  The classical problem of three-wave mixing in a nonlinear optical medium is
investigated using the homotopy analysis method (HAM). We show that the power
series basis builds a generic polynomial expression that can be used to study
three-wave mixing for arbitrary input parameters. The phase-mismatched and
perfectly phase matched cases are investigated. Parameters that result in
generalized sum- and difference-frequency generation are studied using HAM with
a power series basis and compared to an explicit finite-difference
approximation. The convergence region is extended by increasing the auxiliary
parameter.
