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Abstract
The spatial modulation instability phenomenon in soft matter is studied by using linear stability analysis based on the propagation equation of a light beam in soft matter. The gain spectrum of modulation instability in colloidal soft matter, the physical condition for instability to occur, and the relationship between modulation instability and fractal dimension of soft matter are obtained. It is shown that the characteristics of modulation instability strongly depend on the fractal dimension and the initial intensity of the beam. For two different fractal dimensions, the cut-off frequency of modulation instability corresponding to the higher fractal dimension is higher when the initial intensity of the beam is smaller than a critical value. When the initial intensity of the beam is smaller than the critical value, however, the cut-off frequency of modulation instability corresponding to the higher fractal dimension is lower. The maximum growth rate always increases monotonously with the fractal dimension.
Acknowledgements
This work was partially supported by the National Natural Science Foundation of China (Grant nos. 10576012, 10776008, and 60538010) and the Scientific Research Fund of Hunan Provincial Education Department.
The authors wish to thank Dr Huanyou Wang for the helpful discussion on this paper and for the important suggestions to improve it.