A Study on Function-Expansion-Based Topology Optimization without Gray Area for Optimal Design of Photonic Devices
A Study on Function-Expansion-Based Topology Optimization without Gray Area for Optimal Design of Photonic Devices
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DOI：
10.1587/transele.2019esp0005
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发表时间：
2020-11
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影响因子：
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通讯作者：
Masato Tomiyasu;K. Morimoto;A. Iguchi;Yasuhide Tsuji
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文献类型：
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作者：
Masato Tomiyasu;K. Morimoto;A. Iguchi;Yasuhide Tsuji
在本文中，我们重新定义了一种不使用灰色区域的基于函数展开的拓扑优化灵敏度分析方法。在传统的基于函数展开法的介电常数分布方法中，介电常数分布中含有介于芯层和包层介电常数之间的灰色材料，从而使介电常数相对于设计变量具有可导性(Dierentialff)。由于这种利用灰度区的方法不能准确地表示材料边界，因此不适合用于强导波器件的设计问题，特别是等离子体波导管的设计。在这项研究中，我们提出了基于函数展开方法的无灰色区域的拓扑优化。在这种方法中，考虑边界相对于设计变量的偏差率，用线积分代替矩阵导数的面积积分，避免了灰区的使用。通过T支路功率分路器和模序转换器的设计，验证了该方法的有效性。
SUMMARY In this paper, we reformulate a sensitivity analysis method for function-expansion-based topology optimization method without using gray area. In the conventional approach based on function expan- sion method, permittivity distribution contains gray materials, which are intermediate materials between core and cladding ones, so as to let the permittivity di ff erentiable with respect to design variables. Since this approach using gray area dose not express material boundary exactly, it is not desirable to apply this approach to design problems of strongly guiding waveguide devices, especially for plasmonic waveguides. In this study, we present function-expansion-method-based topology optimization without gray area. In this approach, use of gray area can be avoided by replacing the area integral of the derivative of the matrix with the line integral taking into acount the rate of boundary deviation with respect to design variables. We verify the validity of our approach through applying it to design problems of a T-branching power splitter and a mode order converter.