Contribution of physical and system parameters in the determination of optical constants of thin solid phase samples using THz time domain transmission spectroscopy

Abstract

Accurate estimation of complex refractive index of optically thin sample is an important challenge in terahertz time domain spectroscopy (THz-TDS). While majority of the previous studies on this topic consider Fabry-Perot (FP) effect as the primary cause of erroneous optical parameter extraction, advanced application criteria in industrial domains, such as, quality control of pharmaceutical composites or semiconductor heterostructure characterization etc. demand further assessment beyond FP effect only. Instead of conventional time-of-flight calculation pivoted to the reference data (usually obtained separately without any sample through air), we employed the differential data obtained from primary and secondary THz pulse through thin pellets to obtain accurate thickness mapping of the same. We observed that for pelletized samples with significantly larger porosity (>15%), the competing optical process like multiple internal scattering has greater impact on the accuracy of estimated optical properties. While in thin pelletized samples with smaller porosity (<10 %), the principal contributor of error is the non-uniform distribution of pellet thickness. For extremely thin pellets the optical parameter extraction is highly susceptible to uncertainties due to external factors such as environmental and/or system drift because of significantly small sample-THz interaction volume. Our observations indicate that short THz-sample interaction, porosity and non-uniformity of sample thickness are the principal causes of erroneous estimation of complex refractive index. It must be noted, however, that, this description does not specify an absolute value of material thickness but is highly dependent on the complex refractive index of the material itself. We also conclude that for specific material, there exists an optimized optical thickness beyond which the contribution of physical and system parameters in the determination of optical constants becomes minimal: it was determined to be around 3 mm for HDPE and 3.2 mm for PTFE. For most of the materials (with lower values of real and complex parts of optical constant) suitable for THz-TDS transmission spectroscopy, this critical thickness for accurate determination of the optical constant, therefore, is expected to be substantial, based on this present study.