Localization of light waves in Fibonacci dielectric multilayers

We have measured the optical transmission of quasiperiodic dielectric multilayer stacks of ${\mathrm{SiO}}_2$ (A) and ${\mathrm{TiO}}_2$ (b) thin films which are ordered according to a Fibonacci sequence ${\mathit{S}}_{\mathit{j}+1\mathrm{}}$={${\mathit{S}}_{\mathit{j}\mathrm{-}1}$}, with ${\mathit{S}}_0$={B} and ${\mathit{S}}_1$={A} up to the sequence ${\mathit{S}}_9$ which consists of 55 layers. We observe a scaling of the transmission coefficient with increasing Fibonacci sequences at quarter-wavelength optical thicknesses. This behavior is in good agreement with theory and can be considered as experimental evidence for the localization of the light waves. The persistence of strong suppression of the transmission (gaps) in the presence of variations in the refractive indices among the layers is surprising.