# Design of a Double-Matched Cross-Polar Single Antenna Harmonic Tag
## 1 Introduction  
Nowadays, the need for identifying, localizing, tagging, tracking, and sensing objects is highly requested in various sectors, including healthcare, retail, logistics, and agriculture [1, 2, 3, 4, 5]. Radio frequency identification (RFID) is a widely used technology to perform the mentioned tasks. RFID systems operate across a range of frequencies, ranging from low-frequency (LF) bands to microwave ISM (Industrial, Scientific, and Medical) bands, and they are based on both active and passive configurations. Active RFID systems are battery-powered and can achieve extensive read ranges, often exceeding 100 m and, in some cases, extending beyond 1 km [6]. On the other hand, passive RFID systems rely on harvesting energy from incoming electromagnetic (EM) fields, and their read range is constrained by their energy-harvesting capabilities [7]. Passive LF RFID is typically used for short-range communication, covering approximately 5 cm, while ultra-high-frequency (UHF) passive RFID extends the read range to about 6-8 m. The absence of batteries in passive RFID tags contributes to their compact form factor, lower cost, and ease of adoption in various applications. Passive RFID can be categorized into two distinct groups: chipless RFID and chip-based RFID. The fundamental differentiation between these categories lies in the absence or presence of a microchip that essentially increases the capacity of the tag to store and exchange information. Chipless RFID tags, in fact, although they offer the advantages of straightforward circuit design and cost-effectiveness, are constrained by the informationstorage capacity (that is limited) and by the backscattering principle, which imposes limitations on their reading distance. Typically, chipless RFID tags exhibit reading distances of less than one meter, and their data storage capabilities range from a few bits to several tens of bits [8]. In contrast, chip-based RFID tags offer extended read distances, typically spanning from one to twelve meters, and they can store significantly larger amounts of data, often in the range of tens to hundreds of bits [9]. Moreover, chip-based RFID systems provide the capacity to read multiple tags simultaneously, with recent research suggesting the potential to concurrently read up to a thousand tags [9]. Additionally, chipless RFID tags generally require antennas with broader bandwidths, while chip-based RFID tags operate efficiently with narrower-band antennas [10]. The effectiveness of these systems, however, is affected by environmental conditions and, in particular, by the effect of metal structures. Numerous studies have been conducted to mitigate the influence of metallic and other materials on RFID tag performance. [PERSON] et al. [11] investigated the deterioration in performances of UHF RFID tags, taking into account the presence of nearby objects and materials. Another study [12] focused on the surface materials used for RFID tag placement, emphasizing how the materials used for packaging in logistics environments, in conjunction with their contents, often create a complex and non-uniform environment. Furthermore, in-depth analyses of how metals within the environment affect the radiation pattern of RFID tags and, consequently, the overall characteristics of antennas have been detailed in [13,14]. It is clear from [12, 13, 14] that the effect of the electromagnetic interaction of the antenna with the objects close to the tag position makes tag detection difficult since various mismatch processes on the input impedance and on the radiation pattern are not at all negligible. Variations in the performance of passive UHF RFID tags under practical conditions [15] can be attributed to the interactions with objects situated within the environment. The effect of the environment has been addressed by several authors who have proposed methods and models to quantify such effects and to reduce them. In particular, ref. [16] reports special techniques to adjust antenna impedance and improve the efficiency of the tag, ref.