用转移矩阵法数值研究二维正方介质柱光子晶体的传输特性

利用转移矩阵方法对二维正方介质柱光子晶体的传输特性进行了研究,数值计算研究了不同晶格、同一晶格柱体截面面积不同、放置方位角不同时光子晶体的传输特性。数值结果表明光子禁带的宽度与中心频率和晶格结构有很大关系,正方晶格更易形成平坦光子禁带,柱体截面面积大,则形成的禁带较宽,在其他因素相同的条件下柱体放置的方位角对光子禁带有重要影响。数值研究表明在正方介质柱下设计宽平坦光子禁带时,可以首先考虑正方晶格结构,其次设法使柱体截面尽量大一些,最后可通过柱体放置方位角来微调光子禁带的宽度与中心频率以达到设计要求。

Transmission Characteristics of 2-D Photonic Crystals of Square Dielectric Rods by the Transfer Matrix Method

Photonic crystals are artificially fabricated periodic dielectric structures. In recent years, a lot of theories and experiments on the application of photonic crystals have been studied. The two-dimensional photonic crystals have more advantage than one-dimensional photonic crystals and the three-dimensional ones, so the theory and application of two-dimensional photonic crystals are still one of the hottest themes in materials science and photonics science. There are various methods on studying transmission characteristics of photonic crystals: the plane wave expansion method(PWE), the finite-difference time-domain (FDTD), transfer matrix method (TMM), and multiple scattering method (Order-N). Shangshen Feng et al. used the plane-wave method for quickly calculating a band structure of two-dimensional photonic crystal with triangular lattice, but their studies didn't take into account the square cylinder rods photonic crystals, and the corresponding transmission spectrum was not obtained. In this paper, the transfer matrix method is used to study the transmission characteristics of two-dimension cylindrical photonic crystals of square dielectric rods with different lattice structures, section areas and azimuth angles. In numerical simulation the Mur absorbing boundary conditions and periodic boundary conditions are used to eliminate non-physical reflection of electromagnetic waves considered the actual structure. The nume- rical studies show that the photonic band gap width depends on the center frequency and lattice structure, the square lattice is easier to form smooth photonic band gap and the larger cylinder-sectional area is,the wider band gap is. In the same conditions as other factors, azimuth angle of cylinder impacts the photonic crystal band gap. The numerical study shows in the design of smooth photonic band gap of the square dielectric rod, the square lattice structure is considered first, then try to make the cylinder section as large as possible, finally , the photonic band gap width and center frequency can be fine-tuned to reach design requirements by changing the cylinder azimuth angles. In particular, no literature has reported the results that the band gap can be adjusted by the position azimuth angle, which expands the research of two-dimensional photonic crystals.