Study On Two-dimensional Photonic Crystals Band Properties Based On Finite Element Method

Theoretical analysis and experimental study of photonic crystals are hot spots in optical communication and optical device technologies in recent years. And for the application of photonic crystal waveguide and optical passive devices, the tunability of band structure of photonic crystal has been the bottleneck of wide application in optical communication for photonic crystals. Therefore, the effective control theory and method of tunability of photonic crystal band structure must be analyzed systematically. The band properties of photonic crystal and the realization of band tunability were studied by finite element method.First, the physical mechanism of generation of photonic bandgap was theoretically analyzed. The light in medium is considered as electromagnetic wave with certain frequency based on Electromagnetic Wave Theory. And the scalar differential formed of Maxwell Equations for photonic crystal was derived. In addition, according to the analysis procedure of finite element method for electromagnetic field, combined with Bloch theory and brillouin zone theory for photonic crystal, the finite element mathematical model for two-dimensional photonic crystal was established based on variational principle of electromagnetics.Second, two-dimensional photonic crystal with three cylindrical lattice types, triangular lattice, square lattice and hexagonal lattice, was analyzed by use of the finite element model for two- dimensional photonic crystal established. And based on this, the effect of dielectric constant of medium for dielectric cylinder, dielectric constant of background medium and fill ratio of mediums on band properties of two-dimensional photonic crystal with three lattice types has been deeply studied.Finally, the effect of three field-induced-effects namely of temperature effect, photoelastic effect and electro-optic effect on photonic crystal structure were theoretically analyzed. And three field-induced-effects can cause change of refractive index of mediums, combined with the change of refractive index of mediums composing of photonic crystal causing its band variation, the effect of corresponding external variables on band properties of two-dimensional photonic crystal was simulated by finite element model established in the three effects. The results showed that, in terms of characteristics of three field-induced-effects, the effective control and optimization of tunability of two-dimensional photonic crystal band can be realized by optimal selection of dielectric materials of photonic crystal.