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

Abstract

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.

Escape dynamics of photoexcited electrons at catechol:TiO2(110)

“…Photoionization can be described classically for times where the coherence has decayed prior to the arrival of the probe pulse. 66 The contributions of the consecutive spatial positions in the escape process to the 2PPE signal were weighted by i factors, thereby modeling Lambert-Beer's law and also the escape depth of photoelectrons. Thus, the parameters ␥ i and i model the escape of electrons and the detection probability, respectively, in a phenomenological way.…”

Extreme Ultrafast Dynamics of Quasiparticles Excited in Surface Electronic Bands

“…The thus obtained quasiparticle Green's functions are prerequisites for the calculations of PE, IPE, and 2PPE spectra and rates [9][10][11][12][13]. In the case of electron injection into an empty band, GK; n; t can be expressed as [14 -16]:…”

Ultrafast dynamics and decoherence of quasiparticles in surface bands: Preasymptotic decay and dephasing of quasiparticle states

“…A non-Markovian evolution of the survival probability decaying faster than Eq. ͑38͒ will manifest itself through the modifications of relative intensities of direct and indirect transitions in 2PPE and of the peak shapes in PE, IPE, and 2PPE spectra from surface bands relative to the ones deduced from the asymptotic approaches 18,46,47 utilizing Eq. ͑38͒.…”

“…Note also that since we are interested in the response of the system to pulsed photon fields, the relevant quantities to study are the populations of final photoelectron states ͉f͘ above the vacuum level rather than the steady state photoelectron currents as is the case in standard formulation of photoemission in terms of current-current correlation functions. 41,42,47 The required population of a final state ͉f͘ is obtained from the absolute square of the sum of all 2PPE transition amplitudes of the kind shown in Fig. 6, and this is equivalent to the population formulated in the density matrix approach utilizing the Keldysh nonequilibrium Green's function method developed in Ref.…”