摘要
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。
Approximate nonlinear equation about modes is derived by W. K. B. method for waveguide with perfectly matched layer （PML）. Asymptotic solutions for the leaky modes and Berenger modes are derived and the effect of PML is analyzed. Theoretical analysis shows that for leaky modes of transverse electric （TE） case, asymptotic solutions of waveguide are the same as that of open waveguide, but for transverse magnetic （TM） case, asymptotic solutions of waveguide are different from that of open waveguide. For both TE and TM cases of three-layer slab waveguide, if refractive index of top cladding is different form that of bottom cladding, there will be two traces of Berenger modes, otherwise there is only one trace of Berenger modes. Numerical simulations show that these asymptotic solutions of leaky modes and Berenger modes are very close to exact solutions and as the norms of modes become larger, the error will become smaller.
出处
《光学学报》
EI
CAS
CSCD
北大核心
2009年第6期1459-1466,共8页
Acta Optica Sinica
关键词
导波光学
光波导计算
浙近解
W.K.B.方法
完美匹配
泄漏模
guided-wave optics
computing in optical waveguide
asymptotic solutions
W. K. B method
perfectly matched layer （PML）
leaky mode
