基于传输矩阵法,通过计算一维有限光子结构的阻抗,研究了由反转对称层状光子结构构成的组合结构中界面态存在的条件。对于分别由反转对称中心不同的元胞构成的两个光子结构而言,其阻抗虚部在所有奇数带隙内符号相反,在偶数带隙内符号相同,因此两个反转对称结构存在阻抗虚部之和在奇数带隙内为零的特征频率,由两个光子结构构成的组合结构在该特征频率处存在一个界面态,同时整个组合结构的阻抗虚部在该特征频率处也等于零。若由多个反转对称中心不同的有限大层状结构按照交替排列的方式构成组合结构,则在同一个奇数带隙内会出现多个界面态,在这些界面态频率处组合结构的阻抗虚部仍然等于零,各界面态光波的电场分布在组合界面处表现出显著的局域性。通过改变其中一部分结构的元胞数来调控组合结构中出现的多个界面态的位置,可满足不同的应用需求。

Based on the transfer matrix method, we calculate the impedance of a one-dimensional finite photonic structure to study the existing condition of interface states of layered composite structures with inversion symmetry. For two photonic structures with different inversely symmetric centers, the imaginary parts of their impedance have the opposite sign in all the odd bandgaps and the same sign in the even bandgaps. Therefore, The composite structure composed of the two individual photonic structures exhibits one interface state at the characteristic frequency where the sum of the impedance imaginary parts in the odd bandgaps of the two individual structures is equal to zero, and meanwhile the imaginary part of impedance of the composite structure is also zero at the characteristic frequency. If one composite structure is composed of multiple finite layered structures with different inversely symmetric centers in the way of alternating arrangement, and then in the same odd bandgaps, multiple interface states will appear. The imaginary part of impedance of the composite structure at the characteristic frequency is zero, and the electric field distribution of the interface state optical wave shows significant localization at the composite interface. In addition, the positions of multiple interface states can be adjusted to meet different application requirements by changing the unit cell number of one part of the composite structure.