On shape optimization of optical waveguides using inverse problem techniques
On shape optimization of optical waveguides using inverse problem techniques
复制标题
利用反问题技术进行光波导形状优化
DOI：
10.1088/0266-5611/17/4/338
复制
发表时间：
2001
期刊：
影响因子：
2.1
通讯作者：
H. Engl
中科院分区：
文献类型：
--
作者：
T. Felici;H. Engl
光波导是光电子和电信行业的基础。这些系统包括光纤和集成光学元件，它们对输入的光信号进行处理、过滤和发送。锥形是一种普通类型的光波导，其横截面沿其长度z连续沿着变化。锥形用于将光从波导耦合到具有不同横截面轮廓的另一个波导中。众所周知，通过锥形侧壁损失的功率随着锥形长度的增加而减小。然而，出于实际原因，期望保持锥形长度尽可能短。本研究的目的是开发一种配方，通过改变给定的固定长度的锥度轮廓来最大限度地减少功率损耗。事实证明，这种形状优化问题表现出不适定的行为，这将减缓传统的优化程序的收敛。我们将展示如何通过将形状优化问题重新表述为非线性反问题来克服这些问题，然后可以使用已建立的反问题正则化技术来解决这些问题。数值结果表明，这种新的方法可以导致强大的优化算法不太敏感的大离散细化。
Optical waveguides are the basis of the optoelectronics and telecommunications industry. These comprise optical fibres and the integrated optical components which manipulate, filter and dispatch incoming optical signals. A taper is a generic kind of optical waveguide with a cross section that varies continuously along its length z. Tapers are used to couple light from a waveguide into another with different cross sectional profile. It is well known that the power lost through the taper side walls decreases for increasing taper lengths. For practical reasons however, it is desirable to keep the taper length as short as possible. The aim of this study is to develop a formulation to minimize the power loss by varying the taper profile of a given fixed length. It turns out that this shape optimization problem exhibits ill-posed behaviour which would slow down the convergence of traditional optimization routines. We show how these problems can be overcome by reformulating the shape optimization problem as a nonlinear inverse problem, which can then be solved using established inverse problem regularization techniques. Numerical results presented here show that this new approach can lead to robust optimization algorithms less sensitive to large discretization refinements.