# Superconducting Electronic-Photonic Platform for HEB-Based Terahertz Spectrometers
## 2 Materials and Methods  
In this section, we focus on the input optics of an HEB mixer utilizing Si waveguiding structures. The basic concept and expected performance of the mixer are further discussed in terms of both electromagnetic (EM) modeling and prototyping of its key structural elements.  
Transfer of an EM field energy from one point of space to another is one of the most fundamental tasks in number of practical applications. The transfer can be maintained via transmission lines or with the aid of free space optics relying on the use of transmitting and receiving antennas. The choice of antenna type is determined by the demands of a specific application and has to be compliant with requirements on its beam pattern and matching with a feeding network. In turn, these parameters can be noticeably tuned for a given type of antenna if a phased antenna array is implemented [19].  
Upon use of PPDNs, two general options are available for coupling PIC with external signal sources. The first option is to use a grating coupler and to receive signal along the axis perpendicular to the PIC plane. Such a technique is capable of providing input losses as low as 1 dB over a fractional bandwidth of 3-5% [20]. The second option is related to end-fire coupling. This technique relies on the injection of external Gaussian beam into the unloaded end of a dielectric waveguide terminating PIC. The injection is maintained along the waveguide axis either directly or through a mode size transformer [21]. This devise is basically a dielectric taper. It can be effectively used in either a directive reception/transmission of EM radiation from/into a free space or in maintaining transition from hollow metallic waveguides to PPDNs and vice versa. In our design, we choose an end-fire coupling as a proof-of-concept solution. It ensures implementation simplicity at the stage of cleanroom fabrication and, later on, during packaging and assembly at the final stage. We develop a dielectric taper structure acting as DRA [22; 23] in a four-element linear antenna array operated at 2.7 THz. The array output is harvested by a 4 \(\times\) 1 ports multimode interference power combiner (MMIPC), which is terminated by a photonic crystal waveguide (PCWG). The latter, in turn, is integrated with an HEB-loaded tapered slot line (TSL). The coupling scheme is used for the implementation of signal and LO input lines of a nearly all-dielectric mixer.  
Figure 1 provides a three-dimensional (3D) model of a nearly all-dielectric HEB mixer designed for operation at 2.7 THz. Openings in Si are used to define geometries of MMIPC and PCWG. Four-wire biasing of the HEB element is implemented.  
The conversion of an EM wave propagating in dielectric media into an alternating current (AC) inside HEB is the core in the proposed design. The conversion can be maintained by coupling HEB to PCWG either directly or through a planar metallic probe. There are examples of the former implementation in infrared (IR) range [11]. At 2.7 THz, however, the working area of the superconducting film is expected to be quite large, since the wavelength of EM radiation in Si equals 32 \(\upmu\)m. This consequently leads to a drastic increase in the LO power required for operation of the mixer. Potential use of plasmonic antennas for enhanced coupling faces the same issue [24]. Alternatively, when TSL is employed as an EM probe, conventional linear dimensions of the superconducting film not exceeding a few microns can be chosen.