Classical theory of two-dimensional time-domain terahertz spectroscopy

A general theoretical framework of two-dimensional time-domain second-order and third-order terahertz spectroscopy has been presented. The theoretical treatment is based on a classical and phenomenological model with weak nonlinearities. Three types of nonlinearity sources, anharmonicity, nonlinear coupling, and nonlinear damping, were considered. The second-order THz spectroscopy has an exact correspondence to fifth-order off-resonance Raman spectroscopy, and it has been shown that the present treatment gives exactly the same results as of the quantum mechanical theory under the weak nonlinearity condition. General expressions for the nonlinear signal have been obtained for a single-mode system, and numerical calculations for delta-function incident terahertz pulses were shown. For the third-order signal, two-level systems were also considered for comparison. Contributions of two types of incident pulse sequences have been studied separately in the third-order signals. Profiles of the two-dimensional signals were found to depend on the origin and order of the nonlinearity and also on the pulse sequence. The results of the present study show that the two-dimensional signal features of second- and third-order nonlinear terahertz spectroscopy can clarify the nature of the system which is not accessible using linear spectroscopy