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).