  Resonance dielectric response of excitons is studied for the high-quality
GaAs/InGaAs heterostructures with wide asymmetric quantum wells (QWs). To
highlight effects of the QW asymmetry, we have grown and studied several
heterostructures with nominally square QWs as well as with triangle-like QWs.
Several quantum confined exciton states are experimentally observed as narrow
exciton resonances with various profiles. A standard approach for the
phenomenological analysis of the profiles is generalized by introducing of
different phase shifts for the light waves reflected from the QWs at different
exciton resonances. Perfect agreement of the phenomenological fit to the
experimentally observed exciton spectra for high-quality structures allowed us
to obtain reliable parameters of the exciton resonances including the exciton
transition energies, the radiative broadenings, and the phase shifts. A direct
numerical solution of Schr\"{o}dinger equation for the heavy-hole excitons in
asymmetric QWs is used for microscopic modeling of the exciton resonances.
Remarkable agreement with the experiment is achieved when the effect of indium
segregation during the heterostructure growth is taken into account. The
segregation results in a modification of the potential profile, in particular,
in an asymmetry of the nominally square QWs.
