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对带有完美匹配层(PML)的光波导,通过W.K.B.方法,得到了关于波的模式的近似非线性方程。通过对该非线性方程进行渐近分析,得到了完美匹配层对波的各种模式的影响,推导出泄漏模的渐近解和Berenger模的渐近解。理论结果表明,对于光波导的横电(TE)模,泄漏模的渐近解和开放的波导是相同的、而对于横磁(TM)模,泄漏模的渐近解和开波导会有所不同;当上下包层的折射率不同时,Berenger模的轨迹会有两条,而折射率相同时Berenger模的轨迹只有一条。数值模拟表明,泄漏模及Berenger模的渐近解在其精确解附近,且随着模的增大,误差越来越小。
For an optical waveguide with perfectly matched layer (PML), an approximate nonlinear equation for the mode of the wave is obtained by the method of W.K.B. By the asymptotic analysis of the nonlinear equation, the influence of perfect matching layer on various modes of the wave is obtained. The asymptotic solution of the leakage mode and the asymptotic solution of the Berenger mode are deduced. The theoretical results show that the asymptotic solution of the leaky mode and the open waveguide are the same for the transverse mode (TE) mode of the optical waveguide, while for the transverse mode (TM) modes, the asymptotic solution and the waveguide mode of the leaky mode Different; when the upper and lower cladding refractive index is different, Berenger mode trajectory will have two, and the same refractive index Berenger mode trajectory only one. Numerical simulations show that the asymptotic solutions of leaky modules and Berenger modules are close to their exact solutions, and the errors become smaller with the increase of the modes.