Effective Epsilon-Mu-Near-Zero Photonic Crystal With Low-Permittivity Substrate for Broadside-Beam Leaky Wave Antenna

An effective epsilon-mu-near-zero photonic crystal (EMNZPC) can be realized by degenerating three bands at the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Gamma $ </tex-math></inline-formula> point with scattering from the high-permittivity dielectric. This article presents a method to realize an EMNZPC by achieving triply degenerate bands at the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Gamma $ </tex-math></inline-formula> point using gap metal rods in low-permittivity dielectric substrates. Open apertures are utilized as magnetic boundaries to truncate this photonic crystal (PC) into a finite size of two-column unit cells for antenna design. This truncated PC serves as a zero-phase shift line with impedance matching to its feed line. Waves traveling along this zero-phase shift line are fast waves, capable of radiating broadside beams to function as a leaky wave antenna with two symmetrical beams. As an example, a leaky wave antenna with a length of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5.1\lambda _{0}$ </tex-math></inline-formula> (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda _{0}$ </tex-math></inline-formula> is the wavelength in free space at 12 GHz) is designed to verify the proposed truncated PC. The results indicate that the antenna achieves <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert S_{11}\vert \lt -10$ </tex-math></inline-formula> dB impedance matching over the bandwidth of 35.0% or from 9.2 to 13.1 GHz and the realized gain of 9.6 dBi at 12 GHz. This advancement in the implementation and fabrication of the EMNZPC offers the opportunity to apply PCs to antennas and circuit design.