  The Stokes Mueller polarimetry is generalized to include nonlinear optical
processes such as second- and third-harmonic generation, sum- and
difference-frequency generations. The overall algebraic form of the polarimetry
is preserved, where the incoming and outgoing radiations are represented by
column vectors and the intervening medium is represented by a matrix.
Expressions for the generalized nonlinear Stokes vector and the Mueller matrix
are provided in terms of coherency and correlation matrices, expanded by
higher-dimensional analogues of Pauli matrices. In all cases, the outgoing
radiation is represented by the conventional $4\times 1$ Stokes vector, while
dimensions of the incoming radiation Stokes vector and Mueller matrix depend on
the order of the process being examined. In addition, relation between
nonlinear susceptibilities and the measured Mueller matrices are explicitly
provided. Finally, the approach of combining linear and nonlinear optical
elements is discussed within the context of polarimetry.
