# Superconducting Electronic-Photonic Platform for HEB-Based Terahertz Spectrometers
## 3 Results and Discussion
### Prototyping  
We fabricate a 50:1 scale prototype of Si forked antenna via direct machining of a dielectric substrate with relative permittivity of 10.2 and loss tangent of 0.003. A computer-aided milling and drilling process with a resolution in tool positioning of 0.625 \(\upmu\)m is employed. The fabricated prototype utilizes integrated photonic crystals with \(D=1\) mm, \(A_{Z}=1.26\) mm, and \(A_{Y}=2.18\) mm. The following geometric parameters are implemented: \(H_{d}=1.52\) mm, \(W_{pc}=10.46\) mm, \(L_{pc}=11.5\) mm, \(W_{a}=1.65\) mm, \(L_{ext}=1.05\) mm, \(\alpha=12^{\circ}\), and \(d=3\) mm. The prototype is also equipped with a 10\({}^{\circ}\) lateral taper at its output for coupling with hollow metallic waveguides of the measurement equipment.  
Referring to Figure 5, the experimental setup for beam profile measurements comprises a microwave frequency synthesizer, rotary stage, waveguide diode detector, and a lock-in amplifier. The synthesizer provides a 51 GHz continuous waveform (CW), with amplitude modulation (AM) at 1 kHz, widespread into a free space. The antenna prototype is coupled with a WR-15 input of the detector. The latter, in turn, is mounted on the rotary stage placed far behind a Frauhoffer distance in front of the synthesizer. The response voltage from the detector is fed into a lock-in amplifier. We use a microwave absorber to filter out spurious ambient radiation. For peak incident power levels of 0.28 \(\upmu\)W, the detector response voltage equals 550 \(\upmu\)V. Given that the detector noise voltage of 0.04 \(\upmu\)V is measured, we can conclude that the detector is operated within its specified dynamic range of 44-45 dB during the measurements.  
Figure 4: EM model of a nearly all-dielectric 2.7 THz HEB mixer based on integrated Si photonic crystals.  
As one can see in Figure 6, far-field beam of the fabricated 51 GHz forked antenna has a 27\({}^{\circ}\) wide main lobe with high Gaussisity in the antenna plane. The observed side lobe level does not exceed \(-12\) dB, which outperforms similar low-permittivity designs earlier reported in the literature [27]. Experimental data are in good agreement with the results of EM simulations. The latter, in turn, predict the antenna gain of 11.2 dB with a side lobe level of \(-12.1\) dB and a half-power beamwidth of 21\({}^{\circ}\) for the geometry developed. Such a behavior is also consistent with the forecasts of the 2.7 THz EM models for the Si platform. A further increase in the beam directivity is possible upon combining the developed dielectric forked antennas in linear or planar arrays.  
We also consider feasibility of prototyping for the entire PIC of an HEB mixer. A superconducting microbridge can be replaced by a microwave Schottky diode integrated with TSL. However, our machinery enables milling cuts only beyond 200 \(\upmu\)m. It drastically exceeds linear dimensions of a scaled-up 50 \(\Omega\) microbridge acting as an HEB element in EM simulations. This, in turn, largely affects coupling between elements of the PIC. However, specific propagation losses in dielectric waveguides with the chosen photonic crystal geometry of below 0.1 dB/mm were preliminary measured by us in [28]. This suggests that the ultimate sensitivity of the mixer is not compromised by input losses in the developed PPDNs.  
Figure 5: Experimental setup for beam profile measurements at 50–52 GHz.  
Figure 6: Beam profiles of dielectric forked antennas designed for operation at 50–52 GHz.