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In order to better understand the properties of 2D photonic crystals, various simulation techniques have been developed. One such technique is the plane wave expansion method, which can be used to simulate the band structure of 2D photonic crystals. This method involves expanding the electromagnetic fields into a set of plane waves, which can be used to calculate the dispersion relation of the crystal. Another technique is the finite-difference time-domain method, which can be used to simulate the energy transport in 2D photonic crystals. By discretizing Maxwell's equations and solving for the electric and magnetic fields at each point in space and time, this method can provide insight into how light interacts with the crystal structure. Together, these simulation methods can provide a more detailed understanding of the behavior of 2D photonic crystals and their potential applications in optics and photonics.