Prephase-Based Equivalent Amplitude Tailoring for Low Sidelobe Levels of 1-Bit Phase-Only Control Metasurface Under Plane Wave Incidence
Jiexi Yin, Qi Wu, Haiming Wang, Zhi Ning Chen
Abstract
A prephase synthesis method is proposed for sidelobe level (SLL) suppression of a 1 bit phase-only control metasurface under plane wave incidence. The array factor of the metasurface with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N \times N$ </tex-math></inline-formula> unit cells shows that controlling the number of prephases with varying values over the reflective surface can equivalently control the amplitude. Different from optimizing the prephase distribution, selection of the 0 and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi /2$ </tex-math></inline-formula> prephases in specific <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> regions is used to suppress the SLLs. Therefore, the number of parameters in the optimization can be dramatically reduced from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N^{2}$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> . The prephase distribution is then designed based on the optimized number of prephases and a symmetric matrix for SLL suppression in the entire space. The SLLs are further suppressed by optimizing some of the unit cell states based on similar equivalent amplitude tailoring. Simulations and measurements of a set of 1 bit reflective metasurfaces with 20 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 20 unit cells verify that the phase-only control metasurface realizes SLL suppression to −13 dB for multiple beam directions from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$- 30^\circ $ </tex-math></inline-formula> to 30 ° with a 10° step under normal plane wave incidence.