## 3 Experiment Setup for Homodyne Detection  
For the characterization of the TeraFET's homodyne response in a broad frequency range from 0.1 up to 2.2 THz, we used two similar photomixer-based THz sources from the Toptica system in a homodyne scheme (TX1 and TX2, see Figure 1a) with a modulation frequency of 7.9 kHz. For the collimation and focusing of two THz beams onto the test detector, we constructed an imaging system with a two-inch diameter and four-inch effective focal length off-axis parabolic mirrors and a wire grid beamsplitter. The THz radiation is incident on the antenna from the detector's bottom through a hyper-hemispherical silicon lens and a reduced, 280 \(\mathrm{\SIUnitSymbolMicro m}\) thick \(\mathrm{p}\)-doped Si substrate of the chip. The lens has 12 mm diameter and 7.2 mm height with an additional 440 \(\mathrm{\SIUnitSymbolMicro m}\) thick substrate. The THz beams are modulated electrically with a built-in function generator enabling to employ the lock-in amplifier. Similarly, as it is used in a commercial photomixer-based system, we have not performed any additional effort regarding phase stabilization. We relied on a built-in  
Figure 2: (**a**) The measured optical voltage responsivity \(\Psi_{\mathrm{V}}\) (dashed curve, left axis) and optical NEP (solid curve, right axis) of the detector at 609 GHz as a gate voltage function. The VDI source was used for measurements. (**b**) The measured optical NEP dependency on a frequency of the photomixer source used in the homodyne experiment. laser control, which was developed by Toptica GmbH, providing good measurement-to-measurement reproducibility of laser emission frequencies when the lasers are temperature-stabilized; additionally, the external conditions did not vary, thus maintaining the same spatial delay. In order to test the similarity of THz bias-modulated photomixers, we measured the frequency-dependent responses of the detector on both setup arms. The characterization results are presented in Figure 3a. Both sources provide a maximum THz output power at 100 GHz and fade out nearly exponentially with frequency. In a broad range, photomixers exhibited similar power levels except for a narrow band (120-350 GHz) where the difference reached 50%. The difference in the response values for TX1 and TX2 is related to the loss on a wire grid combiner and the differences in the individual sources' performances. The theory predicts that TeraFETs, when excited with low powers, behave as linear power detectors. The response linearity is maintained in different material systems [33] as well as for different biasing regimes [15; 34]. The TeraFET's voltage signal is proportional to the THz beam power and can be expressed using (1) as:  
\[V_{\text{det}}=\Re_{\text{V}}\cdot P_{\text{THz}}\propto\Re_{\text{V}}\cdot V_{ \text{THz}}^{2}, \tag{3}\]  
where the radiation power \(P_{\text{THz}}\) is proportional to the squared excitation amplitude \(V_{\text{THz}}\). The difficulty of detecting a weak signal of sub-millimeter radiation can be reduced using a well-known homodyne technique. In a homodyne detection scheme, the detector is excited with two superimposed beams oscillating with the same angular frequency \(\omega\) but differentiating in phase and/or amplitude (see Figure 1a). The phase can be introduced in  
Figure 3: (**a**) Power of the THz sources in the homodyne experiment setup (marked as TX1, blue line, and TX2, red line). The measurement was provided using the same TerFET detector at the gate voltage of 475 mV. The reference measurement of the original Toptica system’s power with only one source TX1 is also presented for comparison purposes (black line). It was recorded with the pyroelectric detector. (**b**) Measured homodyne signal of TeraFET, which was biased at the same gate voltage. The magnification shows oscillations. the form of a difference in beam paths \(\Delta L\).