# Superconducting Electronic-Photonic Platform for HEB-Based Terahertz Spectrometers
## 3 Results and Discussion
### EM Simulations
To implement a uniform linear array with a zero-phase increment between antennas, we extend two central DRAs by Si ribbon inserts. Details on the geometry developed for the 2.7 THz operation are summarized in Table 2. This geometry ensures simulated gain of 12 dB with a corresponding side lobe level of \(-13.1\) dB and decent matching to a single-mode Si waveguide. The half-power beamwidth equals \(26^{\circ}\) in the DRA array plane. In the EM simulations, as before, dielectric losses in Si are neglected, and its relative permittivity is set to 11.9. When calculating the radiation pattern of the DRA array integrated with MMIPC, we rely on the principle of reversibility and simulate its performance in a transmitting mode. The MMIPC side walls and the DRA array are surrounded by quarter-wave vacuum insets terminated by radiation boundaries. The MMIPC single output is excited by a wave port. The port has linear dimensions of \(0.648\lambda_{0}\,\times\,0.324\lambda_{0}\) (width \(\times\) height), mode polarity is set using integration lines, and no post processing is performed. Footprints of the developed Si antennas and the transition from a Si ribbon waveguide to a 50 \(\Omega\) microbridge are further used in the design of a nearly all-dielectric HEB mixer. Referring to Figure 4, we use the technology of integrated Si photonic crystals to define contours of the mixer structural elements. Hexagonal lattice of openings with a diameter \(D=18\)\(\mu\)m and lattice constants \(A_{Z}=23.4\)\(\mu\)m, \(A_{Y}=40.5\)\(\mu\)m is implemented in a 27 \(\mu\)m thick Si substrate. Driven by the lattice constraints, we choose \(W_{pc}=194.1\)\(\mu\)m and \(L_{pc}=213.2\)\(\mu\)m. The distances are measured between tangents to the inner edges of openings defining contour of MMIPC. Spacing between DRAs \(d=50.9\)\(\mu\)m. Other geometric parameters remain unchanged. \begin{table}
\begin{tabular}{c c c c c c c} \hline \(H_{d}\) [\(\mu\)m] & \(W_{pc}\) [\(\mu\)m] & \(L_{pc}\) [\(\mu\)m] & \(W_{a}\) [\(\mu\)m] & \(L_{ext}\) [\(\mu\)m] & \(\alpha\) [\({}^{\circ}\)] & \(d\) [\(\mu\)m] \\ \hline
27 & 205.6 & 222.2 & 30.6 & 19.5 & 12 Analysis of the EM field pattern in the developed PIC reveals no degradation of the mixer input losses upon integration of its elements. Radiation patterns of THz input lines, however, are affected by the changes in geometry of MMIPCs and boundary conditions at their laterals and outputs. Thus, revised Si forked antennas demonstrate gain of 12.1 dB with a side lobe level of \(-\)11 dB. The half-power beamwidth equals 17\({}^{\circ}\) in the PIC plane. Given that the integrated Si waveguiding structure makes use of photonic crystals and multimode interference effects, its operation frequency band is narrow. However, it covers at least three times the intermediate frequency bandwidth of a typical HEB mixer which is sufficient from a practical point of view. Furthermore, the achievable input losses of 2.4 dB compete with those in the input optics of THz receivers making use of conventional hollow metallic waveguides at 2.7 THz and outperform them in the range of 7-14 THz [9]. To confirm and complete our findings, we perform prototyping of the developed Si structures at an enlarged scale.