Observation of triply coincident nonlinearities in periodically poled KTiOPO 4

We report the simultaneous quasi-phase-matching of all three possible nonlinearities for propagation along the X axis of periodically poled (PP) KTiOPO 4 (KTP) for second-harmonic generation of 745 nm pulsed light from 1490 nm subpicosecond pulses in a PPKTP crystal with a 45.65 m poling period. This confirms the recent Sellmeier fits for KTP by Kato and Takaoka [Appl. Opt. 41, 5040 (2002)]. Such coincident nonlinearities are of importance for realizing compact sources of multipartite continuous-variable entanglement [Pfister et al., Phys. Rev. A 70, 020302 (2004) 5 Such coincidences are extremely difficult to realize with birefringent phase matching but become straightforward with quasi-phasematching (QPM) in, say, periodically poled ferroelectrics. Since the coming of age of reliable periodic poling techniques in ferroelectric nonlinear crystals such as LiNbO 3 , 7 the QPM technique 8 has become accessible. It relies on the spatial modulation of the nonlinear coefficient induced by periodic poling, rather than on birefringence, to compensate for the phase mismatch of any given nonlinear interaction. As a consequence, the same nonlinear material can be used to phase match a wide range of nonlinear optical mixings by simply changing the poling period, with noncritical QPM conditions (no walk-off) always ensured. Moreover, the larger, diagonal (polarization degenerate) nonlinear tensor elements can be used, in contrast to the case of birefringent phase matching, which greatly increases the nonlinear conversion efficiency. Last but not least, sophisticated nonlinear systems can be made by fabricating multiperiod crystals or Fourier engineering the spatial modulation. 9 Initially achieved in LiNbO 3 , periodic poling has also been successfully obtained 10 in RbTiOAsO 4 and KTP, 11 which is of great interest for CV quantum optics, as these crystals present reduced linear and nonlinear absorption and photorefractive damage. However, even though PPKTP is commercially available, the knowledge of its Sellmeier coefficients is not yet quite at the level required for designing QPM concurrences with full confidence. For this reason, we decided to keep the design simple, with but a single poling period, thereby allowing us to also characterize the material further. As proposed in Ref. 5, we sought to implement the concurrence of ZZZ and YZY secondharmonic generation (SHG) in PPKTP (in ZZZ and YZY the first letter denotes the polarization direction of the second-harmonic field with respect to the crystal axes, and the last two letters denote the polarization of the fundamental fields). It has been shown 2d / n; hence we sought the lowest orders. Dashed curves, poling periods calculated by using the Sellmeier equations from Emanueli and Arie, 14 solid curves, poling periods calculated by using Sellmeier equations from Kato and Takaoka