Spiral waves in optical second-harmonic generation
Morten Bache1,2, Peter Lodahl2,
and Mark Saffman3
1) Optics and Fluid Dynamics Department, Risø National
Laboratory
Postbox 49, DK-4000 Roskilde, Denmark
2) Department of Informatics and Mathematical Modelling,
building 321
Technical University of Denmark, 2800 Kongens Lyngby, Denmark
3) Department of Physics, University of Wisconsin,
1150 University Avenue
Madison, Wisconsin, 53706, USA
Abstract:
Materials with second order x(2) nonlinearity show highly
complex behaviour when immersed in a cavity. When diffraction competes
with the nonlinearity of the material rich spatiotemporal structures
can appear, including various types of transverse patterns, solitons
and domain walls. These patterns bear strong reminiscence to the ones
observed in chemical reactions and biological and hydrodynamical
systems. We consider theoretically second-harmonic generation where
the cavity is pumped at frequency w and second-harmonic photons
at frequency 2w are created through nonlinear interaction in
the material. Experimental studies have shown the need for an
extended model of second-harmonic generation where the 2w
photons may decay through a parametric process into nondegenerate
parametric photons w- and w+.
This competing
parametric oscillation leads to formation of e.g. spirals, dark
oscillating solitons and labyrinthine patterns, all novel
spatiotemporal structures in optical second-harmonic generation
[1]. In this talk we will focus on the spirals appearing in
he intensity of the fields [2]. These are observed for
the first time in optical systems where until now only spirals
appearing in the phase of the fields have been reported. The intensity
spirals appear as a second order amplitude instability above the
threshold for the parametric oscillations, and we show through
numerical simulations that they destabilize from traveling rolls and
that a very broad and flat gain band seems to be necessary for them to
appear.
[1] P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. A 63,
023815 (2001).
[2] P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. Lett. 85,
4506 (2000).