# Reflection Propagation Law of Electromagnetic Waves in U-Shaped Roadway  
[PERSON]  
1 College of Electrical and Information Engineering, Anhui University of Science and Technology,  
Huaiwan 2232001, China; [EMAIL_ADDRESS] (L.G. ); [EMAIL_ADDRESS] (X.S. )1 College of Electrical and Information Engineering, Anhui University of Science and Technology,  
Huaiwan 2232001, China; [EMAIL_ADDRESS] (L.G. ); 20  
relationship between the distance from the transmitting point to the receiving point, the number of valid reflection lines, and the change rule of transmission loss in a single reflection line with distance in a three-dimensional roadway environment. [PERSON] [11] used the mirror image method to establish a model for predicting the distribution of the electromagnetic wave field strength in a long straight rectangular mine roadway. [PERSON] and [PERSON] [12] used the mirror image method to divide the top of a semicircular arch mine roadway to form multiple inclined small planes, which were used as reflecting surfaces for calculating the valid reflections of electromagnetic waves on each reflecting surface, and then obtained the total field strength vector at the receiving point. [PERSON] [13] analyzed the attenuation characteristics of rectangular curved and straight roadways and found that the curvature of the roadway increases the attenuation of electromagnetic waves in the roadway, and the field strength attenuation is higher in vertically curved roadways compared with that in horizontally curved roadways. [PERSON] et al. [14; 15; 16; 17; 18] investigated the propagation characteristics of electromagnetic waves under the roadways of mines by using ray-tracing and wave modeling methods. The simulation results are highly consistent with the actual measurement results through the actual measurement of long and straight concrete roadways, wide roadways, and other scenarios, which verify the applicability of the ray-tracing method in roadway modeling. [PERSON] et al. [19] studied the attenuation characteristics of electromagnetic waves in a straight roadway by using the mirror method, taking into account the relative permittivity and roughness of the roadway wall. [PERSON] [20] established a rectangular curved roadway model and analyzed the electromagnetic wave propagation using the emission ray method, and the results showed that the higher-order modes attenuate faster in the curved part of the roadway. [PERSON] [21] used a method combining the Shooting and Bouncing Ray (SBR) method and the mirror image method to predict the path loss, angle of arrival, and root mean square delay spread in a tunnel environment at a frequency of 6 GHz. Although previous research has made significant progress in this field, notable gaps remain in the existing studies. Specifically, systematic investigations into electromagnetic wave propagation in complex structures, such as U-shaped roadways, are lacking. Additionally, existing models addressing electromagnetic wave propagation in mine roadways often struggle to balance computational efficiency with accuracy. This paper presents a U-shaped roadway model constructed using the mirror image method, incorporating relay nodes to streamline the computational process. By identifying the boundaries of each reflective surface, calculating the corresponding mirror and reflection points, and assessing the validity of the mirror points, the effective reflection paths are determined. The simulation results demonstrate that this approach accurately determines the number of valid reflection paths within the U-shaped roadway, allowing for a detailed analysis of the reflected field strength attenuation at the receiving point. This method provides a robust tool for investigating electromagnetic wave propagation in mine roadways and optimizing sensor placement. The main structure of this paper is as follows: In Section 2, the fundamental principles of the mirror image method are introduced. In Section 3, a U-shaped roadway model is established using this method.