Quasi-phase Matching | previous | next | feedback |
You can buy periodically poled nonlinear crystals from:
- Raicol Crystals Ltd.: offering periodically poled LiNbO3, stoichiometric LiTaO3, and KTP
Ask RP Photonics to design a periodically poled crystal for phase matching of a given nonlinear interaction.
(Acronym: QPM)
Definition: a technique of achieving a kind of phase matching, using a periodic structure
Quasi-phase matching is a special technique for achieving similar results as with phase matching of nonlinear interactions, in particular for nonlinear frequency conversion. Instead of a homogeneous nonlinear crystal material, a material with spatially modulated nonlinear properties is used. The idea is essentially to allow for a phase mismatch over some propagation distance, but to reverse (or disrupt) the nonlinear interaction at positions where otherwise the interaction would take place with the wrong direction of conversion.
Figure 1: Growth of second-harmonic power in a nonlinear crystal with phase matching (dashed curve), without phase matching (dotted curve), and with quasi-phase matching (solid curve).
Compared with the perfectly phase-matched case, QPM leads to a lower conversion efficiency if the nonlinear coefficient is the same: the effective nonlinearity deff is reduced by a factor 2 / π. However, QPM often makes it possible to use the same polarization direction for all interacting waves, and this often corresponds to using a stronger element of the nonlinear tensor. In effect, the conversion efficiency can be significantly higher than for perfect phase matching. As an example, consider lithium niobate (LiNbO3), where birefringent phase matching usually utilizes the coefficient d31 = 4.35 pm/V, whereas QPM normally uses the higher d33 = 27 pm/V, which effectively results in 17 pm/V taking into account the above-mentioned factor of 2 / π. As the conversion efficiency is usually proportional to the square of the nonlinear coefficient (in the low-conversion regime), the use of d33 results in significant advances in cases where very high optical intensities cannot be used, e.g. due to a limited pump power. Quasi-phase matching is now widely used for frequency doubling (e.g. in green and blue laser sources), and for parametric devices such as optical parametric oscillators.
Figure 2: Quasi-phase matching for OPOs based on periodically poled lithium niobate (PPLN) at room temperature, with all waves polarized along the z axis. The curves correspond to poling periods between 10 μm (left curve) and 35 μm (right-hand side). The dotted line indicates degeneracy of signal and idler frequencies.
Quasi-phase matching opens many attractive possibilities. In principle it allows for efficient nonlinear interactions with arbitrarily high "natural" phase mismatch, although a large phase mismatch may lead to impractically small poling periods. Typically, the propagation direction is along a crystal axis (noncritical phase matching), so that spatial walk-off is avoided, and the acceptance angle is large. Besides, the quasi-phase matching period can be adjusted in order to obtain a convenient phase-matching temperature. Operation at or near room temperature is thus often possible without resorting to critical phase matching or noncollinear phase matching. Such options are also important for nonlinear interactions in waveguides, where noncollinear beams and interactions with spatial walk-off can usually not be used.
Note that it is possible to arrange for multiple quasi-phase-matched nonlinear interactions in a single crystal. This can be achieved e.g. by using periodically poled crystals with multiple poling periods, or by exploiting different orders of phase matching within a single poled structure. (When the duty cycle deviates from 50%, even-order processes also become possible.) Such multiple interactions can be interesting e.g. for realizing compact RGB sources, but they can also unintentionally occur and lead to various parasitic processes. As an example for the latter, higher-order phase-matched second-harmonic generation (frequency doubling) can occur in optical parametric oscillators based on periodically poled lithium niobate or tantalate.
In some cases, parasitic higher-order processes can be disturbing. For example, relatively strong green light can result from parasitic second-harmonic generation in parametric oscillators and generators made of lithium niobate or lithium tantalate which are pumped in the 1-μm spectral region. This can be detrimental particularly in the context of green-induced infrared absorption (→ photodarkening). On the other hand, weak visible parasitic beams can be quite helpful for alignment of such devices.
Historically, quasi-phase matching was invented very early on [1], but could not be used at that time because suitable fabrication techniques (see below) were not yet developed. Therefore, birefringent phase matching was for a long time the only used technique. In the 1980s, however, quasi-phase matching started to be used more and more extensively. The key for this was the development of advanced fabrication techniques.
Overview on Benefits and Problems
In short, the possible benefits of quasi-phase matching are:
- QPM can work with a very wide range of nonlinear interactions (even in crystals which have e.g. a too small birefringence for birefringent phase matching), and this at a convenient temperature and without spatial walk-off.
- As the method can be applied exactly to crystals with particularly high nonlinearity, and QPM also often makes it possible to utilize a larger nonlinear coefficient than is accessible with birefringent phase matching, many nonlinear conversion processes can be made very efficient.
