Current designs for quasi-phasematched (QPM) nonlinear crystals do not take full advantage of QPM’s potential to completely engineer the crystal's spectral conversion response. By combining an analytic prescription for the QPM conversion response with a simulated annealing optimisation method we have developed a method for designing a QPM grating with an arbitrary second-harmonic generation (SHG) conversion profile.

A general QPM crystal can be visualised as a series of domains with alternating polarities and having lengths qm(1< m < n):

The output SHG field from a QPM crystal containing n inverted domains can be expressed as:

where

The approach can be used not only to shape the spectrum of the output light from such crystals, but also to produced shaped femtosecond pulses from a known input pulse.  We have generated tailored femtosecond pulses with fully engineered intensity and phase profiles by using second-harmonic generation of an Er:fiber laser in an aperiodically-poled lithium niobate crystal in the undepleted pump regime.  Nine second harmonic pulse-shapes, such as Gaussian, stepped, square, triangular, identical but oppositely chirped, double and triple Gaussian pulses have been created experimentally (see above).

Using cross-correlation frequency-resolved optical gating (results above), the intensity and phase profiles of the experimentally created pulses have been compared directly with those predicted by theory, with good agreement being obtained.