Characteristics of gain spectrum of modulation instability in soft matter

We investigate the spatial modulation instability in colloidal suspension based on the nonlinear Schrödinger equation. By a standard linear stability analysis, we obtain the expression for instability gain and identified the relationship between the measurable instability characteristic parameters and the particle radius, the optical beam width. It is shown that the modulation growth rate, the maximum growth rate, cut-off frequency and the fastest growth frequency increase as the particle radius decreases and (or) the beam width increases if the optical intensity is constant. Moreover, the ultimate values of the cut-off frequency and the fastest growth frequency are proportional to the beam width, while are independent of the sphere radius. The results provide a new approach to measure the sphere radius and to control the characteristic parameters of modulation instability through the beam width.