Before introducing the construction of AND logic gate, this article initially uses a two-dimensional photonic crystal lattice to optimize an all-optical AND logic gate. It is polarization independent and operates in both Transverse Electric (TE) and Transverse Magnetic (TM) polarizations with optimal output power and contrast ratio preservation. The structure relies on the interference effect in photonic crystals and its mechanism. The interference effect mechanism significantly reduces the power consumption requirement compared to the other two techniques. The finite-difference time-domain (FDTD) and plane-wave expansion methods are applied. The benefits of such a design include ease of construction, compatibility with integrated optical circuits, small volume, optimal output power, optimized contrast ratio, and appropriate performance in both TE and TM polarizations. These benefits are attributable to the utilization of air holes in the Silicon substrate. The normalized output powers in TM and TE polarizations are equal to 0.94 and 1.63, respectively, and the contrast ratio in such a structure is around 6 dB for both polarizations. The construction has a total area of roughly 83 .