The composition and structure of interstellar dust are important and complex for the study of the evolution of stars and the interstellar medium (ISM). However, there is a lack of corresponding experimental data and model theories. By theoretical calculations based on ab-initio method, we have predicted and geometry optimized the structures of Carbon-rich (C-rich) dusts, carbon (C-12), iron carbide (FeC), silicon carbide (SiC), even silicon (Si-28), iron (Fe-56), and investigated the optical absorption coefficients and emission coefficients of these materials in 0D (zero-dimensional), 1D, and 2D nanostructures. Comparing the nebular spectra of the supernovae (SN) with the coefficient of dust, we find that the optical absorption coefficient of the 2D C-12, Si-28, Fe-56, SiC and FeC structure corresponds to the absorption peak displayed in the infrared band (5-8) mu m of the spectrum at 7554 days after the SN1987A explosion. It also corresponds to the spectrum of 535 days after the explosion of SN2018bsz, when the wavelength was in the range of (0.2-0.8) and (3-10) mu m. Nevertheless, 2D SiC and FeC correspond to the spectrum of 844 days after the explosion of SN2010jl, when the wavelength is within (0.08-10) mu m. Therefore, FeC and SiC may be the second type of dust in SN1987A corresponding to infrared band (5-8) mu m of dust and may be in the ejecta of SN2010jl and SN2018bsz. The nano-scale C-rich dust size is similar to 0.1 nm in SN2018bsz, which is 3 orders of magnitude lower than the value of 0.1 mu m. In addition, due to the ionization reaction in the supernova remnant (SNR), we also calculated the Infrared Radiation (IR) spectrum of dust cations. We find that the cation of the 2D layered (SiC)(2+) has a higher IR spectrum than those of the cation (SiC)(1+) and neutral (SiC)(0+).