臺灣博碩士論文加值系統

動態可調的超穎表面近年來逐漸受到重視，由於其可調製任意位置相位之特性，可應用於自駕車、相機及遙測等領域。我們藉由次波長三明治型光柵理論，提出一個電控可調的液晶超穎表面以控制光束方向和偏振特性。此理論有效率地預測一個可引發共振疊加的結構以達到2π 的相位改變。我們亦以自建之平行化三維時域有限差分法電磁模擬器搭配各向異性材料演算法驗證該理論。我們設計之超穎表面是以內含液晶的矽柱為最小單元組成之陣列，隨著施加偏壓以改變約0.2的液晶分子折射率變化範圍，此設計針對1550 奈米波長的近紅外線達到1.96π 相位調製範圍及超過99% 的反射率。藉著控制反射波的相位，我們個別演示了光束偏轉器及偏振轉換器之應用。該可調式光束偏轉器的最大的偏轉角度為40.23 度。該偏振轉換器能將線偏光轉換成與之互相垂直之線偏光、左右旋極化光，甚至是橢偏光，並具有接近全反射的效率及超過30 dB 的優異消光比。

Dynamic metasurfaces with arbitrary phase manipulation are favorable for numerous applications in the fields of self-driving cars, cameras, and sensing. We propose an electrically tunable liquid crystal (LC) metasurfaces for beam steering and polarization manipulation by exploiting the modal method of subwavelength sandwich gratings. This method efficiently predicts a resonance overlapping structure for 2π phase tuning. The in-house parallelized three-dimensional finite-difference time-domain (FDTD) electromagnetic numerical solver for anisotropic materials is established to verify the correctness of modal method. The delicate metasurface consisting of embedded LC silicon pillar resonator array achieves 1.96π phase tuning and ultrahigh reflectance over 99% with a small LC refractive index change of approximately 0.2 for a single wavelength 1550 nm. By controlling the phase of reflected wave, the metasurface realizes a tunable beam deflector or a polarization converter. The proposed beam deflector has a maximum deflected angle of 40.23◦. The proposed polarization converter can transform linear to crossed linear, circular, or elliptical polarization with near total reflection and excellent polarization extinction ratios over 30 dB.

1 Introduction 1
1.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Introduction to Computational Electromagnetics . . . . . . . . . . . . . . 4
1.3 Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 The FiniteDifference
TimeDomain
Method 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 The Courant Stability Limit . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 The TotalField
/ ScatteredField
Technique . . . . . . . . . . . . . . . . 11
2.4 Convolutional Perfectly Matched Layer . . . . . . . . . . . . . . . . . . 13
2.5 Periodic Boundary Condition (PBC) . . . . . . . . . . . . . . . . . . . . 16
2.6 Implementation of Dispersive Material Models . . . . . . . . . . . . . . 17
2.6.1 The Drude Model . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6.2 The DrudeLorentz
Model . . . . . . . . . . . . . . . . . . . . . 19
2.6.3 The Auxiliary Differential Equation (ADE) Method . . . . . . . . 20
2.7 The FDTD Algorithm for Anisotropic Material . . . . . . . . . . . . . . 23
2.8 Mathematical Description of Liquid Crystals Rotation in Space . . . . . . 28
2.9 Parallelized FDTD Method . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.10 Validation of FDTD Simulated Results with Analytical Solutions . . . . . 32
2.10.1 Phasor Calculation for 2D
Circular Cylinders . . . . . . . . . . . 32
2.10.2 Phasor Calculation for 3D
Silver Sphere . . . . . . . . . . . . . 33
2.10.3 Calculation of Total Scattering CrossSection
. . . . . . . . . . . 37
2.10.4 Reflectance Calculation for Periodic Structure . . . . . . . . . . . 39
2.10.5 Phase Calculation for Anisotropic material . . . . . . . . . . . . 40
2.11 Periodic NeartoFarField
Transformation . . . . . . . . . . . . . . . . . 43
3 Mechanism of HighContrast
Grating in Subwavelength Region 45
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Theoretical Analysis of Binary Subwavelength Grating . . . . . . . . . . 46
3.2.1 TMPolarized
SurfaceNormal
Incidence . . . . . . . . . . . . . 48
3.2.2 Comparison of TM Analytic and FDTD Simulation . . . . . . . . 55
3.2.3 TEPolarized
SurfaceNormal
Incidence . . . . . . . . . . . . . . 58
3.2.4 Comparison of TE Analytic and FDTD Simulation . . . . . . . . 61
3.2.5 Calculation of Periodic Waveguide ω − β Relation by Finite Difference
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.3 Theoretical Analysis of Sandwich Subwavelength Grating . . . . . . . . 64
3.4 Mode Mechanism of HighContrast
Grating in Dual Mode Region . . . . 69
3.4.1 Types of Periodic Waveguide Array Modes . . . . . . . . . . . . 70
3.4.2 High Transmittance and Reflectance Mechanism . . . . . . . . . 75
3.5 Mechanisms of HighContrast
Grating and Huygens’ Metasurface . . . . 77
4 PhaseTunable
Liquid Crystal Metasurfaces 81
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.2 Static Metasurfaces for Controlling Light Propagation . . . . . . . . . . . 82
4.2.1 Transmitted Beam Deflection Subwavelength Grating . . . . . . 82
4.2.2 Reflected Beam Deflection Subwavelength Grating . . . . . . . . 85
4.3 Tunable Liquid Crystal Metasurfaces for Beam Steering . . . . . . . . . 88
4.3.1 Steering of ±1st Diffracted Beams . . . . . . . . . . . . . . . . . 90
4.3.2 Steering of a Single Diffracted Beam . . . . . . . . . . . . . . . 93
4.4 HighQ
SandwichShaped
Resonator for Full Phase Coverage . . . . . . 96
4.4.1 HighQ
Resonant Beam Deflector . . . . . . . . . . . . . . . . . 97
4.4.2 HighQ
Resonant Polarization Converter . . . . . . . . . . . . . 102
5 Conclusion 109
Bibliography 111

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