| Summary: | Abstract 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 $${\mathrm{TM}}_{01}$$ TM 01 , $${\mathrm{TM}}_{11}$$ TM 11 , $${\mathrm{TM}}_{21}$$ TM 21 , $${\mathrm{TM}}_{02}$$ TM 02 , $${\mathrm{TM}}_{12}$$ TM 12 Mie bandgap modes in which $${\mathrm{TM}}_{01}$$ TM 01 , $${\mathrm{TM}}_{11}$$ TM 11 , and $${\mathrm{TM}}_{21}$$ TM 21 tolerate high rod-position disordering of $$50\%$$ 50 % and rod-radius disordering of 34 and $$27\%$$ 27 % , respectively. Results for germanium metamaterials show Mie bandgap modes $${\mathrm{TM}}_{01}$$ TM 01 , $${\mathrm{TM}}_{11}$$ TM 11 , and $${\mathrm{TM}}_{21}$$ TM 21 , in which $${\mathrm{TM}}_{01}$$ TM 01 and $${\mathrm{TM}}_{11}$$ TM 11 tolerate rod-position disordering of $$50\%$$ 50 % , and rod-radius disordering of 34 and $$20\%$$ 20 % , respectively. Using these characteristics of $${\mathrm{TM}}_{11}$$ TM 11 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 $${\mathrm{TE}}_{01}$$ TE 01 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 $${\mathrm{TM}}_{01}$$ TM 01 , $${\mathrm{TM}}_{11}$$ TM 11 , and $${\mathrm{TM}}_{21}$$ TM 21 in metamaterials with a lower refractive index such as silicon appear. In silicon-based metamaterials, $${\mathrm{TM}}_{01}$$ TM 01 tolerates high rod-position and rod-radius disordering of $$40\%$$ 40 % and $$34\%$$ 34 % , respectively, and $${\mathrm{TM}}_{11}$$ TM 11 shows robustness to rod-position and rod-radius disordering of $$20\%$$ 20 % . 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.
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