Cellular automata dynamics of nonlinear optical processes in a phase-change material

Changes in the arrangement of atoms in matter, known as structural phase transitions or phase changes, offer a remarkable range of opportunities in photonics. They are exploited in optical data storage and laser-based manufacturing, and have been explored as underpinning mechanisms for controlling laser dynamics, optical and plasmonic modulation, and low-energy switching in single nanoparticle devices and metamaterials. Comprehensive modeling of phase-change processes in photonics is, however, extremely challenging as it involves a number of entangled processes including atomic/molecular structural change, domain and crystallization dynamics, change of optical properties in inhomogeneous composite media, and the transport and dissipation of heat and light, which happen on time and length scales spanning several orders of magnitude. Here, for the first time, we show that the description of such complex nonlinear optical processes in phase-change materials can be reduced to a cellular automata model. Using the important example of a polymorphic gallium film, we show that a cellular model based on only a few independent and physically-interpretable parameters can reproduce the experimentally measured behaviors of gallium all-optical switches over a wide range of optical excitation regimes. The cellular automata methodology has considerable heuristic value for the study of complex nonlinear optical processes without the need to understand details of atomic dynamics, band structure, and energy conservation at the nanoscale.