## Appendix A Frequency-Domain Photomixing Spectrometer  
Like TDS, frequency-domain photomixing utilizes ultrafast photoconductive emitters and detectors, but is driven by single frequency temperature-tunable distributed feedback (DFB) semiconductor lasers rather than mode-locked lasers. The photomixer provides a tunable difference frequency output from below 100 GHz to \(\sim\)1.5 THz, with an instantaneous linewidth of \(\sim\)50 MHz or better [18; 33]. The difference frequency can be monitored accurate to \(\sim\)100 MHz using a commercial wavemeter, such as the one shown in Figure 1. The photomixers are fabricated at the center of a compact planar square-spiral antenna, which radiates a primarily circular polarized beam above \(\sim\)200 GHz. Including antenna impedance effects, the bandwidth of each photomixer is roughly 1.0 THz. One photomixer acts as the transmitter (Tx) and the other acts as the receiver (Rx), as shown in the photograph of Figure 11. The radiation from the transmit photomixer is coupled from the antenna to free space through a high-resistivity silicon hyperhemispherical lens. The THz beam is then collimated using an aspherical optic, an off-axis paraboloid. The reverse process occurs between free space and the receive photomixer.  
The nanofluidic chip is located immediately below the transmit photomixer coupling lens (a silicone hyperhemisphere) where the spot diameter is small (\(\sim\)3 mm diameter), as determined by the photomixer spiral antenna and the thickness of the lens. Assuming an average power of 1.0 \(\mu\)W and an instantaneous linewidth of 50 MHz, the THz beam at this point has a spatial intensity of \(\sim\)1.4 \(\times\) 10\({}^{-5}\) W/cm\({}^{2}\), and the power spectral intensity is \(\sim\)0.7 \(\times\) 10\({}^{-3}\) W/cm\({}^{2}\)-GHz. We have found the latter quantity to be a good performance metric for THz sources in high-resolution spectroscopy.  
Because the lasers driving the transmit and receive photomixers are both single frequency and coherent, the THz beam at the receive photomixer is mixed down in frequency by quasi-homodyne conversion. A simple amplitude modulation of the bias voltage on the transmit photomixer then allows for DC offset and straightforward synchronous detection of the receiver output using a lock-in amplifier, the same benefits as traditional homodyne transceivers. With no samples in the THz path, this spectrometer can produce a high dynamic range, up to 70-80 dB at 100 GHz and 40-50 dB at 1.0 THz. This assumes good alignment of the THz beam between the transmitter and receiver, which is non-trivial when there are substrate-based samples located in the beam path, since such samples can steer the beam. The stated dynamic range values can be achieved without evacuation of the free space portion of the spectrometer so that water vapor absorption lines do appear, especiallywhen the ambient humidity is high. Unless one of these water vapor lines coincides with a signature from the sample of interest, this does not pose a big problem. On the contrary, because the water vapor lines are highly resolved, their known shape and strength is sometimes used to monitor the absolute frequency and dynamic range of the instrument.  
An important practical aspect of our photomixing spectrometer is scan time. Because the DFB laser frequencies are temperature tuned, and because the temperature is set by thermoelectric modules, significant time is required for each sample frequency point. For the 0.5 GHz steps in the present experiments, that time is about 1 s per point, so that a 500 GHz scan takes about 20 min. This is why it is important to establish a fluidic steady state in the nanochannels prior to starting the THz frequency scans.