A unified view of one-electron mechanisms for non-linear refraction in a semiconductor

Abstract

An expression is derived for the third-order polarization of a two-level electronic system induced by a plane polarized light pulse, including the effects not only of recombination and dephasing, but also of the rise time of the pulse. It is shown that the expression encompasses all three main electronic mechanisms that lead to an intensity-dependent refractive index, namely the blocking of interband optical transitions by free carriers (the band filling effect), virtual interband transitions, and the motion of free carriers in the non-parabolic band. It also shows explicitly the regimes in which each mechanism dominates. It is also shown (i) how the transition from the virtual interband transition regime to the band filling regime is brought about by the frequency dependence of the dephasing time, (ii) that near resonance the virtual interband transition mechanism is just a casual consequence of the optical Stark effect and (iii) that the intensitydependent refractive index resulting from the motion of free carriers is the causal consequence of the intensity-dependent shifts in the energy levels, leading to an intensity-dependent effective mass. How the non-linear response of the semiconductor changes as the frequency of the light pulse is changed is discussed in physical terms

The relationship between real and virtual excitation mechanisms for nonlinear refraction

“…In a previous paper (Burt 1990a), the author used a simple two-level model to clarify the relationship between the various one-electron mechanisms that give rise to nonlinear refraction in semiconductors; one algebraic expression for the third-order polarization was able to account for the state filling effect, virtual transitions (adiabatic coherent excitation) near resonance, and at low frequencies, the band non-parabolicity effect on free carriers. Implicit in Burt (1990a), and highlighted in a subsequent paper (Burt 1990b), is the well known result (Wherrett 1983(Wherrett , 1984 and references therein) that the nonlinear refraction near resonance due to state filling is augmented by a factor 2Tl/T, compared with that due to virtual transitions (q is the lifetime and is the dephasing time). One of the purposes of this paper is to give a physical explanation of this factor.…”