International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2013 |
International Tables for Crystallography (2013). Vol. D, ch. 1.7, p. 211
Section 1.7.3.3.4.2. SFG () with undepletion at^{a}Institut Néel CNRS Université Joseph Fourier, 25 rue des Martyrs, BP 166, 38042 Grenoble Cedex 9, France, and ^{b}Laboratoire de Photonique Quantique et Moléculaire, Ecole Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235 Cachan, France |
or .
The undepleted wave at ω_{p}, the pump, is mixed in the nonlinear crystal with the depleted wave at ω_{s}, the signal, in order to generate the idler wave at . The integrations of the coupled amplitude equations over () with , , and givewith and , whereThus, even if the up-conversion process is phase-matched (), the power transfers are periodic: the photon transfer efficiency is then 100% for , where m is an integer, which allows a maximum power gain for the idler. A nonlinear crystal with length is sufficient for an optimized device.
For a small conversion efficiency, i.e. ΓL weak, (1.7.3.85) and (1.7.3.86) becomeand The expression for P_{i}(L) with is then equivalent to (1.7.3.83) with or , and or .
For example, the frequency up-conversion interaction can be of great interest for the detection of a signal, ω_{s}, comprising IR radiation with a strong divergence and a wide spectral bandwidth. In this case, the achievement of a good conversion efficiency, P_{i}(L)/P_{s}(0), requires both wide spectral and angular acceptance bandwidths with respect to the signal. The double non-criticality in frequency and angle (DNPM) can then be used with one-beam non-critical non-collinear phase matching (OBNC) associated with vectorial group phase matching (VGPM) (Dolinchuk et al., 1994): this corresponds to the equality of the absolute magnitudes and directions of the signal and idler group velocity vectors i.e. .
References
Dolinchuk, S. G., Kornienko, N. E. & Zadorozhnii, V. I. (1994). Noncritical vectorial phase matchings in nonlinear optics of crystals and infrared up-conversion. Infrared Phys. Technol. 35(7), 881–895.