## 1 Introduction  
With the rapid growth of mobile telecommunications and electronic technology, the antennas of implantable wireless medical devices have become a popular research topic [1]. These devices can collect and transmit physiological data, such as blood glucose monitors, and pulmonary artery pressure monitors [2; 3; 4]. To enable these devices to communicate with external devices stably and in real time, it is necessary to develop implantable antennas that provide reliable performance. There are stringent requirements and restrictions for human-implantable devices; therefore, designing implantable devices is a great challenge, and the devices must perform with appropriate characteristics such as miniaturization, polarization diversity, biocompatibility, and reliability [5]. In [6; 7; 8; 9], the authors utilized slotting techniques to achieve a miniaturized design. In [6], the authors minimize the volume of an antenna by cutting two appropriate rectangular slots in the annular ring, resulting in a total size of about 120.69 mm\({}^{3}\) including the substrate and superstrate. In [10], the authors chose a Rogers RO 3010 (\(\epsilon_{\mathrm{r}}\) = 10.2) as a dielectric substrate and used a slotting method to extend the current path, which also achieved a reduction in the antenna's size, obtaining a size of 88.09 mm\({}^{3}\). In [11; 12], both the radiation patch and GND were slotted to achieve a miniaturized design. However, the main drawback of miniaturized antennas is the loss of efficiency and gain, particularly when placed in lossy peripheral tissues, such as in the human body. Therefore, to meet these demands, many engineers have suggested different techniques for realizing such trade-offs [13; 14]. In addition, saving energy and extending the lifetimes of implantable medical devices are other challenges. In [15; 16; 17; 18; 19; 20; 21; 22], scholars used the low power consumption of an antenna in a higher-frequency band to wake up the device; using a higher level of power consumption in a lower-frequency band to transmit data could extend the life of a device. In [16], a compact dual-band antenna was proposed to extend the device's lifetime, and its volume was 103.7 mm\({}^{3}\). In [18], the dual-band was achieved via unfolding a circular patch antenna, and the antenna's dimensions were \(\pi\times 10^{2}\times 2.54\) mm\({}^{3}\). In addition, circularly polarized (CP) antennas are important for achieving high-quality telecommunications with outside devices as the human body's posture and movement change [23; 24; 25; 26]. In [25], the antenna's dimensions were \(11\times 11\times 1.27\) mm\({}^{3}\) with a bandwidth of 889-924 MHz, and its axial ratio (AR) bandwidth was only \(11\) MHz. Therefore, interest in devising a compact, multi-frequency, implantable antenna with dual-polarization or multi-polarization characteristics to meet the needs of biological devices has been increasing. In this work, a miniaturized dual-band, dual-polarized implantable antenna for biotelemetry communications was designed by using the characteristic pattern method and slotting method. Its total size is only \(47.4\) mm\({}^{3}\) (\(7.4\) mm \(\times\) \(7.2\) mm \(\times\) \(0.889\) mm). Its measured peak gain is \(-20.85\) dBi at \(1.4\) GHz and \(-22.15\) dBi at \(2.45\) GHz. Its measured effective AR bandwidth in the WMTS band is \(170\) MHz (\(1.33\)-\(1.50\) GHz, \(12.0\%\)), and its measured impedance bandwidth in the ISM band is \(390\) MHz (\(2.21\)-\(2.60\) GHz, \(16.2\%\)). We simulated and measured radiation patterns with quasi-omnidirectional characteristics at those two operating frequency points. The simulated maximum \(1\) g average SAR values are \(376\) W/Kg and \(318\) W/Kg at \(1.4\) GHz and \(2.45\) GHz, respectively. Therefore, the largest transmit power must be less than \(4.26\) mW and \(5.03\) mW to comply with the IEEE C95.1-1999 standard.