We propose an all-optical half adder based on two different cross structures in two-dimensional photonic crystals. One cross structure contains nonlinear materials and functions as an "AND" logic gate. The other one only contains linear materials and acts as an "XOR" logic gate. The system is demonstrated numerically by the FDTD method to work as expected. The optimal operating speed without considering the response time of the nonlinear material, the least ON to OFF logic-level contrast ratio, and the minimum power for this half adder obtained were 0.91 Tbps, 16 dB and 436 mW, respectively. The proposed structure has the potential to be used for constructing all-optical integrated digital computing circuits.

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An optical logic NOT gate (OLNG) is presented based on photonic crystal (PhC) waveguides without nonlinear materials and optical amplifiers. Also, a way of determining the operating parameters is presented. It is demonstrated through finite-difference time-domain simulations that the structure presented can operate as an OLNG. The optimized contrast ratio, defined as the logic-"1" output power divided by the logic-"0" output power, is found to be 297.07 or 24.73 dB. The size of the OLNG can be as small as 7a×7a, where a is the lattice constant of the PhC. Further, the OLNG presented in this paper can operate at a bit rate as high as 2.155 Tbit/s, which is much higher than that of electronic or optical logic gates developed until now. Moreover, as it is not based on the nonlinear effect, the OLNG can operate at very low powers and a relatively large operating bandwidth. This is favorable for large-scale optical integration and for developing multiwavelength parallel-processing optical logic systems.

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