Discrete quadratic cavity solitons

We predict the existence of various types of discrete solitons in arrays of coupled optical cavities endowed with a quadratic nonlinearity. We derive mean-field equations and determine their range of validity by comparing results with those from the original round-trip model. By using an analytical approach we identify domains in parameter space where solitons can potentially exist and describe their asymptotic behavior. Taking advantage of these results, we numerically find discrete solitons of different topologies. Some of them are unique to discrete models. Ultimately, we study the stability of these soliton solutions and find that discreteness appreciably influences this behavior.