Spatio-temporal sub-harmonic cascade in a non-linear interferometer with a liquid-crystal light valve

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A bounded spatio-temporal period-doubling sequence is shown to occur in the Ahkmanov et al. non-linear interferometer. This happens when the pattern is a rotating 2k-armed spiral. First, all arms are identical and the period is the time required for any arm to rotate by the angle 2 pi /2k. As the control parameter increases, the time trace at some location on the pattern displays period doubling as the arms develop progressively distinct spatial modulations. Period 2 behaviour occurs when the nearest patterns similar to arm 'i' are arms 'i+or-2', period 4 behaviour occurs when arm 'i' has arms 'i+or-4' as its nearest similar neighbours, and so on until period 2k when all arms are distinct and the pattern must complete a full revolution for the time series to repeat. Such a cascade is shown to be qualitatively modelled by a mapping.