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We present Maxwell equations with source terms for the electromagnetic fieldinteracting with a moving electron in a spin-orbit coupled semiconductorheterostructure. We start with the eight--band ${\bm k}{\bm p}$ model andderive the electric and magnetic polarization vectors using the Gordon--likedecomposition method. Next, we present the ${\bm k}{\bm p}$ effectiveLagrangian for the nonparabolic conduction band electrons interacting withelectromagnetic field in semiconductor heterostructures with abrupt interfaces.This Lagrangian gives rise to the Maxwell equations with source terms andboundary conditions at heterointerfaces as well as equations for the electronenvelope wave function in the external electromagnetic field together withappropriate boundary conditions. As an example, we consider spin--orbit effectscaused by the structure inversion asymmetry for the conduction electron states.We compute the intrinsic contribution to the electric polarization of thesteady state electron gas in asymmetric quantum well in equilibrium and in thespin Hall regime. We argue that this contribution, as well as the intrinsicspin Hall current, are not cancelled by the elastic scattering processes.

Intrinsic electric polarization in spin-orbit coupled semiconductor heterostructures