In digital the detection techniques, the half adder is a component of electronic systems that performs calculations faster than the other logic gates. This article focusses on an all-optical half adder logic gate using a two dimensional T-shaped photonic crystal waveguide and silicon in an air medium. The half adder design is predicated on the concept of constructive (in-phase) and destructive (out-of-phase) interferences. The high-intensity output is achieved by carefully selecting the lattice constant, rod radius and refractive index of the half adder structure. The effectiveness of the half adder is investigated using finite-difference time-domain and plane-wave expansion techniques at 1.55 μm wavelength. The suggested structure features a minimal size of 8.4 μm × 8.4 μm. For this structure, the CARRY has a greater contrast ratio of 18.96 dB and SUM of 8.7 dB, as expressed by the results. SUM and CARRY have bit rates of 28.5 Tbps and 23.8 Tbps, respectively. The proposed circuit’s primary objective is to be compact and to have a high contrast ratio.