# Superconducting Electronic-Photonic Platform for HEB-Based Terahertz Spectrometers
## 1 Introduction  
Over the past few decades, the terahertz (THz) frequency band has attracted the attention of the scientific community in a variety of applications. The unique properties of THz radiation to harmlessly penetrate through non-metallic objects and biological tissues are useful for imaging and spectral measurements in medical and security systems, materials science and so forth [1; 2; 3; 4]. Number of recent studies suggests that THz photonic integrated circuits (PICs) are worth using in the next-generation wireless communications for an ultrafast on-chip THz signal generation and processing [5; 6]. Above 300 GHz, they mostly rely on a silicon platform and make use of either a topological or photonic crystal waveguides. Silicon PICs enable creation of THz circuits with numerous passive and active components interacting through low-loss dielectric media. They are especially in demand at frequencies beyond 1 THz, where performance of planar metallic waveguides conventionally used in THz electronic circuits is compromised [7; 8]. Use of photonic power distribution networks (PPDNs) not only enable reduction of on-chip propagation losses, but aids to avoid numerous issues related to packaging and assembly. With the appearance of modern solutions in THz PPDNs [9], flexibility in designing PIC grows. Synergy of electronic and photonic handling of THz signals is recognized as one of the most promising options [10]. However, development of non-linear frequency conversion devices naturally compatible with silicon PIC platform is at an early stage. In this study, we propose design of a THz hot electron bolometer (HEB) mixer that comprises a silicon photonic crystal waveguide integrated with two dielectric rod antenna (DRA) arrays through multimode interference power combiners. These arrays are to couple an HEB element with local oscillator (LO) and signal at 2.7 THz. The proposed design is based on low-loss conversion of a THz wave propagating in dielectric media into currents inside an HEB element. In contrast to the recently reported HEB-based PIC for classical and quantum photonics at telecommunicationwavelengths [11], our study addresses the issue of coupling efficiency between a dielectric waveguide and a superconducting microbridge much smaller than the guided wave. Superconducting HEB mixers are well known for their decent performance in the THz frequency band above 1 THz. They are traditionally in demand by radio astronomy for THz spectral line measurements, when superconductor-insulator-superconductor (SIS) and Schottky diode mixers face their fundamental limits and technological barriers [12; 13]. An HEB mixer requires extremely low LO power as compared to the semiconductor competitors. Furthermore, it is intrinsically a frequency non-selective electronic device, whose spectral features are predefined by the input optics design [14]. Modern THz HEB-based spectrometers rely on both quasioptical and waveguide designs of the mixers. Their operating bands are determined by the scientific interest to spectral signatures for different phases of the interstellar medium (ISM). The ISM phase tracers of interest are presented by [CII] at 1.9 THz, [HD] at 2.7 THz, [NII] at 2.45 and 5.23 THz, [OI] at 2.1 and 4.7 THz, and [OIII] at 3.4 and 5.8 THz [15]. Heterodyne HEB-aided observations at 4.7 THz are the focus of several upcoming balloon and space missions [16; 17]. Atmospheric transmittance of beyond 40% in number of windows within 7-14 THz enables ground-based observations in Antarctica [18]. This provides a good opportunity for studies of exoplanet formation and energy balance in ISM. At these frequencies, however, fabrication and packaging of electronic devices become technologically challenging. There are no examples of spectral instruments for radio astronomy operated beyond 7 THz so far. We believe that use of a superconducting electronic-photonic platform can simplify implementation of an HEB-based spectrometer for 7-14 THz operation.