Material and optical approaches to exciton polaritons in multiple quantum wells: Formal results

The theory of exciton polaritons in multiple quantum wells with arbitrary interwell spacings between successive wells is approached from two alternative viewpoints. The material approach considers the Green’s function for the coupled exciton-electromagnetic modes of the structure viewed as the interband elementary excitations of the crystal. The optical approach considers the light transmitted and reflected given an incident electromagnetic wave in linear-dispersion theory or, equivalently, the behavior of the modes of the vacuum fluctuations in the context of quantum electrodynamics. The optical approach is formulated in terms of transfer matrices. The complementary nature of the two methods is discussed. The theory describes T-mode polaritons and also a type of LZ-mixed-mode polaritons [a special case of LT-mixed-mode polaritons, in the terminology of K. Cho, Solid State Commun. 33, 911 (1980)] in multiple quantum wells. It is shown, however, that the effects of LZ mixing are negligibly small for GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As multiple quantum wells in which the constituent wells are of width much less than the relevant optical wavelength.