for BBO, but much less for LBO.

Yttrium calcium oxyborate (YCOB) and YAl₃(BO₃)₄ (YAB) are also available in rare-earth-doped form for use as laser gain media, and can then simultaneously generate and frequency-convert laser light.

Less frequently used are strontium beryllium borate (Sr₂Be₂B₂O₇ = SBBO) and K₂Al₂B₂O₇ (KAB).

LBO, BBO, CLBO, CBO and other borate crystals are suitable for the generation of relatively short wavelengths, e.g. in green and blue laser sources, and for UV generation (→ ultraviolet lasers) because their band gap energy is relatively high, the crystals are relatively resistant to UV light, and there are suitable phase-matching options.

Borates such as LBO and BBO also work well in broadly tunable optical parametric oscillators and optical parametric chirped-pulse amplification.

Mid-IR Crystals

For mid-infrared (and partly also terahertz) generation, one requires crystal materials with a transparency range extending far into the infrared spectral region. The most important of these media are zinc germanium diphosphide (ZGP, ZnGeP₂), silver gallium sulfide and selenide (AgGaS₂ and AgGaSe₂), gallium selenide (GaSe), and cadmium selenide (CdSe). Gallium arsenide (GaAs) has also become useful for mid-infrared applications, since it is possible to obtain quasi-phase matching in orientation-patterned GaAs [13, 21]. There are also various barium-based crystal materials such as BaGa₄S₇, BaGa₄Se₇, BaGa₂GeS₆ and BaGa₂GeSe₆ [26].

Lifetime of Nonlinear Crystals

In many cases, a nonlinear crystal used for nonlinear frequency conversion has a very long lifetime, which is longer than that of the whole laser system. The crystal material is essentially not modified during operation. However, a reduced crystal lifetime can occur under various circumstances:

• Excessive optical intensities during operation may instantly damage a crystal. Unfortunately, nonlinear crystals often need to be operated not far from their optical damage threshold in order to achieve a sufficiently high conversion efficiency. This implies a trade-off between conversion efficiency and crystal lifetime. Note that even if the nominal intensity is below the nominal damage threshold, there may be problems due to fluctuations of the beam power or local intensity (e.g., if a beam profile has “hot spots”), or due to isolated defects in a crystal, which are more sensitive than the regular crystal material.
• Even well below the threshold for instant damage, some crystal materials exhibit a continuous degradation within the used volume, e.g. in the form of “gray tracking”. Such phenomena are particularly common for operation with ultraviolet light. Note that a gradual degradation can also lead into instant catastrophic damage via excessive heat generation.
• Hygroscopic crystal materials deteriorate when they are not always kept in sufficiently dry air (or a dry purge gas). This applies e.g. to KDP and BBO, and in a lesser extent to LBO. It can be helpful to keep such a crystal at a somewhat elevated temperature, which makes it easier to keep it dry.
• Operation of nonlinear crystals at temperatures below room temperature (in order to achieve phase matching) is generally problematic, as it may lead to condensation of water on the crystal surfaces if the surrounding air is not very dry. Even if the crystal material or coating is not sensitive to water, small water droplets may focus laser radiation more tightly than under normal operation, and thus damage the crystal material.
• Crystals which are non-critically phase-matched in a crystal oven may exhibit problems when the crystal temperature is changed too rapidly or too often. In particular, anti-reflection coatings may be damaged due to different thermal expansion coefficients of the involved materials.

Crystal lifetime can also be strongly dependent on the material quality, although certain degradation phenomena appear to be intrinsic limitations of the material.

For high-power UV generation, nonlinear crystals may become consumables: they rapidly degrade and need to be replaced quite often within the lifetime of the whole laser system (e.g., every few hundred hours of operation). Often, several problematic aspects come together in the regime UV generation:

• Crystal materials are generally more sensitive to ultraviolet light (having high photon energies).
• Crystals exhibit a higher absorption in that spectral region.
• In the case of ultrashort pulses the high group velocity mismatch enforces the use of a shorter crystal, which requires high optical intensities for a given conversion efficiency.

Very Thin Nonlinear Crystals

For some applications, nonlinear crystals with a very small thickness of well below 1 mm are used. This may be necessary for minimizing the group velocity mismatch, e.g. in optical autocorrelators for extremely short pulses.

A common method for obtaining ultrathin crystals is to first optically contact a thicker nonlinear crystal with some substrate (e.g. of fused silica) and then to polish the crystal down to the required thickness of e.g. 20 μm. The group velocity mismatch in the thicker substrate material may not matter, as the nonlinear interaction takes place only in the thin crystal. The substrate only serves to mechanically stabilize the thin nonlinear crystal.

It is also possible to fabricate free-standing crystals with a thickness of only 100 μm, sometimes even below 30 μm.

More to Learn

Encyclopedia articles:

• nonlinear frequency conversion
• frequency doubling
• effective nonlinear coefficient
• ultraviolet lasers
• optical parametric oscillators

Blog articles:

• The Photonics Spotlight 2007-05-26: “Optical Isotropy: Nonlinear Interactions are Different!”