applied sciences Article  
Broadband Dielectric Characterization of High-Permittivity Rogers Substrates via Terahertz Time-Domain Spectroscopy in Reflection Mode [PERSON]  
[PERSON]  
[PERSON]  
[PERSON]  
[PERSON]  
Cosiglio Nazionale delle Ricerche, Istituto per la Microelettronica e Microsistemi, 00133 Rome, Italy  
\({}^{\star}\) Correspondence: [EMAIL_ADDRESS]  
Fuscaldo  
At such high frequencies, the dielectric properties of widely employed PCB materials can significantly change from those provided by the manufacturer at lower frequencies, thus calling for an accurate characterization, which is also capable of dealing with the possible non-negligible frequency dispersion of the generally complex-valued dielectric constant. This aspect is of key importance for the design of future components, whose performance can be dramatically influenced by the frequency dispersion of both the dielectric permittivity and loss tangent. That said, commercial laminates such as those from Rogers and Taconic are potential candidates for applications in millimeter-wave or (sub-)THz frequencies [8]. However, only few works [1, 9, 10, 11] reported thus far a characterization of the dielectric properties of common laminates at millimeter-wave and/or sub-THz frequencies. In [1], Rogers and Taconic substrates were characterized in the W-band (namely, 75-110 GHz) through a voltage network analyzer (VNA) approach: the dielectric properties were extracted from the S-parameters of a substrate-integrated waveguide (SIW) resonator. In [11], Rogers substrates were characterized through THz time-domain spectroscopy (TDS) at higher frequencies (viz., 0.2-1.8 THz), whereas the works in [9, 10] compared and complemented the THz-TDS measurements of low-temperature cofired ceramics [9] and Rogers substrates [10] with VNA measurements. Indeed, THz-TDS measurements cannot provide accurate results at frequencies below 300 GHz where there is not enough dynamic range with respect to the noise floor. Conversely, VNA measurements provide accurate results below 300 GHz but extensions are available only up to 1.5 THz (with a substantial increase of equipment cost). The two approaches, namely THz-TDS and VNA, can thus be seen as complementary, yet they produce comparable results [12]. Notwithstanding, most THz-TDS measurements are performed in transmission mode (see, e.g., [13]), and only in few cases the reflection mode [14, 15, 16, 17] has been exploited; in none of these cases the properties of the Rogers materials have been characterized. However, as recently emphasized in [17], the reflection mode not only represents a powerful, effective technique for retrieving the complex-valued frequency dispersion of the dielectric properties of moderately reflective and lossy materials, but it also represents a natural environment (as opposed to the transmission mode) for backmetallized substrates. The latter represents a key component in systems such as THz antenna [18, 19, 20] and static or reconfigurable reflective metasurfaces for THz-wave manipulation, e.g., absorption [21, 22] or beam steering [23]. For this purpose, we report here for the first time a THz-TDS characterization in reflection mode of three types of high-permittivity Rogers laminates (RO3010, RO/duroid 6010.2 LM, and TMM10i), representative of different product series, in the sub-THz range (namely, from 0.3-1 THz). The frequency dispersion of their complex dielectric permittivity is described by a single standard Lorentzian term, which is shown to accurately reproduce the experimentally measured reflectance spectra through a fitting optimization procedure based on an analytical transmission-line model. Despite the fact that all three materials have similar nominal properties in the microwave X-band, the study clearly demonstrates their different dielectric properties in the investigated sub-THz spectrum. It is shown that RO3010 and RO/duroid 6010.2 LM exhibit significant frequency dispersion, which cannot be neglected in the design of broadband THz components.