An ultrafast all-optical half adder using nonlinear ring resonators in photonic crystal microstructure

Half adder and half subtractor are the basic building blocks of an arithmetic logic unit used in every optical central processing unit (CPU) to provide computational operators. In this paper, we aim to design an ultrafast all-optical half adder based on nonlinear ring resonators. The proposed structure consists of the concurrent designs of the AND and XOR logic gates inside a rod-based photonic crystal microstructure. The linear dielectric rods made of silicon and nonlinear dielectric rods composed of doped glass are used to design the nonlinear ring resonators as the fundamental blocks of a half adder. We demonstrate as the intensity of the incoming light increases, the nonlinear Kerr effect appears, and the total refractive index increases. It diverts the direction of light propagation to the desired nonlinear ring resonator depending on the signal wavelength, the radius of rods and lattice constant. Finally, after several resonances, the light is coupled to the output. Our numerical simulations using a two-dimensional finite-difference time-domain method reveal depending on the light intensity, the maximum and minimum transmissions of the half adder are 100% and 96%, respectively. The calculations also show the delay of the designed half adder is 3.6 ps. Due to the small area of 249.75 µm2, the proposed half adder is an appropriate candidate for photonic integrated circuits used in the next generation of all-optical CPUs.