Abstract: This paper introduces the concept of photonic crystals and the main methods to calculate the band structure of photonic crystals. Firstly, it introduces the PWM in the plane wave expansion method, which has the outstanding advantages of simple principle, convenient calculation and programming, and fast calculation speed, and is the method to calculate the widest band. Then the FDTD method is introduced, which is more efficient than PWM, and can simulate the propagation of optical behavior in time domain, so this method has gradually become the mainstream calculation method in photonic crystal research. Finally, other numerical methods are briefly introduced, such as finite element method, transfer matrix method and Order-N method.
Key words: photonic crystal band; Plane wave expansion method (PWM); Finite difference time domain (FDTD); "finite element method (FEM)"
Anhui Demonstration University School of Physics and Electricity
Abstract: The concept of photonic crystal energy band and the main methods of calculating photonic crystal energy band structure are introduced. Firstly, the plane wave expansion PWM method is introduced, which has the outstanding advantages of simple principle, convenient calculation and programming, fast operation speed and so on, and is the most widely used energy band calculation method at present. Secondly, FDTD method is introduced, which is more efficient than PWM and can dynamically simulate the propagation behavior of light in time domain, so this method has gradually become the mainstream calculation method in photonic crystal research. Finally, other numerical calculation methods, such as finite element method, transfer matrix method and n-order method, are briefly introduced.
Keywords: photonic crystal energy band; Plane wave expansion method (PWM); Finite time domain difference method (FDTD); Finite element method