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Abstract: The integration of electric field enhancement structures (EFES) with rydberg atomic sensors (RASs) has garnered considerable interest due to their potential to enhance detection sensitivity in quantum measurement systems. Despite this, there is a dearth of research on the directional response of EFES, and the analysis of the three-dimensional (3D) patterns of RAS remains a formidable challenge. RASs are employed in non-destructive measurement techniques and are responsive to electric fields, primarily serving as reception devices. However, analyzing their reception patterns is a complex task that requires a sophisticated approach. To address this, we have adopted characteristic mode (CM) analysis to illustrate on the omnidirectional performance of RAS. According to CM theory, the reception pattern can be calculated by a series of modal currents and their corresponding coefficients. The analytical representation of these coefficients negates the need for time-consuming full-wave (FW) numerical simulations, which are typically required to generate EFES patterns due to the necessity of scanning numerous angle parameters. This approach significantly reduces the complexity of solving EFES patterns and provides insightful guidance for the design process. To validate the efficacy of our proposed method, we constructed three prototypes. The results indicate that the final model resonates at 1.96GHz, achieving an electric field gain of 25dB and an out-of-roundness of 2.4dB. These findings underscore the effectiveness of our method for analyzing EFES patterns, highlighting its potential for future applications in the field.