Polarization dependence of the optical interband transition defined by the spatial variation of the valence p-orbital Bloch functions in quantum wires

We developed a method to express wave functions of hole states in semiconductor quantum wire (QWR) structures based on spatial variation of the valence p-orbital Bloch functions, to show how envelope wave functions relate to polarization-dependent interband transition. A wave function of a hole state is obtained solving the Schrödinger equation based on the 4 × 4 Luttinger Hamiltonian, and then recomposed by means of six bases of three p-orbital Bloch functions with two spin components. As a result, the hole wave function is expressed by six envelope wave functions for the six bases. Then, interband optical transition matrix elements with x-, y-, and z-polarizations are separately given by overlap integrals between envelope wave functions of holes for p_x, p_y, and p_z orbitals and those of electrons. We also calculate the wave functions for a modeled ridge QWR structure with mirror symmetry as well as for an asymmetric structure, and discuss the polarization dependence of the optical transition.