Analytic Synthesis of Focused Fields of Low Sidelobe Levels Inside Metallic Cavity by 3-D Eigenmodes Mapping

Flexibly generating the desired focused electric fields within a target area inside a metallic cavity is a challenging problem relevant in many applications. This letter proposes an analytical method for synthesizing the focused fields based on the eigenmode mapping (EMM) from 2-D to 3-D. Initially, the desired focused fields within the target area are expressed by the superposition of 2-D eigenmodes. These 2-D eigenmodes are then mapped onto 3-D eigenmodes, which can be excited at the same frequency. Subsequently, the antenna array excites the synthesized field, with the excitation coefficients determined by the excitation matrix and the 3-D eigenmode expansion vector of the desired electric field. Owing to its analytical properties, this method rapidly calculates the excitation coefficients, enabling real-time control of the focused field generation inside the cavity. Furthermore, the proposed method not only prevents the excitation of a limited number of 3-D eigenmodes and unwanted higher-order 3-D eigenmodes, but also takes into account the field distribution outside the focal spots, effectively reducing sidelobe levels. Full-wave simulations demonstrate that the proposed method successfully generated two focused fields with sidelobe levels 6 dB lower than the traditional time reversal (TR) method.