A Petrov-Galerkin Finite Element Method For The Band Structure Computation Of Plasma Phononic Crystals

Plasma photonic crystals(PPCs)are periodic structures composed of plasma and other dielectric materials or vacuum.It is a new material proposed and developed rapidly in recent years.As a periodic material different from ordinary photonic crystals,the tunability of its band gap is of great significance in the fabrication of microwave devices and military stealth.Based on Maxwell’s equations,the mathematical model of plasma photonic crystals is derived,and a new Petrov-Galerkin finite element method is developed,which can deal with plasma photonic crystals with various interface shapes.For the Bloch periodic boundary condition in the model,the basis function space and test function space with reciprocal coefficients on the boundary are constructed.When discretized,the projected body fitted grid is constructed,and the Bloch periodic boundary condition is transformed into continuity condition,which reduces the degree of freedom while eliminating the boundary integral.After discretization,the stiffness matrix is assembled according to the integral element to form the eigenvalue equation.After solving the eigenvalue equation,the band structure is obtained.The algorithm programming compiled in this paper realizes the calculation of the band structure of PPCs.The numerical results show that the electron density,filling ratio and shape of the plasma can tune the band gap:(1)With the increase of the electron density of the plasma,the first band gap of the TM modes increases and moves to high frequency;(2)With the increase of filling ratio,the width of the band gap increases at first and then decreases,and moves to high frequency;(3)The shape and the angle can also affect the band structure.In addition,the models and methods in this paper are also applicable to metal/dielectric photonic crystals,which is of great significance to the study of the band structure of dispersive dielectric photonic crystals.