## 1 Introduction  
Applications of high-speed and broadband communication services are expected to broaden across diverse frequency bands as a result of the surge in information volume driving an increase in demand. The W-band (75 GHz to 110 GHz) stands out as a prospective candidate for sub-terahertz communications in sixth-generation mobile communications, along with its applications in radar systems, automobile collision avoidance systems, and image sensing [1; 2; 3]. The W-band, distinguished by the short wavelength inherent to millimeter waves, is able to facilitate compact hardware implementation for the propagation of electromagnetic waves. However, it is accompanied by drawbacks such as atmospheric attenuation and high path loss due to its short wavelength. An antenna system with enhanced radiation characteristics (high gain) becomes essential to overcome these limitations [4]. The subsequent studies serve as examples of W-band high-gain radiation characteristics. A modular array antenna for an electron cyclotron emission imaging system [5], a substrate-integrated waveguide (SIW) for microwave power transmission (MPT) and wireless communications [6], and a folded Fresnel reflector (FFR) for a helicopter collision avoidance radar and a microstrip patch array antenna fed by SIW for an operating range from 91 GHz to 97 GHz [7] were all previously designed and studied. The mentionedantennas use dielectrics. As the operating frequency increases, dielectric loss increases, and thus antenna radiation efficiency decreases. In addition, these antennas belong to the category of resonant antennas; they suffer from the drawback of having a narrow operating bandwidth. A parabolic reflector antenna has the benefits of providing high gain, radiation efficiency, and wide bandwidth compared to the other types of antennas. Therefore, a parabolic reflector antenna is a good candidate for W-band applications. In Refs. [8; 9], parabolic antennas were designed and studied for W-band satellite communication (SATCOM) applications. Parabolic reflector antennas can be used in more diverse ways in addition to inducing high-gain radiation characteristics for the W-band. In Ref. [10], a monopulse tracking system was designed based on a parabolic antenna for W-band wireless communications. In Ref. [11], W-band multi-beam antenna systems and millimeter-wave image systems were designed with multi-fed parabolic reflector antennas. In Ref. [12], a multi-band shared aperture reflector antenna was designed for the Ka- and W-bands. It is also necessary to be able to analyze the radiation characteristics of the defocus-fed parabolic reflector antenna for the various mentioned applications. Electromagnetic field analysis is necessary for analyzing the radiation characteristics of antennas. For this purpose, various efficient methods have been developed to simulate an electromagnetic field. Representative methods include the method of moment (MOM) [13], the finite element method (FEM) [14], the finite difference time domain (FDTD) [15], the finite difference method (FDM) [16], and the finite integration technique (FIT) [17]. However, in a high-frequency regime or with electrically large objects such as reflector antennas, the computational burden associated with the mentioned methods is prohibitively high. Therefore, high-frequency asymptotic methods, such as geometrical optics (GO) [18; 19] or physical optics (PO) [20; 21; 22; 23], have been extensively applied to solve approximate solutions for reflector antennas with a limited computing cost while maintaining good accuracy. The GO method is based on the description of an electromagnetic field in terms of optical rays. It focuses on the reflection of rays as they interact with the parabolic surface and is commonly used to predict the path and concentration of electromagnetic energy in large-scale antenna structures. The PO method considers electromagnetic waves as a combination of incident and scattered fields based on the equivalent currents on the surface.