Time-domain calculation of surface nonlinear susceptibilities

Abstract

Linear and nonlinear optical methods play an important role in surface science. On a microscopic level the theoretical understanding of the surface-specific second-order response is still incomplete. We discuss the calculation of linear and nonlinear optical response functions for Si(111) surfaces within a real-space and time-dependent approach. The electronic structure is modeled by cyclic-cluster configurations in real space using a tight-binding parametrization of the system hamiltonian. We apply a time-dependent formalism based on an equation of motion for the one-electron density matrix to obtain the linear S(τ) and nonlinear S(τ1, τ2) response functions for the optical polarization which also describe the corresponding response to ultrashort pulses. The Fourier transforms of S(τ) and S(τ1, τ2) are the frequency-dependent optical susceptibilities for the linear X(1)(-ω;ω), and second-order response, X(2)(-ω1-ω2; ω1,ω2), for sum-frequency and second-harmonic (ω1=ω2) generation from surfaces. By a time-dependent Hartree-Fock method we treat the excitonic effects due to the Coulomb interaction between the photoexcited electrons and holes. Results for the spectral dependencies of the linear and nonlinear optical susceptibilities are presented.