## 1 Introduction  
Thanks to the considerable absolute bandwidth, terahertz (THz) communication promises to have the advantages of large capacity, high transmission rate, high security, strong directivity and good penetration. However, due to the serious atmospheric attenuation in THz bands [1], the effective detection of ultrasensitive THz receivers is highly demanded. Due to the limitation of low power and high cost of THz source, harmonic mixer is more popular than fundamental mixer. The higher the number of harmonics, the lower the frequency and cost of the local oscillator (LO).  
Semiconductor-based THz heterodyne receivers, generally operating at room temperature, have been widely developed using Schottky barrier diodes [2], high-electron-mobility transistors [3], complementary metal-oxide-semiconductor [4] and silicon-germanium [5] technologies. However, the maximum harmonic number up to 20 is from the Schottky barrier diode produced by Virginia Diodes, Inc. (VDI) [6]. Nowadays, high-\(T_{\text{c}}\) superconducting (HTS) YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-6}\) (YBCO) Josephson junction (JJ) is becoming the most attractive harmonic mixer for THz heterodyne receiver, caused by the advantages of excellent sensitivity, wide bandwidth, high harmonic number and low LO power requirement [7]. Broadband antennas with complementary structure have been extensively used in superconducting mixers to enhance the THz signal coupling, such as log-periodic and log-spiral antennas [8]. However, the impedances of this kind of antennas are very high (approximately 188.5 \(\Omega\) with self-complementary structure in free space), while the normal-state resistances of the YBCO JJs are only several ohms, still resulting in the low coupling efficiencies between antennas and JJs. Thus, the maximum harmonic number cannot be improved in the mixing because of the impedance mismatch. Recently, many works have been reported to enhance the mixing performance of YBCO JJ mixers, including the harmonic number in the mixing [9; 10; 11]. It shows that the maximum harmonic number from YBCO step-edge JJ is around 30, a bit higher than that with a semiconducting THz mixer. Thus, the enhancement of the maximum harmonic number of the YBCO JJ mixer urgently needs to be explored for THz communications.  
In reported traditional antennas, slot antennas [12; 13; 14; 15] were the main choices to match the impedance of JJ, such as double-slot antenna [16] and ring-slot antenna [17; 18]. However, these kinds of antennas have to be fed by coplanar waveguide (CPW), meaning the shape of the ground has to be changed during the impedance matching. The impedance matching to a low-input impedance based on traditional antennas with coplanar striplines (CPSs) feeding for a JJ mixer is little reported. The influence of ground shape on the antenna impedance would no longer be considered if the differential CPSs were adopted. The bowtie structure was first proposed by [PERSON] et al. [19] and applied to many THz detectors [20; 21; 22; 23; 24]. Because of the simple structure and low cost, it is a good choice to match the impedance with YBCO JJ mixer and feed it by CPSs. Traditional bowtie antennas often have impedances as high as hundreds of ohms.  
In this paper, we adopt two types of stub tuners on bowtie antennas to reduce antenna impedances. The performance of YBCO bicrystal JJ harmonic mixers coupled with these two antennas and fed by CPSs are reported, respectively. Since one of the THz windows is located at 0.21 THz [1], we study the maximum harmonic number of mixers at 0.21 THz. Up to the 88 th harmonic has been measured in the mixing when one mixer is coupled with a pair of open-end stubs of the bowtie antenna, while the other one, which coupled with a pair of lumped-element stubs of the bowtie antenna, has a maximum harmonic number of 30. Later, numerical simulations are carried out to analyze the reasons for different performance.