Quasi-phase-matched grating characterization using minimum-phase functions

Measurement of the second-harmonic power generated by a quasi-phase-matched (QPM) grating as a function of the frequency detuning parameter yields the Fourier transform (FT) magnitude of the complex nonlinear coefficient profile along the QPM device. This FT magnitude can be measured by tuning either the wavelength of the fundamental laser beam or the temperature of the QPM grating. However, the measured magnitude of the FT cannot be unambiguously inverted without the FT phase to uniquely recover the complex nonlinear coefficient profile of the QPM grating. As we demonstrate in this work, this ambiguity can be completely eliminated by placing a stronger and thinner nonlinear sample against the input or output of the QPM device of interest and measuring the detuning curve of this composite structure. By construction, the nonlinear profile of this assembly has a sharp peak due to the thinner sample, followed by the weaker, broader profile of the QPM grating, which essentially constitutes a minimum-phase function. Therefore, its FT phase can be calculated uniquely from its measured FT magnitude, for example by applying to the FT amplitude the logarithmic Hilbert transform or an iterative error-reduction algorithm. This processing then enables the full recovery of the complex nonlinear coefficient profile of the QPM device from its measured detuning curve. In this paper, we demonstrate with numerical examples that this powerful new technique can accurately recover the period, envelope, and chirp parameters of any QPM grating.