Pattern formation in laser-induced melting

A laser focused onto a semiconductor film can create a disordered lamellae pattern of coexisting molten-solid regions. We present a continuum model based on the higher reflectivity of the molten regions. For a large latent heat, this model becomes equivalent to a dynamical model of block copolymers. The characteristic wave number of the lamellae is the one marginally stable to slow variations in the orientation (the zigzag instability) and can be obtained via systematic expansions from two limits. The lamellae can also become unstable to the zigzag instability and Eckhaus instability (slow variations in the wave number) simultaneously. This instability is a signal of dynamic steady states. We numerically study the behavior after a quench. The lamellar size is in agreement with the analytic results and with experiments. For shallow quenches, locally parallel stripes slowly straighten out in time. For deep quenches, a disordered lamellar structure is created. We construct the director field and determine the orientational correlation length. Near onset, the correlation is fixed by the system size. Far from onset, the correlation length saturates at a finite value. We study the transition to the time-dependent asymptotic states as the latent heat is decreased.