Super strong wide TM Mie bandgaps tolerating disorders

This study demonstrates the appearance of super intense and wide Mie bandgaps in metamaterials composed of tellurium, germanium, and silicon rods in air that tolerate some disordering of rod position and rod radius under transverse magnetic (TM) polarized light waves. Tellurium metamaterials reveal [Formula: see text] , [Formula: see text] , [Formula: see text] , [Formula: see text] , [Formula: see text] Mie bandgap modes in which [Formula: see text] , [Formula: see text] , and [Formula: see text] tolerate high rod-position disordering of [Formula: see text] and rod-radius disordering of 34 and [Formula: see text] , respectively. Results for germanium metamaterials show Mie bandgap modes [Formula: see text] , [Formula: see text] , and [Formula: see text] , in which [Formula: see text] and [Formula: see text] tolerate rod-position disordering of [Formula: see text] , and rod-radius disordering of 34 and [Formula: see text] , respectively. Using these characteristics of [Formula: see text] in germanium metamaterials under position and radius disordering, ultra-narrow straight, L-shaped, and crossing waveguides that contain 14, four, and two rows of germanium rods in air are designed. Also, it is shown that [Formula: see text] Mie bandgap appears in metamaterials containing a high refractive index, and disappears in metamaterials with a lower refractive index such as silicon; in contrast, a new phenomenon of intense and broadband [Formula: see text] , [Formula: see text] , and [Formula: see text] in metamaterials with a lower refractive index such as silicon appear. In silicon-based metamaterials, [Formula: see text] tolerates high rod-position and rod-radius disordering of [Formula: see text] and [Formula: see text] , respectively, and [Formula: see text] shows robustness to rod-position and rod-radius disordering of [Formula: see text] . This strong tolerance of disordering of TM modes in tellurium, germanium, and silicon metamaterials opens a new way to design small, high-efficient, and feasible fabrication optical devices for optical integrated circuits.