  The generalized theory of Stokes Mueller polarimetry is employed to develop
the third-order optical polarimetry framework for third-harmonic generation
(THG). The outgoing and incoming radiations are represented by 4-element and
16-element column vectors, respectively, and the intervening medium is
represented by a $4\times 16$ triple Mueller matrix. Expressions for the THG
Stokes vector and the Mueller matrix are provided in terms of coherency and
correlation matrices, and expanded by four-dimensional $\gamma$ matrices that
are analogues of Pauli matrices. Useful expressions of triple Mueller matrices
are presented for cylindrically symmetric and isotropic structures. In
addition, the relation between third-order susceptibilities and the measured
triple Mueller matrix is provided. This theoretical framework can be applied
for structural investigations of crystalline materials, including biological
structures.
