We proposed compact and individual basic logic gates AND and OR in TE mode, which is designed using Silicon on Insulator material. The proposed design is formed by coupling effect of waveguides and achieved compact size. The performance of logic gates has been analyzed using FDTD simulation method. Footprint of AND and OR gate design is 2.4μm×13.4μm and 7.5μm×13.9μm respectively. The operating wavelength range of logic gates is 1.5μm-1.6μm. The logical operation of all gates is analyzed with given range. Proposed design can be used for future photonics integrated optical circuits due to small size and individual performance. We also proposed design of 2×1 optical MUX has been demonstrated using proposed logic gates.