Nonlinear optical frequency conversion is one of the driving research areas in photonics. Its quasi instantaneous response and the promise of low power consumption in integrated structures could cover the demand for fast signal processing with minimal energy loss. Frequency conversion based on four-wave-mixing takes place in any material independently from its structure. However, second-order nonlinear processes such as difference and sum-frequency generation unlock a range of applications including f-2f self-referencing scheme for the carrier-envelope offset detection for femtosecond laser stabilization or spontaneous parametric down-conversion for the generation of entangled photon-pairs in quantum computing. Unfortunately, most of the CMOS compatible materials do not possess second-order susceptibility due to their centrosymmetric nature. Recently we showed that all-optical poling of silicon nitride waveguides provides a versatile method for symmetry breaking while not requiring any dedicated extra fabrication steps. Due to the photogalvanic mechanism of grating inscription, the quasi-phase-matching (QPM) condition is fulfilled spontaneously between the pump and its second harmonic (SH). In addition, the wavevector associated with the inscribed grating could be leveraged to satisfy the QPM condition in other three-wave processes. It, however, requires the precise control of the waveguide dispersion and the selection of the appropriate pump wavelength in all-optical poling. The goal of this work is the practical application of the second-order nonlinear processes enabled by all-optical poling. My recent work shows that bandwidth engineering and temperature tunability facilitate the observation of the near degenerative difference frequency generation (DFG). We prove that the parameters of the inscribed grating extracted from the SH QPM spectra allow us to predict the conversion efficiency and bandwidth of the generated DFG idler, reaching a conversion efficiency of 0.9 %/W. Also, I demonstrate the advantage of group velocity matching (GVM) of the pump and its second harmonic by the proof-of-concept frequency carrier-envelope offset detection in the standard f-2f scheme. QPM and GVM lead to the efficient SHG in the pulsed regime and result in beating between the second harmonic and the dispersive wave generated by an engineered supercontinuum. The obtained signal-to-noise ratio is sufficient for ensuring frequency comb stabilization without phase slips.