基于硅纳米结构和稀土离子掺杂二氧化硅基质增益介质的光放大器波导的时域有限差分法模拟：与Er3 +或Nd3 +离子掺杂剂可实现增益的比较
Modeling of optical amplifier waveguide based on silicon nanostructures and rare earth ions doped silica matrix gain media by a finite-difference time-domain method: comparison of achievable gain with Er3+ or Nd3+ ions dopants
摘要：
在波导光放大器的增益实现进行了比较研究，其有源层是由含有硅纳米颗粒作为敏化剂的钕离子（Nd 3+）或铒离子（Er 3+）的二氧化硅基质构成。由于布居能级特征时间（ms）和有限差分时间步长（10 ~ 17 s）之间存在较大差异，传统的辅助微分方程时域有限差分（ADE-FDTD）方法不适合处理此类系统。因此，提出了一种新的基于ADE-FDTD方法的双环算法来模拟这种波导光放大器。我们调查的稳定状态制度的稀土离子和硅纳米粒子的水平人口以及不同的泵浦功率范围从1到10 - 4 mW.mm-2的电磁场。此外，在此泵浦范围内，每单位长度可获得的增益的三维分布已被估计。掺Nd 3+波导在1064 nm处的单位长度总增益（达30 dB·cm-1）比掺Er 3+波导在1532 nm处的单位长度总增益（达2dB·cm-1）高。考虑到这些波导上的实验背景损耗，我们证明了一个显着的正净增益只能与Nd 3+掺杂波导实现。所开发的算法是稳定的，适用于具有宽范围的特征寿命的发射器的光学增益材料。
英文摘要：
A comparative study of the gain achievement is performed in a waveguide optical amplifier whose active layer is constituted by a silica matrix containing silicon nanograins acting as sensitizer of either neodymium ions (Nd 3+) or erbium ions (Er 3+). Due to the large difference between population levels characteristic times (ms) and finite-difference time step (10 --17 s), the conventional auxiliary differential equation and finite-difference time-domain (ADE-FDTD) method is not appropriate to treat such systems. Consequently, a new two loops algorithm based on ADE-FDTD method is presented in order to model this waveguide optical amplifier. We investigate the steady states regime of both rare earth ions and silicon nanograins levels populations as well as the electromagnetic field for different pumping powers ranging from 1 to 10 4 mW.mm-2. Furthermore, the three dimensional distribution of achievable gain per unit length has been estimated in this pumping range. The Nd 3+ doped waveguide shows a higher gross gain per unit length at 1064 nm (up to 30 dB.cm-1) than the one with Er 3+ doped active layer at 1532 nm (up to 2 dB.cm-1). Considering the experimental background losses found on those waveguides we demonstrate that a significant positive net gain can only be achieved with the Nd 3+ doped waveguide. The developed algorithm is stable and applicable to optical gain materials with emitters having a wide range of characteristic lifetimes.
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