Adjoint Topology Optimization Theory for Nano-Optics

ISBN-13: 9789811679681 / Angielski / Twarda / 2022 / 174 str.

Yongbo Deng

Spis treści

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Self consistency of adjoint analysis for topology optimization in

frequency domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Dielectric material based topology optimization for wave optics . . . . 4

1.3 Metal material based topology optimization for wave optics . . . . . . . 5

1.4 Topology optimization on two dimensional manifolds for wave

optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Self-consistent adjoint analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.1 Topology optimization problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2 Split of wave equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3 Adjoint analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.4 Numerical implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.5 Numerical examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.5.1 Optical cloak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.5.2 Nanostructures for localized surface plasmon resonances . . . 36

2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.7.1 Adjoint analysis of topology optimization problem for two

dimensional optical waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.7.2 Adjoint analysis of topology optimization problem for

three dimensional optical waves . . . . . . . . . . . . . . . . . . . . . . . . 49

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3 Dielectric material based topology optimization for wave optics . . . . . 55

3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.1.1 Magnetic field formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.1.2 Adjoint analysis for magnetic field based topology

optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.1.3 Electric field formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.1.4 Adjoint analysis for electric field based topology

optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.1.5 Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.2.1 Cloak for perfect conductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.2.2 Dielectric resonator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.2.3 Beam splitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.2.4 Cloak for dielectric resonator . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.2.5 Metalens with optical vortices . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4 Metal material based topology optimization for waves optics . . . . . . . . 103

4.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

4.1.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.1.2 Analyzing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

4.1.3 Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

4.2.1 Nanostructures for localized surface plasmonic resonances . 109

4.2.2 Nanoslits for extraordinary optical transmission . . . . . . . . . . . 111

4.2.3 Nanoantennas for coupling free space and metal-insulatormetal

waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

4.2.4 Cloak for surface plasmonic polaritons . . . . . . . . . . . . . . . . . . 133

4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

4.4 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

5 Topology optimization on two dimensional manifolds for wave optics . 157

5.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

5.1.1 Two dimensional manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

5.1.2 PDEs for physical fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

5.1.3 Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

5.1.4 Topology optimization problem . . . . . . . . . . . . . . . . . . . . . . . . 160

5.1.5 Adjoint analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

5.1.6 Numerical implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

5.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

O autorze

Yongbo Deng is a professor at Changchun Institute of Optics Fine Mechanics and Physics (CIOMP), Chinese Academy of Sciences, China. In 2012, he received his Ph.D. from Changchun Institute of Optics Fine Mechanics and Physics (CIOMP), Chinese Academy of Sciences (CAS). In 2018, he derived a Humboldt Research Fellowship for Experienced Researchers and was elected as the member of Youth Innovation Promotion Association of Chinese Academy of Sciences in the same year. During the period from September of 2018 to February of 2020, he worked in the Institute of Microstructure Technology, Karlsruhe Institute of Technology as a Humboldt Fellow. During the periods from May to July of 2016 and from September to November of 2017, he worked in the Institute of Microstructure Technology, Karlsruhe Institute of Technology, based on support of a Guest Professor Fellowship. During the period from December of 2014 to March of 2015, he worked in IMTEK, University of Freiburg, for his research collaboration on electromagnetic metamaterial. His research mainly focuses on topology optimization, microfluidics, and nano-optics.

Blurb

The book focuses on the topology optimization method for nano-optics. Both principles and implementing practice have been addressed, with more weight placed on applications. This is achieved by providing an in-depth study on the major topic of topology optimization of dielectric and metal structures for nano-optics with extension to the surface structures for electromagnetics. The comprehensive and systematic treatment of practical issues in topology optimization for nano-optics is one of the major features of the book, which is particularly suited for readers who are interested to learn practical solutions in topology optimization. The book can benefit researchers, engineers, and graduate students in the fields of structural optimization, nano-optics, wave optics, electromagnetics, etc.