N × 2N Butler Matrix for Odd-/Even-Mode OAM Generation Based on 3-D SIW

Uniform circular antenna array (UCA) connected to the Butler matrix (BM) is an effective method for generating high-order and multimode orbital angular momentum (OAM) of electromagnetic waves. However, as the number of input and output ports of the BM increases, the number of components and the connection complexity of the N × N BM grow exponentially. To address this, this study proposes an N × 2 N BM with reduced complexity for OAM generation. The number of components and the overall complexity of the N × 2 N BM are comparable to those of the N × N BM, and substantially less than half that of 2N × 2 N BM. Consequently, the proposed design substantially reduces complexity, enabling the realization of BMs with more ports for OAM generation. To validate the proposed method, two types of 8\times 16 BMs for odd- and even-mode OAM generation were fabricated using a 3-D substrate-integrated waveguide (SIW) to enhance integration. The measured transmission amplitude imbalance and phase error of the BMs are less than 1.5 dB and 15°, respectively, at 30 GHz. The BM for odd-mode OAM generation achieves ±1, ±3, ±5, and ±7 modes, while the BM for even-mode OAM generation achieves 0, ±2, ±4, and ±6 modes when connected to UCAs. The proposed N × 2 N BMs greatly simplify the structure and offer substantial potential for high-order and multimode OAM generation, with promising applications in areas such as communication rate enhancement, multitarget communication, and beyond.