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Abstract

The reflection of electrons from standing light waves is known as the Kapitza-Dirac effect. This thesis investigates the two-photon Kapitza-Dirac effect for electrons in the Bragg regime with elliptically polarized light fields. This means that the electrons can gather exactly two photon momenta in the standing light wave which is composed of two counterpropagating light waves of elliptical polarization. For this purpose, the time evolution of an electron is simulated by means of the Dirac equation in a one dimensional model. If the two light waves have equal helicity, the scattering process becomes suppressed for elliptical polarization and vanishes completely for circular polarization. If the two light waves have opposite helicity, the scattering is not suppressed and for sufficiently long interaction times spin effects arise that influence the scattering process. The spin expectation value of the electron oscillates and this oscillation is a superposition of two oscillations. These oscillations become fastest for circular polarization and vanish for linear polarization. It is shown that both cases can effectively be described by wave equations with time independent Hamiltonians. In the case of equal helicity the wave function obeys a Schrödinger equation while in the case of opposite helicity it obeys a Pauli equation with relativistic corrections.