Super Strong Wide TM Mie Bandgaps Tolerating Disorders

This study demonstrates the appearance of super intense and wide Mie bandgaps in metamaterials composed of germanium rods in air that tolerate some disordering of rod position and rod radius under transverse magnetic (TM) polarized light waves. Results for Mie bandgap modes TM 01 and TM 11 tolerate rod-position disordering of 50%, and rod-radius disordering of 34 and 20%, respectively. Using these characteristics of TM 11 under position and radius disordering, ultra-narrow straight, L-shaped and crossing waveguides that contain 14, four, and two rows of Ge rods in air are designed. Also, it is shown that TE 01 Mie bandgap appear in metamaterials contain high refractive index, and disappear in metamaterials with lower refractive index such as silicon; in contrast, a new phenomenon of intense and broadband TM 01 , TM 11 , and TM 21 in metamaterials with lower refractive index such as silicon appear. Also, in Si-based metamaterials, TM 01 tolerates high rod-position and rod-radius disordering of 50% and 34%, respectively, and TM 11 shows robustness to rod-position and rod-radius of 20%. This strong tolerance of disordering of TM modes in silicon and germanium metamaterials opens a new way to design small, high-efficient, and easy-fabricable optical devices for optical integrated circuits.