Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers-Kronig relations

Abstract

In THz reflection spectroscopy the complex permittivity of an opaque medium is determined on the basis of the amplitude and of the phase of the reflected wave. There is usually a problem of phase error due to misplacement of the reference sample. Such experimental error brings inconsistency between phase and amplitude invoked by the causality principle. We propose a rigorous method to solve this relevant experimental problem by using an optimization method based upon singly subtractive KramersKronig relations. The applicability of the method is demonstrated for measured data on an n-type undoped (100) InAs wafer in the spectral range from 0.5 up to 2.5 THz.

Design and Analysis of CMOS-Based Terahertz Integrated Circuits by Causal Fractional-Order RLGC Transmission Line Model

“…One criteria to verify causality by tabulated S-parameters is to measure the error difference between imaginary part and its Hilbert transform of real part (25) Whether a system is causal or noncausal is determined by the error threshold that can be tolerated in the numerical analysis [38]. A smaller is usually desired to ensure the accuracy and the convergence in simulation.…”

Robust and accurate terahertz time-domain spectroscopic ellipsometry

“…This method is straightforward but has a significant phase misalignment problem, which is the bottleneck for achieving high accuracy [12]. Although many approaches have been published for calibrating this phase error [13][14][15], they still have some limitations on either the accuracy or the sample type [16,17]. Window-based reflection and attenuated total reflection (ATR) have a fixed window or prism surface providing a reference signal without phase misalignment, but they are basically only applicable for liquid or soft tissues, as solid samples would have a contact problem [18][19][20][21].…”

Spin‐density‐wave gap in (TMTSF)2PF6 probed by reflection‐type terahertz time‐domain spectroscopy

“…Compared to the widely used transmission-type systems, the reflection geometry has its own difficulty associated with the great sensitivity of the sample position and the incident angle. In particular, the precise determination of the sample position is difficult but essential to properly determine the phase spectra ( ) φ ω , where various experimental [8][9][10] and numerical [11,12] methods to correct the phase errors have been proposed. Another difficulty to study the SDW ground state is the smallness of the sample size.…”