For stimulates great developments in high-speed and high-capacity Cloud Computing Technologies (CCT) systems in the future. The all-optical logic gate based on planar photonic crystal (PPC) waveguide is a promising technology. We design an all-optical AND gate in PPC, as an ultracompact component for planar lightwave circuit integration with suitable choice of parameters, perform this task. The PPC waveguides are composed of circular dielectric rods set in two-dimensional triangular lattice. To realize the AND logic function, as predicted using 2D finite-difference time-domain simulations. The combination of the ring and line defect coupler waveguides forms the device. On the basis of our simulations, we found that the optimized scheme maximizes the power transmission above 80% at a wavelength of 1.55 um. Besides, this device can apply to all-optical Arithmetic Logic Unit (ALU) in all-optical computing and potentially applicable for photonic integrated circuits (PICs) in the future.