## 1 Introduction  
Smartwatches (SWs) have become an integral part of our lives, as they are used for health and fitness parameter tracking, entertainment, phone calls, controlling other Internet of Things (IoT) devices, Global Positioning System (GPS) navigation, and so on [1]. In 2023 alone, it is estimated that there are 210.8 million SW users globally, which is expected to grow to 229.51 million users by 2027 [2]. With the rapid development in technology, SWs are loaded with sophisticated sensors to record physiological data such as respiratory [3], cardiac activity [4; 5], and blood pressure [6]. The telemetry of these data from SW to the remote diagnostic center via the internet requires seamless connectivity. A precisely tailored antenna with a compact design, a low specific absorption rate (SAR), a good radiation pattern, a high gain, and an ease of embedding in SWs can bridge this gap. The 0.472\(\lambda_{0}\)\(\times\) 0.472\(\lambda_{0}\) (with \(\lambda_{0}\) at 2.44 GHz) antenna can house a ground plane with four vertical metal rims [7]. This results in a low SAR of 1.24 and 1.44 W/kg for SW applications at 2.44 and 3.5 GHz, respectively. In [7], a metal ring-shaped antenna of 23 mm for bezel SW is proposed. The antenna efficiency and low electric-field distribution on the wrist were improved by placing a metal plate at the bottom. However, the actual bandwidth (BW) was 66 and 101 MHz at 1.55 and 2.4 GHz, respectively. As described in [8], multiple inverted L-shaped structures were etched on a 0.3\(\lambda_{0}\)\(\times\) 0.35\(\lambda_{0}\) substrate operating at 0.88-0.96, 2.4-2.48, 3.3-50, and 5.1-5.8 GHz, achieving SAR in the range of 0.84-1.21 W/kg. In the later designs, the SW screen effect was not considered. Generally, the SW screen has a printed circuit board (PCB) with perfect electric conductor (PEC) cladding that supports the SW screen. Thus, embedding the antenna below the screen affects the radiation pattern. In [9], these effects were studied by considering flexible printed circuit (FPC) communication strips. The FPC strips carried signals to/from the PCB board to the SW screen. Two conductive tape-based structures were carved on a flexible printed circuit (FPC) to provide shielding. The length of these tapes was tuned to achieve resonances at 1.6, 2.4, 3.5, and 4.8 GHz with a structure dimension of 0.23\(\lambda_{0}\)\(\times\) 0.28\(\lambda_{0}\). The above-discussed structures have a large antenna profile with narrow bandwidths. The forthcoming SW is expected to support video calling and video streaming. Therefore, the millimeter wave spectrum that offers a wide bandwidth with low latency is the solution for personal area IoT applications [10]. In [11], a triple-band CPW monopole antenna was proposed for IoT applications with bandwidths of 22-30, 37-39, and 56.5-61 GHz. They achieved a SAR in the 0.9-0.62 W/kg range and a gain of 5.29, 7.49, and 9 dBi. Another design in [12] proposed a triple-band antenna for IoT applications. The structure with a dimension of 2.8\(\lambda_{0}\)\(\times\) 2.35\(\lambda_{0}\) (with \(\lambda_{0}\) at 28 GHz) combined two varied-length monopoles with a conducting stub at the bottom. The achieved bandwidths were 445 MHz, 657 MHz, and 5.14 GHz at 3.5, 5.8, and 28 GHz, and an antenna gain of 1.86, 2.55, and 4.41 dBi. Very few designs exist that are suitable for SW IoT applications. Therefore, we designed a compact dual-band 0.51\(\lambda_{0}\)\(\times\) 0.51\(\lambda_{0}\) (with \(\lambda_{0}\) at 25.5 GHz) antenna with measured antenna bandwidths of 1.5 (25-26.5 GHz) and 2.5 GHz (37-39.5 GHz) and gains of 7.4 and 7.9 dBi, respectively. The antenna evolved through characteristic mode analysis (CMA), which was first proposed by [PERSON] [13; 14], providing a physical insight into an arbitrarily shaped antenna. Recently, CMA has been used to aid the design and configuration of MIMO, circular polarization, dual-polarization [15], and reconfigurable antennas [16; 17].