We proposed an optical half-adder design using nonlinear materials, photonic crystal structure shape of hexagonal lattice layout, and silicon dielectric rods in the air bed. The optical half-adder structure is designed and optimized by combining the AND and XOR logic gates. The compound AlGaAs is used as a nonlinear material in the structure. The linear part of AlGaAs material is n1=1.4, and the nonlinear part is n2=1.5×10-17. The main performance for all-optical logic gates is set at an operating wavelength of 1.55 µm. The time delay at all optical gates provided has a 3.1 PS response time with on/off contrast ratio for SUM and CARRY ports of 12.78 dB and 12.9 dB, respectively, and the bit rate is 0.322 Tb/s. In the best case, the 1/0 contrast ratio between input = 1 and input = 0 is 4.59 dB. The computations are performed using the finite difference two-dimensional method.