Fourier transform spectral interferometry is applied to measure both amplit
ude and phase of the electric field in different types of semiconductor nan
ostructures, thus determining the real and imaginary parts of the dielectri
c function, The importance of measuring the phase is shown and discussed in
three studies. First, the phase measurement is used to access directly the
refractive index across excitonic resonances in bulk GaAs and AlGaAs-GaAs
quantum wells, with unprecedented resolution. Second, we measure the densit
y dependence of the full dielectric function across a Fano resonance in bul
k GaAs and show that this allows us to obtain some information on the colli
sional broadening of the usually hidden linewidth of the coupled esciton/co
ntinuum. Third, the phase is studied in a complex heterostructure, a semico
nductor microcavity. We investigate and discuss the effect of the cavity de
tuning and of the excitation density.