Active optical lattice filters as programmable ODE solvers

Take a two stage active Dowling-MacFarlane optical lattice filter with fixed transmission and reflection coefficients and with a stable all pole (in the open left half plane) transfer function in transmission. Consider a second order ordinary differential equation with a stable all pole transfer function and consider a bounded bandlimited input signal. To find an approximate solution to the ODE with zero initial conditions optically, we introduce the following procedure in solving the higher order differential equations using filters with more stages.