Author: Ronen Shekel
The generation of pure nonclassical states of light is one of the most important goals of optical quantum information science. A popular and versatile source for creating such states is spontaneous parametric down-conversion (SPDC) – a nonlinear process where a pump beam hits a nonlinear crystal and produces pairs of lower energy photons [1]. Indeed, in the past several decades, SPDC has been widely used for generating heralded single photons and entangled photon pairs, used for applications such as quantum communications and quantum metrology.
For the SPDC process to be efficient, both energy and momentum must be conserved, as depicted in Fig. 1a. In an ideal scenario without chromatic dispersion, phase matching would work trivially, since the frequency and wavevector are simply related by a factor of the speed of light. However, real optical materials exhibit chromatic dispersion, which means that the refractive index varies with wavelength, resulting in a wavevector mismatch Δk_z.
One way to overcome the wavevector mismatch, named birefringent phase matching [2], is by taking advantage of the difference in phase accumulation for different polarizations. In this technique, the polarization of the pump and generated photons are chosen such that this effect will compensate for the chromatic dispersion.
A second popular technique, named quasi-phase matching, was proposed as early as 1962 [3]. This technique resolves the mismatch by splitting the crystal into domains, where alternating domains have nonlinear coefficients of opposite signs (Fig. 1b). This technique may be understood using a phasor diagram (Fig. 1c). The wavevector mismatch causes the phases to accumulate differently, and after a finite propagation distance, they will begin to interfere destructively. With quasi-phase matching, the domain periodicity Λ is chosen such that when the process reaches the destructive interference region, the sign of the phasors are flipped, and the process is allowed to continue to build constructively.
Interestingly, it took until the mid-1980s for this technique to become widespread experimentally [4], using periodic polling. This is because the creation of such domains is challenging, and typically uses ferroelectric domain engineering [5]. This involves the application of a strong electric field to a ferroelectric crystal via patterned electrodes on the crystal surface. This strong field changes the crystal orientation under the electrodes and thus reverses the sign of its nonlinear coefficient. Periodic poling is especially challenging to perform on large-aperture crystals and with small poling periods.
The advantages of quasi-phase matching are that it allows the use of materials with stronger nonlinear coefficients, avoids spatial walk-off, and does not add requirements on the polarization of the different fields. Another advantage is that by tailoring the poling period, different SPDC parameters may be controlled.
For example, as has been shown in [6], using different poling periods could determine whether a type-0 or type-II process will take place. A Type-0 process, where the pump and both generated photons have the same polarization, could be desirable due to its high pair-generation rate. However, it is relatively sensitive to temperature changes and has a large bandwidth. In a type-II process, the two resulting photons have orthogonal polarization, and a narrow spectrum, but the process tends to be weaker.
It is very important to understand the specific application and desired figure of merit before choosing a crystal configuration. For instance, is the total flux the important measure? Or perhaps the total flux per nm of wavelength? Is spatial entanglement a desired feature or something to avoid? Depending on the exact application, a different configuration of pump beam, crystal dimensions, temperature, and poling periodicity may be the best fit [7].
Raicol Crystals is a world-leader in quasi phase matched crystals, and provides periodically poled nonlinear crystals such as PPLN, PPKTP, and PPSLT, allowing a wide range of periodicities and crystal dimensions. Please contact us for further details! We also provide aperiodically poled KTP (APKTP) crystals, which allow even further control of the resulting quantum state. This will be the subject of another post, so stay tuned!
[1] Walborn, S.P., Monken, C.H., Pádua, S. and Ribeiro, P.S., 2010. Spatial correlations in parametric down-conversion. Physics Reports, 495(4-5), pp.87-139.
[2] Boyd, R.W., Gaeta, A.L. and Giese, E., 2008. Nonlinear optics.
[3] Armstrong, J. A., N. Bloembergen, J. Ducuing, and Peter S. Pershan. “Interactions between light waves in a nonlinear dielectric.” Physical review 127, no. 6 (1962): 1918.
[4] R. Paschotta, article on “Quasi-phase Matching” in the RP Photonics Encyclopedia, retrieved 2024-08-21, https://doi.org/10.61835/kj9
[5] Yamada, M., Nada, N., Saitoh, M. and Watanabe, K., 1993. First‐order quasi‐phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second‐harmonic generation. Applied Physics Letters, 62(5), pp.435-436.
[6] Steinlechner, F., Gilaberte, M., Jofre, M., Scheidl, T., Torres, J.P., Pruneri, V. and Ursin, R., 2014. Efficient heralding of polarization-entangled photons from type-0 and type-II spontaneous parametric downconversion in periodically poled KTiOPO 4. JOSA B, 31(9), pp.2068-2076.
[7] Schneeloch, J., Knarr, S.H., Bogorin, D.F., Levangie, M.L., Tison, C.C., Frank, R., Howland, G.A., Fanto, M.L. and Alsing, P.M., 2019. Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion. Journal of Optics, 21(4), p.043501.
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