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We investigated a high-quality MgB$_{2}$ thin film with a thickness of$\sim$1000 nm on an Al$_{2}$O$_{3}$ substrate using optical spectroscopy. Wemeasured the reflectance spectra of the film at various temperatures bothbelow, and above, the superconducting transition temperature, $T_c$ $\simeq$ 40K. An earlier study showed that when the sample surface is exposed to air theoptical properties of the surface change immediately, however, the saturatedchange is negligibly small in the far-infrared region. The optical conductivityspectrum in the normal state shows two (narrow and broad) Drude modes, with thenarrow Drude mode being dominant in the low frequency region below 1000cm$^{-1}$. Our study, which uses a good-quality sample, provides more reliabledata on the optical properties of MgB$_2$, in a similar spectral range. Theoptical data is analyzed further using an extended Drude model, and theelectron-phonon spectral density function, $\alpha^2F(\omega)$, is extracted.The spectral density function $\alpha^2F(\omega)$ features two peaks: a smallone near 114 cm$^{-1}$, and a strong peak around the 550 cm$^{-1}$ where theB-B bond stretching phonon exists. Our data in the superconducting state doesnot show the expected energy shift of the onset of scattering associated withthe $\alpha^2F(\omega)$ peaks.

Revisiting optical properties of MgB$_{2}$ with a high-quality sample prepared by a HPCVD method