Tables for
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 1.7, pp. 195-196

Section Quasi phase matching

B. Boulangera* and J. Zyssb

aInstitut Néel CNRS Université Joseph Fourier, 25 rue des Martyrs, BP 166, 38042 Grenoble Cedex 9, France, and bLaboratoire de Photonique Quantique et Moléculaire, Ecole Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235 Cachan, France
Correspondence e-mail: Quasi phase matching

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When index matching is not allowed, it is possible to increase the energy of the generated wave continuously during the propagation by introducing a periodic change in the sign of the nonlinear electric susceptibility, which leads to a periodic reset of π between the waves (Armstrong et al., 1962[link]). This method is called quasi phase matching (QPM). The transfer of energy between the nonlinear polarization and the generated electric field never alternates if the reset is made at each coherence length. In this case and for a three-wave SFG, the nonlinear polarization sequence is the following:

  • (i) from 0 to Lc, [{\bf P}^{NL}(\omega_3) =] [\varepsilon_0\chi^{(2)}(\omega_3){\bf e}_1{\bf e}_2 E_1E_2\exp\{i[k(\omega_1)] [+] [k(\omega_2)]Z\}];

  • (ii) from Lc to 2Lc, [{\bf P}^{NL}(\omega_3) =] [-\varepsilon_0\chi^{(2)}(\omega_3){\bf e}_1{\bf e}_2 E_1E_2\exp\{i[k(\omega_1)] [+] [k(\omega_2)]Z\}], which is equivalent to [{\bf P}^{NL}(\omega_3) =] [\varepsilon_0\chi^{(2)}(\omega_3){\bf e}_1{\bf e}_2 E_1E_2\exp(i\{[k(\omega_1)] [+] [k(\omega_2)]Z-\pi\})].

QPM devices are a recent development and are increasingly being considered for applications (Fejer et al., 1992[link]). The nonlinear medium can be formed by the bonding of thin wafers alternately rotated by π; this has been done for GaAs (Gordon et al., 1993[link]). For ferroelectric crystals, it is possible to form periodic reversing of the spontaneous polarization in the same sample by proton- or ion-exchange techniques, or by applying an electric field, which leads to periodically poled (pp) materials like ppLiNbO3 or ppKTiOPO4 (Myers et al., 1995[link]; Karlsson & Laurell, 1997[link]; Rosenman et al., 1998[link]).

Quasi phase matching offers three main advantages when compared with phase matching: it may be used for any configuration of polarization of the interacting waves, which allows us to use the largest coefficient of the [\chi^{(2)}] tensor, as explained in the following section; QPM can be achieved over the entire transparency range of the crystal, since the periodicity can be adjusted; and, finally, double refraction and its harmful effect on the nonlinear efficiency can be avoided because QPM can be realized in the principal plane of a uniaxial crystal or in the principal axes of biaxial crystals. Nevertheless, there are limitations due to the difficulty in fabricating the corresponding materials: diffusion-bonded GaAs has strong reflection losses and periodic patterns of ppKTP or ppLN can only be written over a thickness that does not exceed 3 mm, which limits the input energy.


Armstrong, J. A., Bloembergen, N., Ducuing, J. & Pershan, P. (1962). Interactions between light waves in a nonlinear dielectric. Phys. Rev. 127, 1918–1939.
Fejer, M. M., Magel, G. A., Jundt, D. H. & Byer, R. L. (1992). Quasi-phase-matched second harmonic generation: tuning and tolerances. IEEE J. Quantum Electron. 28(11), 2631–2653.
Gordon, L. A., Woods, G. L., Eckardt, R. C., Route, R. K., Feigelson, R. S., Fejer, M. M. & Byer, R. L. (1993). Diffusion-bonded stacked GaAs for quasi-phase-matched second-harmonic generation of carbon dioxide laser. Electron. Lett. 29, 1942–1944.
Karlsson, H. & Laurell, F. (1997). Electric field poling of flux grown KTiOPO4. Appl. Phys. Lett. 71, 3474–3476.
Myers, L. E., Eckardt, R. C., Fejer, M. M., Byer, R. L., Bosenberg, W. R. & Pierce, J. W. (1995). Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3. J. Opt. Soc. Am. B, 12, 2102–2116.
Rosenman, G., Skliar, A., Eger, D., Oron, M. & Katz, M. (1998). Low temperature periodic electrical poling of flux-grown KTiOPO4 and isomorphic crystals. Appl. Phys. Lett. 73, 3650–3652.

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