Photomixing of two near-infrared lasers is well established for continuous-wave terahertz spectroscopy. Photomixing of three lasers allows us to measure at three terahertz frequencies simultaneously. Similar to Fourier spectroscopy, the spectral info
rmation is contained in an nterferogram, which is equivalent to the waveform in time-domain spectroscopy. We use one fixed terahertz frequency u_ref to monitor temporal drifts of the setup, i.e., of the optical path-length difference. The other two frequencies are scanned for broadband high-resolution spectroscopy. The frequency dependence of the phase is obtained with high accuracy by normalizing it to the data obtained at u_ref, which eliminates drifts of the optical path-length difference. We achieve an accuracy of about 1-2 microns or 10^{-8} of the optical path length. This method is particularly suitable for applications in nonideal environmental conditions outside of an air-conditioned laboratory.
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 Deltaphi( u) betwee
n transmitter arm and receiver arm. A simple model based on three contributions yields a quantitative description of the overall behavior of Deltaphi( u). 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 (dDeltaphi / d u) is dominated by the contribution of periodic modulations of Deltaphi( u) 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.
In a continuous-wave terahertz system based on photomixing, the measured amplitude of the terahertz signal shows an uncertainty due to drifts of the responsivities of the photomixers and of the optical power illuminating the photomixers. We report on
a simple method to substantially reduce this uncertainty. By normalizing the amplitude to the DC photocurrents in both the transmitter and receiver photomixers, we achieve a significant increase of the stability. If, e.g., the optical power of one laser is reduced by 10%, the normalized signal is expected to change by only 0.3%, i.e., less than the typical uncertainty due to short-term fluctuations. This stabilization can be particularly valuable for terahertz applications in non-ideal environmental conditions outside of a temperature-stabilized laboratory.
