Volterra Integral Equation Approach to the Electron Dynamics in Intense Optical Pulses

Recent advances in laser technology have made it possible to utilized very high intensity optical pulses with wide range of wave-length to pump electrons in materials. This opened a new era in experimental physics to use pulse-lasers as a tool to manipulate electrons not only for the ultrafast probe into electronic states in materials, but also for a new means to obtain light with much higher frequebecause it is morencies than the pump-pulse. From theoretical side, this requires to establish a coherent theoretical framework to analyze the ultra fast dynamics of the electrons driven by high intensity light fields. In this article, I propose a novel theoretical technique to approach this subject. We formulate the Volterra integral equationsIntegral equation of second kind for that purpose. Although this is equivalent to the differential equations of Schrödinger, it has an advantage to treat the light-matter interactions as two independent modules; the intra-band drivingIntra-band driving and the inter-band drivingInter-band driving. The expression for the former can be obtained analytically in many cases and is incorporated into the theory as an integral kernelIntegral kernel. The formalism is applied to two simple models, the population inversionPopulation inversion in the molecules under intense laser beams in air, and the high harmonic generationsHigh harmonic generation in solids.