Controlling optical beam thermalization via band-gap engineering

We establish dispersion engineering rules that allow us to control the thermalization process and thermal state of an initial beam propagating in a multimode nonlinear photonic circuit. To this end, we have implemented kinetic equation (KE) approach systems whose Bloch relation exhibits bands gaps. When ratio between gap-width band-width is larger than critical value, KE has stationary solutions which differ from standard Rayleigh-Jeans (RJ) distribution. The theory also predicts relaxation times above such non-conventional states occur. tested validity our results for prototype SSH model connectivity composite elements allows band-gap structure. These spectral can be extended more complex networks lack periodicity but their spectra consist groups modes are separated by