Arithmetic logic unit (ALU) is the core of any digital processing systems. For creating an all optical ALU one needs basic logic gates such as optical NOT, OR and AND gates along with an optical full adder and optical multiplexer. In this paper we aim to design and propose these three basic logic gates using nonlinear photonic crystal ring resonators. The simulations will be done using plane wave expansion and finite difference time domain methods. The proposed structures work based on controlling the optical behavior of the nonlinear resonators using optical power. The simulation results show that the switching threshold for this resonant ring is about 15 mW/μm2. Reduced delay times and switching optical power are the main advantages of the proposed structures. Also by adding two resonant rings in input ports we reduced the cross reflection between the input ports.

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