Subwavelength 8 × 8 Butler Matrix With Pixel Metamaterial for Space Limited Systems

In this letter, a subwavelength <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$8\times 8$ </tex-math></inline-formula> Butler matrix (BM) with inverse-designed pixel metamaterial is proposed for space limited systems. With inverse-designed metamaterial, the broadband asymmetric 3-dB couplers with arbitrary phase difference are constructed, which eliminates the space for phase delay lines in BM, significantly reducing the overall size. Finally, a prototype of the proposed BM is fabricated and measured, which exhibits a bandwidth of 21.6% by occupying a compact size of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.95\lambda _{0}\times 0.70\lambda _{0}\times 0.01\lambda _{0}$ </tex-math></inline-formula>. With a subwavelength scale, the proposed ultracompact BM can be easily integrated with antenna array for applications in compact multibeam systems.