Finding an optimal phase pattern in a multidimensional solution landscape becomes easier and faster if local optima are suppressed and contour lines are tailored towards closed convex patterns. Using wideband second harmonic generation as a coherent control test case, we show that a linear combination of spectral phase basis functions can result in such improvements and also in separable phase terms, each of which can be found independently. The improved shapes are attributed to a suppressed nonlinear shear, changing the relative orientation of contour lines. The first order approximation of the process shows a simple relation between input and output phase profiles, useful for pulse shaping at ultraviolet wavelengths.
van der Walle, P., Offerhaus, H., Herek, J., & Jafarpour, A. (2010). Tailoring a coherent control solution landscape by linear transforms of spectral phase basis. Optics express, 18(2), 973-987. https://doi.org/10.1364/OE.18.000973