Spatial Structures in the Presence of Modulated Backgrounds

It is generally believed that modulated backgrounds in spatially
extended nonlinear systems introduce trivial changes. So, for example,
one can split a Bose-Einstein condensate in an optical lattice or make
spatial solitons to move up phase gradients in order to pin them at
maxima of the modulations. We have checked what happens when the
frequency of small amplitude background modulations is changed. In
spite of the perturbative character of the modulations, diffractive
effects coupled with the nonlinearity lead to surprising results. I
will first present how spatial solitons can slow down, stop and even
reverse gear when progressively increasing the wavevector of the input
modulation. This phenomenon is general and evidence is presented for
few sample cases: the optical parametric oscillator, the Kerr cavity,
the two level absorber, the parametrically forced Ginzburg- Landau
equation and the real Swift-Hoenberg model. A simple inspection method
to establish if a given spatial soliton is provided with reverse gear
or not is also discussed. I will then conclude with a second intriguing
phenomenon where increasing wavevectors of the pump modulation are
capable to cancel phase modulations on the signal field in parametric
down conversion.

We means Andrew Scroggie, John Jeffers, Graeme McCartney, Damia
Gomila, Roberta Zambrini and myself. This work is supported by the
EC (Quantim), SGI and, for few pence, by EPSRC.