Second-order optical processes and harmonic fields in solids

Abstract

A consistent method has been developed to calculate induced electromagnetic fields and optical transitions of electrons in a solid, in response to an incident laser beam of (circular) frequency ω. The analysis is based upon the independent-particle Schrodinger equation for electrons and Maxwell's equations for the electromagnetic fields. General expressions for linear and bilinear currents as well as second-order optical transition probabilities have been derived. It is shown that the second-order transition probability, which is proportional to the fourth power in the incident field, contains two different types of terms, describing double-photon transitions of the incident frequency ω and single-photon transitions of the harmonic frequency 2ω. An estimate has been made to show that in the case of centrosymmetric solids like metals, the relative contribution due to the single second-harmonic photon transition is of the order (e²/hc)²«1 in the optical region, compared with the double-fundamental-photon transition. However, in the case of solids lacking inversion symmetry, the contributions due to these two processes are estimated to be of the same order in magnitude.