Classical theory of two-dimensional time-domain terahertz spectroscopy

Abstract

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.

Influence of terahertz pulse width on two-dimensional terahertz spectroscopy

“…The nonlinearity can be introduced in three ways, i.e. anharmonicity, nonlinear damping and nonlinear coupling, respectively, as follows [8]:…”

“…kT, so the system has a classical nature in most cases. As a result, the second and other higher order nonlinear polarizations can be analyzed via a classical Lorentz oscillator model using a perturbative method [8]. Compared to the tedious procedures involved in derivation of the nonlinear response function by using semi-classical models [4,5,[19][20][21][22]25] method is much simpler and more effective.…”

“…With the development in generation techniques for intense THz pulses [1][2][3], we are now able to observe many nonlinear phenomena in the THz region. Various theoretical [4][5][6][7][8][9] and experimental [10][11][12][13][14][15][16] studies on THz nonlinearity have been carried out in recent years. Compared to linear THz spectroscopy, a nonlinear alternative is expected to supply richer information.…”

“…That is, by illuminating two THz pulses on a sample, 2DTS is firstly obtained in time-domain via measuring the nonlinear signal caused by the two THz pulses and then performing the 2D Fourier transform along the two time variables to obtain the frequency diagram. However, in previous investigation on 2DTS [4,5,8,9], the incident THz pulse was treated as a delta function. As a result, the information about the influence of the width of THz pulses on 2DTS was missed.…”

“…In fact, two-dimensional optical and infrared spectroscopes have been investigated widely both theoretically and experimentally [17][18][19][20][21][22][23][24][25][26][27]. Up to now, although few experiments on 2DTS have been performed [28], some numerical simulations and theoretical research on 2DTS have been carried out [4,5,8,9] because 2DTS has many tempting prospects. Like conventional linear THz spectroscopy, which is measured in time-domain firstly and then transformed into frequency-domain via a Fourier transform, 2DTS is proposed to be obtained by using a similar approach.…”