# Voltage Tunable Spoof Surface Plasmon Polariton Waveguide Loaded with Ferroelectric Resonators
## 1 Introduction  
As is well-known, the spoof surface plasmon polariton (SSPP) concept proposed by [PERSON] is a kind of artificial EM wave propagating in corrugated metal, which mimics the natural inherent electron oscillation on the metal surface, named surface plasmon polaritons (SPPs) [1, 2, 3]. Since SSPPs can expand the SPP effect to GHz and THz bands through subwavelength engineering in metal, they have become more flexible and have generated increasing enthusiasm since their proposal. In 2012, [PERSON] et al. proposed the concept of a localized spoof surface plasmonic (LSSP), which refers to the 2D or 3D periodical plasmonic structures on the surface of metal particles, resonating in the excited standing wave mode [4]. The EM field of the resonating LSSP is highly confined near the metal interface, with a strong enhancement effect, and is highly sensitive to the geometry and local dielectric environment [5, 6]. For example, in 2021, [PERSON] proposed a ring plasma resonator to achieve both high efficiency and high Q capture mode excitation [7]. In particular, when utilizing coupled mode theory, multipolar plasmonic modes can be excited [8, 9, 10, 11, 12], which have sharper resonances than the basic dipole mode, and hence provide a higher Q value. Owing to these priorities, LSSPs have been widely used in optical antennas [13, 14, 15, 16], chemical and biological sensors [17, 18, 19, 20, 21], and superlenses [22, 23]. However, the previously designed LSSP was mostly static, which means the resonantproperties had been solidified once the structure was fabricated. This unitary resonance is not conducive to modern complex communication environments. Thus, the real-time adjustability and experimental flexibility of multiple LSSPs become a major challenge. Certain researchers started utilizing diverse measurement techniques to adjust LSSPs. For example, PIN diodes for the electric tuning of LSSPs have been employed [24; 25; 26]. [PERSON] et al. utilized Yttrium Iron Garnet (YIG) ferrite for magnetically adjusting the ferromagnetic resonance field of the LSSP resonator [27]. Furthermore, a varactor diode and micro-electro-mechanical system (MEMS) have also been used as active elements for tuning LSSPs [28; 29; 30]. However, due to the complexity and variability of the communication environment, more regulatory measures need to be continuously expanded. Ferroelectric materials can realize the exotic regulation of dielectric permittivity with an applied DC electric field, which has potential applications in tunable LSSP resonators [31; 32; 33; 34; 35]. The advanced features of ferroelectrics include their capability for continuous tunability, with high permittivity, low loss, and fast responses [36; 37; 38; 39]. It is emphasized that the efficiency of the electrical tunability of ferroelectric resonators is larger than that of conventional liquid crystal devices [40; 41; 42; 43]. The frequency stability, precision, durability, reliability, and vibration resistance of ferroelectric resonators are obviously superior to MEMSs and phase-change materials [44; 45]. Also, ferroelectric resonators can be flexibly regulated by employing structure engineering as well as composition fluctuation [46; 47; 48; 49; 50; 51]. However, until now, few works have comprehensively exploited the modulation mechanism of the ferroelectric resonator. In this paper, we use the promising environmentally friendly ferroelectric Ba\({}_{0.85}\)Ca\({}_{0.15}\)Zr\({}_{0.9}\)Ti\({}_{0.1}\)O\({}_{3}\) (BCZT) layer for fabricating an LSSP resonator. An exhaustive study on the structure engineering as well as the voltage tunability in the BCZT layer is conducted, which possesses high dielectric permittivity as well as a low loss at microwave frequencies, and will be beneficial for a compact microwave device with a low insertion loss [52; 53; 54; 55].