Spatiotemporal modulation instability of coherent light in noninstantaneous nonlinear media

Summary form only given. Periodic pattern of optical modulation instability (MI) results from the interplay between the diffraction and self-focusing effects. This interplay amplifies the noise, carried by the light beam, of certain spatial frequency. If the noise is from a static source (e.g. material defects), the resulted MI patterns are no different in either instantaneous or noninstantaneous media. However, it is not the case if the noise is from a dynamic source (e.g. random light scattering). In instantaneous media, MI patterns form instantly depending on the noise distribution. If the material response is noninstantaneous, the always-changing noise cannot alter the index dramatically at any moment, but only to modify the index and consequent MI pattern a bit. Thus, the cumulative MI pattern movement will only be noticeable after a time longer than the material response time. Here, we report on the theoretical derivation and experimental observation of such spatiotemporal MI of coherent light beam in noninstantaneous media. We obtain the MI growth rate as a function of the noise frequency and the material response time. In the experiment, we observe that the varying speed of the MI patterns increases with the decreased material response time. We also observe that increasing the material response time can arrest the MI, agreeing with the theory.