Modeling nonlinear optics of nanosystems with sum-over-states model

Three-stage strategies (ladder rule, few state model (FSM), and parallelization) were proposed to improve the computational efficiency of the sum-over-states (SOS) model in nonlinear optics (NLO) modeling. Ladder rule decomposes NLO coefficients of the nth state into the (n-1)th term and the contribution from the (n-1)th to the nth state without loss of rigor in theory. FSM singles out the states with substantial contribution to NLO. Those strategies are universal to all (including revised and simplified) SOS models. The computing cost reduces roughly to C/(n(i-1)) (C is a constant and i is the rank (order) of the NLO coefficients).