Group delay in THz spectroscopy with ultra-wideband log-spiral antennae

TL;DR

This paper investigates the group delay in THz spectroscopy using ultra-wideband log-spiral antennas, modeling phase differences, and analyzing their impact on time-domain signal interpretation.

Contribution

It introduces a quantitative model of phase contributions in THz spectroscopy with log-spiral antennas, enabling improved understanding and correction of group delay effects.

Findings

Phase difference contributions are modeled and quantified.

Log-spiral antennas cause frequency-dependent group delay.

Correcting phase contributions sharpens time-domain signals.

Abstract

We report on the group delay observed in continuous-wave terahertz spectroscopy based on photomixing with phase-sensitive homodyne detection. We discuss the different contributions of the experimental setup to the phase difference \Delta\phi(\nu) between transmitter arm and receiver arm. A simple model based on three contributions yields a quantitative description of the overall behavior of \Delta\phi(\nu). Firstly, the optical path-length difference gives rise to a term linear in frequency. Secondly, the ultra-wideband log-spiral antennae effectively radiate and receive in a frequency-dependent active region, which in the most simple model is an annular area with a circumference equal to the wavelength. The corresponding term changes by roughly 6 pi between 100 GHz and 1 THz. The third contribution stems from the photomixer impedance. In contrast, the derivative (d\Delta\phi / d\nu) is dominated by the contribution of periodic modulations of \Delta\phi(\nu) caused by standing waves, e.g., in the photomixers' Si lenses. Furthermore, we discuss the Fourier-transformed spectra, which are equivalent to the waveform in a time-domain experiment. In the time domain, the group delay introduced by the log-spiral antennae gives rise to strongly chirped signals, in which low frequencies are delayed. Correcting for the contributions of antennae and photomixers yields sharp peaks or "pulses" and thus facilitates a time-domain-like analysis of our continuous-wave data.