Study On Time Domain Simulation Method For Photonic Crystal Band Gap

Photonic crystal, a new optical material, is invented in the late 1980s.The material has a periodical structure, which make it possess photonic band gap and photonic local area characters. The photonic crystal has widespread foreground and develops quickly, recently, lots of achievements are obtained. And enormous development is achieved in photonic communication, photonic fiber, antenna and so on. In the future, photonic crystal will effect information and communication significantly.The finite-difference time-domain method (FDTD) is a powerful numerical method for the modeling of the electromagnetic wave. The Maxwell equations are transformed to finite-difference equations, in both time and space domain. The electromagnetic fields in each time and space point can be obtained by FDTD method with good stability and convergence. The FDTD method is widespread applied in the complex engineering electromagnetic area.FDTD method has less calculation, precision result, and dynamic distribution of electromagnetic, so it is suitable for calculating photonic crystal band gap. This thesis presents FDTD method in tow-dimensional (2-D) ideal photonic crystal band gap, and it's numeric stability and numeric dispersion, form and position of motivation source. All of these are the bases of 3-D photonic crystal band gap.To decrease the calculation time, three methods are proposed in this thesis. First, periodical boundary condition is used to make space domain in a photonic crystal unit cell, and for non-orthogonal crystal, non-orthogonal coordinate system is adopted. Then, according to FFT characters, all the rest time steps are not calculated, after stability. Last, variational expression is employed to decrease space mesh number, without reducing calculation precision.Base on the theory above, both square and triangular photonic crystal band gap have been calculated. Results show that FDTD code is stable and accurate. It can be applied to calculate all shapes 2-D photonic crystal band gap, and increase calculation speed and keep result more precision.