## 1 Introduction  
Holographic antennas (HAs) consist of and operate with a hologram pattern synthesized by the interferometry of a reference wave and an objective wave. These characteristics provide a simple design procedure for adjusting the hologram pattern and achieving the desired radiation pattern and polarization characteristics [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13]. In addition, HAs are characterized by distinct advantages such as low profile, high directivity, and frequency scanning capability, thereby satisfying the requirements of systems for signal transmission and reception in various communication environments in the next generation beyond 5G/6G communication environments and wireless power transfer systems [4; 5]. Therefore, as the need for the development of HAs in various systems and applications is rapidly increasing, various studies such as those on beam-scannable HAs, polarization-diverse HAs, and multi-beam HAs have been conducted to address this demand [1; 2; 3; 5; 6; 7]. In particular, there are many requirements for the development of HAs in the implementation of full-duplex systems capable of large data transmissions by exploiting polarization diversity and beamforming [8]. Therefore, a single antenna structure with dual-polarization characteristics, high isolation, and the ability to realize different beam patterns at each polarization is essential. Consequently, several dual-polarized HAs have recently been investigated for these applications [10; 11; 12; 13] to provide a viable solution for reducing the fabrication complexity and antenna profile of millimeter-wave systems. However, the design of the previously proposed dual-polarized HAs faces unique challenges. To ensure appropriate radiation characteristics, the reference surface waves satisfying dual polarization should use feeding structures that travel in orthogonal directions to each other without any interference between the polarizations. Previous studies used orthogonally placed parallel plate waveguides (PPWs) [10; 11; 12] or substrate-integrated waveguide (SIW) horn arrays [13] to generate plane reference waves in orthogonal directions. However, the feeding methods used, including orthogonally placed PPWs and SIW horn arrays, suffer from increased coupling and low isolation between the feeding ports due to the reference wave feeding structures located near the radiating apertures [10; 11; 12]. In addition, in the case of the array system, each feeding element necessitates a large space, thereby increasing system size [13]. To overcome these drawbacks, a previous study used a pillbox feeding structure in a single-polarization HA to minimize the size of the feeding structure, reducing the overall antenna size [14; 15]. However, the conventional pillbox feeding structure is only designed for single-polarized HAs, rendering it difficult to support dual-polarized HAs [14]. Therefore, an innovative compact feeding structure suitable for dual-polarized HAs must be designed. In addition, it is necessary to develop a novel structure using the pillbox design to ensure high isolation and low cross polarization. As a result, the proposed dual-polarized HA suppresses the open stopband (OSB) phenomenon during continuous scanning in each polarization, thereby preventing a decrease in radiation efficiency, especially in the broadside direction [13]. To overcome all the above drawbacks and design an HA with a compact structure, this study presents the design of an HA that employs a low phase distortion feeding structure for high polarization purity and a hologram pattern that has the ability to operate each polarization independently without correlation. The proposed three-layer pillbox feeding structure generates independent orthogonal reference waves traveling along the radiation aperture to feed the hologram pattern with two orthogonal fields. Furthermore, each polarization field is separated into a different layer to improve isolation between the feeding ports.