Group Delay in THz Spectroscopy with Ultra-Wideband Log-Spiral Antennae

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 Δφ(ν) between transmitter arm and receiver arm. A simple model based on three contributions yields a quantitative description of the overall behavior of Δφ(ν). Firstly, the optical path-length difference gives rise to a term linear in frequency ν. 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 6π between 100 GHz and 1 THz. The third contribution stems from the photomixer impedance. In contrast, the derivative ∂Δφ/∂ ν is dominated by the contribution of periodic modulations of Δφ(ν) 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.