Several, nearly-1-µ$\mathrm{m}$-thick, pure, unhydrogenated amorphous-silicon (a-Si) thin layers were grown at high rates by non-equilibrium rf-magnetron Ar-plasma sputtering (RFMS) onto room-temperature low-cost glass substrates. A new approach is employed for the optical characterization of the thin-layer samples, which is based on some new formulae for the normal-incidence transmission of such a samples and on the adoption of the inverse-synthesis method, by using a devised Matlab GUI environment. The so-far existing limiting value of the thickness-non-uniformity parameter, $\Delta d$, when optically characterizing wedge-shaped layers, has been suppressed with the introduction of the appropriate corrections in the expression of transmittance. The optical responses of the H-free RFMS-a-Si thin films investigated, were successfully parameterized using a single, Kramers–Krönig (KK)-consistent, Tauc–Lorentz oscillator model, with the inclusion in the model of the Urbach tail (TLUC), in the present case of non-hydrogenated a-Si films. We have also employed the Wemple–DiDomenico (WDD) single-oscillator model to calculate the two WDD dispersion parameters, dispersion energy, $E_{\mathrm{d}}$, and oscillator energy, $E_{\mathrm{so}}$. The amorphous-to-crystalline mass-density ratio in the expression for $E_{\mathrm{d}}$ suggested by Wemple and DiDomenico is the key factor in understanding the refractive index behavior of the a-Si layers under study. The value of the porosity for the specific rf-magnetron sputtering deposition conditions employed in this work, with an Ar-pressure of ~4.4 Pa, is found to be approximately 21%. Additionally, it must be concluded that the adopted TLUC parameterization is highly accurate for the evaluation of the UV/visible/NIR transmittance measurements, on the H-free a-Si investigated. Finally, the performed experiments are needed to have more confidence of quick and accurate optical-characterizations techniques, in order to find new applications of a-Si layers in optics and optoelectronics.