Image analysis for the destabilization process of the petal pattern in a liquid crystal light valve with rotational optical feedback

The destabilization process from the static petal pattern to the fluctuating petal pattern in a liquid crystal light valve with optical rotational feedback is investigated experimentally. When a spatial rotation of π/6 is imposed on the feedback, the six-fold static petal pattern appears. At a threshold voltage of the bifurcation, rotationally propagating patches arise on the petals. With the increase of applied voltage, the motion of the patches becomes irregular and fluctuations of the pattern develop. By measuring the time correlation function for the spatial wave numbers along the azimuthal direction in polar coordinates, it is found that a half of the fundamental spatial mode relevant to the six-fold petal pattern plays an important role in the bifurcation process. The development of fluctuations is also analyzed by the Karhunen-Loéve decomposition in detail.