Developing 3D computational models to capture the spatial, temporal and thermal behavior as laser beams propagate through photo-thermally responsive gels

Gaussian laser beams propagating through photo-thermally responsive gels exhibit self-trapping and attraction. Two beams can cross each other if the interaction is sufficiently strong. By developing a new 3D computational model for laser beams propagating through photo-thermally responsive hydrogels, we investigate the complex feedback that occurs as the propagating beam forms a waveguide, which in turn affects the passage of light through the sample. As the beam passes through a poly-( N -isopropylacrylamide) (pNIPAAm) hydrogel, the pendent spiropyran (SP) chromophores isomerize to a hydrophobic state. In water, the resultant localized collapse of the hydrogel leads to a local increase the refractive index, which alters the spatial distribution of light in the sample and leads to the formation of the waveguide. The system displays self-trapping as the light is confined to propagate within the generated waveguide. Our 3D model captures the cooperative interactions among the light propagation, photochemical reaction, hydrogel dynamics, and local heating due to the absorption of light and thereby allows us to characterize the spatial, temporal and thermal variations in the system as the beam traverses the gels. Consequently, the simulations reveal the spatiotemporal behavior as heating due to absorption of light promotes the waveguide formation and leads to a strong attractive interaction between two beams. The strength of interaction between two beams can be tuned by varying the beam intensity, ambient temperature and inter-beam distance. Our results show that two Gaussian beams can cross each other if the interaction is sufficiently strong. The simulations also reveal the long-time dynamics and further elucidate the evolution of the cooperative behavior that leads to this non-linear optical phenomenon.