The first part of this talk covers adiabatic processes in nonlinear optics,
in which the phase mismatch and/or the nonlinear coupling are slowly
changing along the nonlinear crystal, thereby enabling robust, broadband and
efficient frequency conversion. First it is shown that sum frequency
generation with undepleted pump is analogous to other familiar two level
systems, hence can be represented by Bloch sphere or eigenvalue diagrams.
Adiabatic following can therefore be used for complete frequency conversion
of broadband and ultrashort pulses. The method can be further extended for
multiple cascaded process, and in particular enables conversion through dark
intermediate frequencies. Finally, adiabatic conversion with depleted pump
is presented.
The second part discusses methods to spatially and spectrally shape the
wavefunction that is generated in a nonlinear three-wave mixing process. It
relies on coding schemes that were developed in the 1960's for computer
generated holography, but rather than modulating the amplitude or phase
profile of a standard hologram, here the quadratic nonlinear coefficient is
modulated and the reconstructed wave is obtained at a new wavelength. As an
example for spectral shaping, superoscillating modulation is used, enabling
to obtain a frequency doubler with arbitrarily narrow central lobe.