Response theory for time-resolved second-harmonic generation and two-photon photoemission

A unified response theory for the time-resolved nonlinear light generation and two-photon photoemission (2PPE) from metal surfaces is presented. The theory allows one to describe the dependence of the nonlinear optical response and the photoelectron yield, respectively, on the time dependence of the exciting light field. Quantum-mechanical interference effects affect the results significantly. Contributions to 2PPE due to the optical nonlinearity of the surface region are derived and shown to be relevant close to a plasmon resonance. The interplay between pulse shape, relaxation times of excited electrons, and band structure is analysed directly in the time domain. While our theory works for arbitrary pulse shapes, we mainly focus on the case of two pulses of the same mean frequency. Difficulties in extracting relaxation rates from pump–probe experiments are discussed—for example due to the effect of detuning of intermediate states on the interference. The theory also allows one to determine the range of validity of the optical Bloch equations and of semiclassical rate equations, respectively. Finally, we discuss how collective plasma excitations affect the nonlinear optical response and 2PPE.