Terahertz time-domain spectroscopy for simultaneous measurement of optical constants, and material thickness with deep-subwavelength precision

We present a method of terahertz time-domain spectroscopy (THz-TDS) in transmission configuration, which allows one to obtain the frequency-resolved complex-valued optical constants of the material, and to simultaneously determine the thickness of the investigated material sample with sub-micrometer precision. The thickness estimation achieves deep-subwavelength precision of the order of λ/1000. Our method is based on the numerical solution of transcendental transmission equations of Fourier-transformed main and echo THz pulses. It can be universally applied to materials with arbitrary absorption and refractive index dispersion as long as the echo THz signal in transmission is clearly discernible. As a first demonstration, several common dielectric materials such as MgO, Al₂O₃, GaAs, and SiO₂ were characterized. We also demonstrate that the conventionally employed THz time-of-flight thickness measurement approach leads to a systematic error when applied to absorptive materials.