运用非线性传输矩阵法对Sinc函数型光子晶体非线性微腔光学双稳态进行了理论推导与数值分析。结果表明:随着周期数的增大,双稳态阈值趋于减小;随着微腔线性折射率的增大,或者微腔偏离周期结构中心越远,双稳态阈值趋于增大,这些规律与常规光子晶体相类似;然而,函数型光子晶体可以通过选择适当的介质层折射率分布函数,运用对称性结构就可以实现比常规光子晶体更宽阔的光子带隙,同时隧穿模频带更狭窄且附近场分布高度局域,使得实现光学双稳态较常规光子晶体更容易,双稳态阈值更低。 The nonlinear transfer matrix method is used to theoretically deduce and numerically analyze the nonlinear microcavity optical bistability of Sinc function photonic crystal. The results show that the bistability threshold tends to decrease with the increase of the number of cycles. The bistable threshold tends to increase with the increase of the linear refractive index of the microcavities or the distance of the microcavities from the center of the periodic structure. These laws are similar to those of conventional photonic crystals; however, functional photonic crystals can achieve a wider photonic bandgap than conventional photonic crystals by selecting the appropriate refractive index distribution function of the dielectric layer and using a symmetrical structure, while the tunneling mode band A narrower and highly localized near-field distribution makes it easier to achieve optical bistability than conventional photonic crystals with lower bistability thresholds.