- Periodically poled crystals may have a reduced tendency for photorefractive problems, if effects in differently oriented domains cancel each other.
Possible problems are:
- The fabrication of periodically poled crystals (see below) with high and reliably confirmed quality is challenging, and is possible only with certain crystal materials. The details and success rates of the required procedures strongly depend on material details – not only material type, but also defect density, surface treatment and the like.
- Periodic poling can be applied only to crystals with quite limited thickness, which excludes large aperture devices for very high power levels.
- For different processes, many different poling periods are required. This makes it less likely that a manufacturer can have the required crystal in stock. Even if the required period is in principle not problematic, a new value may require an expensive new lithographic mask. Note also that precise refractive index (Sellmeier) data are required for accurate predictions of the required poling period.
- Parasitic higher-order processes can generate light at additional wavelengths, which can be disturbing in various ways.
Fabrication of Quasi-phase-matched Nonlinear Crystals
The most popular technique for generating quasi-phase-matched crystals is periodic poling of ferroelectric nonlinear crystal materials such as lithium niobate (LiNbO3), lithium tantalate (LiTaO3) or potassium titanyl phosphate (KTP, KTiOPO4) by ferroelectric domain engineering. Here, a strong electric field is applied to the crystal for some time, using microstructured electrodes, so that the crystal orientation and thus the sign of the nonlinear coefficient is permanently reversed only below the electrode fingers. The poling period (the period of the electrode pattern) determines the wavelengths for which certain nonlinear processes can be quasi-phase-matched. Typical poling periods are between 5 μm and 50 μm. See the article on periodic poling for more details.
More recently, interesting work has been done on quasi-matching in orientation-patterned gallium arsenide (OP-GaAs). This material has a very high nonlinear coefficient and a wide transparency range of 0.7-17 μm, making it very attractive e.g. for optical parametric oscillators emitting in the mid-infrared spectral range. There are several different techniques to fabricate orientation-patterned GaAs. An older method is based wafer bonding [2]: several GaAs wafers are bonded to each other with different crystal orientations. This allows for large apertures, but does not allow for small periods and for easy mass production. Another technique is epitaxial growth of patterned GaAs films on a suitable template [3,4]. The template itself may be fabricated with wafer bonding, but there are also all-epitaxial techniques, as developed e.g. at Stanford University. The quality of such epitaxial material can be very high, but the possible film thickness and thus the beam aperture is limited to a few hundred microns. Epitaxial techniques are often applied to waveguide structures, where a large thickness is not required, but are also used for bulk devices.
An extension of quasi-phase matching involves slightly non-periodic (nonuniform) poling of the nonlinear material. This approach allows e.g. to compensate imperfections due to the Gouy phase shift [5]. When the poling is done with a mask, the non-periodic poling is not necessarily more difficult to achieve than exactly periodic poling.
Bibliography
| [1] | J. A. Armstrong, "Interactions between light waves in a nonlinear dielectric", Phys. Rev. 127 (6), 1918 (1962) |
| [2] | L. Gordon et al., "Diffusion-bonded stacked GaAs for quasiphase-matched second-harmonic generation of a carbon dioxide laser", Electron. Lett. 29 (22), 1942 (1993) |
| [3] | M. J. Angell et al., "Growth of alternating <100>/<111>-oriented II-VI regions for quasi-phase-matched nonlinear optical devices on GaAs substrates", Appl. Phys. Lett. 64, 3107 (1994) |
| [4] | L. A. Eyres et al., "All-epitaxial fabrication of thick, orientation-patterned GaAs films for nonlinear optical frequency conversion", Appl. Phys. Lett. 79 (7), 904 (2001) |
| [5] | C. Zhang et al., "Perfect quasi-phase matching for the third-harmonic generation using focused Gaussian beams", Opt. Lett. 33 (7), 720 (2008) |
| [6] | M. Charbonneau-Lefort et al., "Optical parametric amplifiers using chirped quasi-phase-matching gratings I: practical design formulas", J. Opt. Soc. Am. B 25 (4), 463 (2008) |
| [7] | M. Charbonneau-Lefort et al., "Optical parametric amplifiers using nonuniform quasi-phase-matched gratings. II. Space-time evolution of light pulses", J. Opt. Soc. Am. B 25 (5), 680 (2008) |
See also: periodic poling, phase matching, birefringent phase matching, coherence length, nonlinear frequency conversion
Categories: methods, nonlinear optics
This encyclopedia is authored by Dr. Rüdiger Paschotta, the founder and executive of RP Photonics Consulting GmbH. Contact this distinguished expert in laser technology, nonlinear optics and fiber optics, and find out how his technical consulting services (e.g. product designs, problem solving, independent evaluations, or staff training) could become very valuable for your business!
