This paper presents a model of the optical waveguide of GaN/ AlN on a sapphire based on the different refractive index (n) between the wave's guideline regions and surrounding medium (cladding). The model analysis is done by using finite-difference mode (FDM) solver simulation is performed by FDTD (finite-difference-time-domain). In the infrared area, this study reveals a fully unique and rigorous modal analysis waveguide. The investigation includes both primary and single-mode polarization; the waveguide is reliant on the refractive index of the layers, thickness, and substrate type. The primary novelty here for the micro-waveguide single-mode is to realize optical characteristics such as attenuation, amplitude, and full width half maximum (FWHM),which has not been done previously for specific thickness (given thickness) and for that geometrical design. Despite we investigated how Optical waveguides are structures that confine and direct optical signals in a region of a higher effective index than its surrounding media. Our experiment (simulation) aims to investigate the single-mode waveguide of Gallium Nitride/ Aluminum Nitride GaN/ AlN on sapphire of a specified thickness in order to obtain infrared waveguide mode with minimum attenuation. Attenuation refers to any decrease in the propagated signal power that does not affect its waveform while the input wavelength is1.55μm. Additionally describe the characterization of the mode, in keeping with our modal analysis. The waveguides have many applications in various fields such as Optical fiber communication and Photonic integrated circuits.