The ever-growing demand for larger integration density, higher bandwidth, and lower power consumption in conventional electronic technology has made photonics one of the key drivers in global data communications. The success and ongoing trend of nanophotonic anticipate a photonic roadmap leading to ultra-compact, broad bandwidth, high-speed optoelectronic devices. However, there is a severe deadlock imposed on the miniaturization of nanophotonic devices as long as conventional propagating light is used. This view dramatically changed due to the emerging field of nonlinear photonic crystals. To meet these purposes all optical 4-port Directional Coupler is a potentially important components for future optical integrated circuits. This project proposes the design of a Directional Coupler where the propagation of the electromagnetic wave is simulated at the wavelength of 1.55 µm in dielectric material Silicon of refractive index 3.4757 with the hexagonal lattice of the lattice constant of 0.750 µm in 2D photonic crystal using Finite Difference Time Domain (FDTD) method. The Photonic Bandgap (PBG) of the material can be observed using Plane Wave Expansion (PWE) method and a photonic bandgaps width of 0.148 GHz and 0.152 GHz at a normalized frequency of 0.379 GHz, 0.653 GHz respectively was obtained which leads to an opportunity for a number of applications that can be used in ultrafast optical circuits and future optical networks.