Measuring Complex Refractive Indices of a Nanometer-Thick Superconducting Film Using Terahertz Time-Domain Spectroscopy with a 10 Femtoseconds Pulse Laser

Superconducting thin films are widely applied in various fields, including switching devices, because of their phase transition behaviors in relation to temperature changes. Therefore, it is important to quantitatively determine the optical constant of a superconducting material in the thin-film state. We performed a terahertz time-domain spectroscopy, based on a 10 femtoseconds pulse laser, to measure the optical constant of a superconducting GdBa2Cu3O7−x (GdBCO) thin film in the terahertz region. We then estimated the terahertz refractive indices of the 70 nm-thick GdBCO film using a numerical extraction process, even though the film thickness was approximately 1/10,000 times smaller than the terahertz wavelength range of 200 μm to 1 mm. The resulting refractive indices of the GdBCO thin film were consistent with the theoretical results using the two-fluid model. Our work will help to further understand the terahertz optical properties of superconducting thin films with thicknesses under 100 nm, as well as provide a standard platform for characterizing the optical properties of thin films without the need of Kramers–Kronig transformation at the terahertz frequencies.