Quantum-well reflectivity and exciton-polariton dispersion

We prove that reflectivity measurements as a function of angle of incidence allow the measurement of the exciton-polariton modes in quantum wells. The resonant polaritons at ${\mathit{k}}_{\mathrm{?}}$<${\mathit{k}}_0$=ω/v manifest themselves as peaks in the reflectivity while surface polaritons at ${\mathit{k}}_{\mathrm{?}}$>${\mathit{k}}_0$ manifest themselves as dips in the attenuated total reflection. A comparison of the reflectivities with polarization perpendicular and parallel to the plane of incidence allows us to detect the different polariton modes and to measure the dispersion relation. We also give expressions to compute reflectivity and transmission for the case of multiple quantum wells, including the effects of multiple reflections. Examples are given for standard reflectivity of GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells and for attenuated total reflection of CuCl/${\mathrm{CaF}}_2$ quantum wells.