The research carried out in the field of optics and photonics with an idea to design and develop the all optical logic devices in the fascinating material known as photonic crystals (PhCs). The structural investigation reveals that the two dimensional (2-D) PhCs is more suitable for fabrication of optoelectronic components. In this article we have designed basic logic gates in 2-D PhCs as they are the building blocks for the construction of optical devices and in these, refractive index is periodically modulated with the wavelength. The understanding of light behaviour in complex PhCs helps in creating photonic band gap (PBG) that can prevent light of certain wavelength propagating in crystal lattice structure. For the selected geometry structure, three PBG bands will exists out of which two of them are transverse electric (TE) and one is transverse magnetic (TM) mode. The PBG bands in the TE mode ranges from 0.31(a/λ) to 0.46(a/λ) , 0.61(a/λ) to 0.63(a/λ) and TM mode ranges from 0.86(a/λ) to 0.93(a/λ). The free space wavelength of 1550 nm is set for the finite difference time domain (FDTD) simulation of the structure. The response time and computational overhead required for the proposed OR gate is 0.128ps and 4.4MB is obtained. Also we calculated the extinction ratio for AND gate and NOT gate as 6.19 dB and 10.21 dB respectively
