Constrained order in frustrated 2D optical patterns

In 2D optical patterns obtained in a Liquid Crystal Light Valve with optical feedback, we show a new kind of geometrical frustration which comes from the imposed form of the boundaries. The circular section of the incoming laser beam presents a symmetry which belongs to the O(2) group, whereas the optical feedback selects patterns with a symmetry restrained to a dihedral subgroup of O(2). By imposing boundaries which respect the symmetry of the dihedral group, we lift the frustration and obtain perfectly ordered patterns. Received 19 January 2001 and Received in final form 2 June 2001