  In this paper, we propose an all-optical high-speed half adder based on
linear defects in a photonic crystal (PhC) structure composed of silicon rods.
The proper design of half adder results in no need to increase the intensity of
the input optical signal for the appearance of the nonlinear Kerr effect, which
leads to diverting the incoming light toward the desired output. The proposed
device consists of four optical waveguides and a defect in a square lattice
PhC. Two famous plane wave expansion and finite difference time domain methods
are used to study and analyze photonic band structure and light propagation
inside the PhC, respectively. The presented structure, the ON-OFF contrast
ratios for Sum and Carry, are 16dB and 14dB, respectively. Our simulation
results reveal the proposed half adder has a maximum delay time of 0.7 ps with
a total footprint of 158 um2. Due to very low delay time, high contrast ratio,
and small footprint that they are more crucial in modern optoelectronic
technologies, this structure can be used in the next generation of all-optical
high-speed central processing units.
