Transverse patterns in a Kerr medium

M. Hoyuelos, Pere Colet, Maxi San Miguel

Ashat M. Basharov, Andrei I. Maimistov

M. Hoyuelos, Alice Sinatra, Pere Colet +2 more

We consider a vectorial Kerr-medium model including transverse spatial effects. We analyze cases in which, immediately above the threshold of the spatial instability, the homogeneous pump wave gives rise to two tilted waves corresponding to a stripe pattern in the near field. We analyze both the self-focusing and the self-defocusing case and we point out the existence of anti-correlations between the quantum fluctuations of the intensity of the pump and the sum of the intensities of the two tilted waves creating the transverse pattern in the near field. We also evaluate the efficiency of this scheme as a quantum nondemolition (QND) scheme which uses the tilted waves as a ``meter'' to measure the intensity fluctuations of the pump. Our results show the posibility of a QND measurement in the self-defocusing case. In this case, and for a linearly polarized pump, the output pump beam (uniform in the transverse plane) and the pattern have orthogonal polarization and could be easily separated experimentally.

Damià Gomila, Pere Colet

Summary form only given. Transverse optical patterns are capable of allowing noteworthy aspects linked to quantum fluctuations. These issues have been mainly studied in stripe patterns, which present only two modes in the far-field. We address the study of the fluctuations and correlations in a hexagonal pattern in a ring cavity filled with a self-focusing Kerr medium. The dynamics of the electric field is described, in the mean-field approximation, by a Langevin equation for the scaled slowly varying amplitude of the field. We show that the pattern fluctuations can be understood in terms of the neutral modes of the pattern and modes with small damping. These modes are obtained from a stability analysis of the hexagonal pattern. We find strong correlations between the intensity fluctuations of the modes of the pattern, not only among the fundamental harmonics, but also with the higher order ones. We also find strong anticorrelations between the intensity fluctuations of the modes of the pattern and the homogeneous mode which are related to energy conservation.

James F. Scholl, Daniel N. Rogovin

Robert Frey, Jeremy Graham Frey