The Semiconductor Optical Amplifier (SOA) is a device fabricated to amplify optical signals. The amplification is achieved by guiding the signal light through a semiconductor single-mode waveguide, serving as the gain medium. SOA chips are designed similarly to SLDs, solving similar challenges. It is essentially like a fiber-coupled laser diode where the end mirrors have been replaced by anti-reflection coatings; a tilted waveguide can be used to further reduce the end reflectivities. Our proprietary epitaxial growth techniques and advanced waveguide architecture enable SemiNex devices to achieve superior gain and saturation output. Analytic expression do not predicted behavior that depends on z varying n.