Observation of Nanoscopic Thermal Expansion in Solids by Echo-Resolved Terahertz Spectroscopy

Thermal expansion of solids is a ubiquitous phenomenon in both everyday life and condensed matter physics [1]. However, this effect remained inaccessible for terahertz time-domain spectroscopy (THz-TDS) due to limitations caused by the relatively long sub-millimeter wavelengths of THz radiation. We address this challenge by introducing echo-resolved THz spectroscopy (ERTS) [2], which simultaneously determines frequency- dependent complex optical constants and material thickness by utilizing THz main and echo pulses in standard time-domain measurements. The rigorous numerical solution of complex transcendental transmission equations enables ERTS to disentangle temperature-dependent changes in both the complex refractive index and thickness of materials. We applied this approach to the technologically-relevant materials such as magnesium oxide (MgO) and sapphire (Al<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>O<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf>), and established their temperature-dependent properties in the temperature range of 10–300 K.