Augmented reality (AR) technology blends digital content with the real world to create immersive experiences. Diffractive waveguides, a key AR component, are popular because they balance weight, size, image quality, and ease of production. However, traditional glass-based waveguides have drawbacks like narrow viewing angles, blurry images, and rainbow-like distortions. To solve these issues, we developed ultra-thin, lightweight AR glasses using silicon carbide (SiC) and a new design method called the Period-Limited theory (PL theory). Our simulations show that the system works efficiently across red, green, and blue colors, removing rainbow distortions while keeping images clear and vibrant. Tests confirm that the design eliminates rainbow effects, provides a wide 55° field of view (FOV), and keeps each lens extremely light (just 2.12 g). This work offers a practical way to make compact, high-performance AR glasses with excellent display quality.