Sub-wavelength Resolution in Ultrasonic waves by hyperbolic metamaterials
하이퍼볼릭 메타물질을 응용한 초음파의 회절한계 이상 해상도 구현

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dc.description학위논문 (박사)-- 서울대학교 대학원 : 기계항공공학부, 2014. 2. 김윤영.-
dc.description.abstractThe research in this dissertation aims at realizing sub-wavelength resolution by newly designed elastic metamaterial lens. Generally, elastic wave based imaging technology has been considered as highly useful imaging method, but its resolution is relatively low compared to other imaging method. The most critical resolution issue in elastic wave based imaging is diffraction limit which forbids resolution over certain limit in general media. Thus, the following question had been risen – how to overcome diffraction limit?. In recent years, a big progress in metamaterial has realized hyperlens which allow resolution over diffraction limit. However, although proposition of hyperlens made a big break-through, researches on hyperlens were mainly focused on electromagnetic waves. Researches on hyperlens for elastic waves have been rare, and the performance of the previously designed elastic hyperlens was still limited. Motivated by this, a new elastic hyperlens that exhibits much improved performance than the previously proposed one is proposed in this work.
The study of new elastic hyperlens performed in this work not only deals proposition of the new hyperlens but also covers physical, numerical, experimental and analytic approaches. After reviewing background physics related to diffraction limit and hyperlens, the way to break the previous hyperlens limitation is presented. New elastic metamaterial that satisfies pre-considered design requirements is engineered, and new elastic hyperlens is designed from the metamaterial. To verify the proposed elastic metamaterial and hyperlens, finite element analysis is formulated and numerical wave simulation is performed. For confirmation of performance improvement, numerical simulations with sub-wavelength sources are conducted for both the proposed hyperlens and the previous one, and the results are directly compared. In the experimental approach, the proposed hyperlens is realized in aluminum plate and sub-wavelength resolution of the hyperlens is experimentally shown. To achieve desired sub-wavelength sources, a new elastic wave transducer is developed. During experiments, actuation pulse tailoring and measured signal calibration is introduced to facilitate the experiment. Finally, analytic approach for the elastic metamaterial and hyperlens is performed. Equivalent mass-spring system for the designed metamaterial is constructed, and wave dispersion equation is analytically formulated. From the constructed analytic mass-spring system, design guidelines for further improvement of the proposed elastic hyperlens are shown.
dc.description.tableofcontentsAbstract i
List of Figures vi

Chapter 1. Introduction 1
1.1 Research motivation 1
1.2 History of metamaterial and sub-wavelength resolution 5
1.2.1 What is metamaterial? 5
1.2.2 Sub-wavelength imaging via metamaterial 7
1.3 Research objectives and coverage 11
1.4 Organization of the thesis 13

Chapter 2. Theories of metamaterial-based sub-wavelength resolution 15
2.1 Chapter overview 15
2.2 Physical origin of diffraction limit 16
2.3 Physics behind sub-wavelength resolution by hyperlens 26
2.3.1 Hyperlens with hyperbolic EFC 26
2.3.2 Hyperlens with elliptic EFC 36

Chapter 3. Proposition of new elastic hyperlens based on hyperbolic elastic metamaterial 43
3.1 Chapter overview 43
3.2 Design of hyperbolic elastic metamaterial and hyperlens 45
3.2.1 Design requirements of proposed hyperbolic elastic metamaterial 45
3.2.2. How to obtain the desired hyperbolic elastic metamaterial? 49
3.2.3 Proposition of new hyperbolic elastic metamaterial and hyperlens 59
3.3 Numerical verification of hyperbolic elastic metamaterial 64
3.3.1 Finite element formulation for wave dispersion characteristics of the proposed elastic metamaterial 64
3.3.2 EFC calculation for the proposed elastic metamaterials 72
3.4 Numerical simulation for the proposed elastic hyperlens 77
3.4.1 Numerical simulation for sub-wavelength resolution 77
3.4.2 Numerical simulation for resolution improvement of the proposed hyperlens 84

Chapter 4. Experimental approach for the proposed elastic hyperlens 89
4.1 Chapter overview 89
4.2 Development of new elastic wave actuator for the experiment 90
4.3 Experimental procedure 98
4.3.1 Experimental setting 98
4.3.2 Signal post-processing 104
4.4 Experimental results 108

Chapter 5. Analytic approach for the proposed elastic hyperlens 110
5.1 Chapter overview 110
5.2 Analytic modeling along circumferential directions 112
5.2.1 Analytic calculation of the dispersion relation of mass-spring model along circumferential directions 112
5.2.2 Calculation of the equivalent mass/spring coefficients along circumferential directions 115
5.2.3 Verification of the analytic modeling along circumferential directions 121
5.3 Analytic modeling along radial directions 123
5.3.1 Analytic calculation of the dispersion relation of mass-spring model along radial directions 123
5.3.2 Calculation of the equivalent mass/spring coefficients along radial directions 129
5.3.3 Verification of the analytic modeling along radial directions 134
5.4 Design improvement by the proposed analytic method 136

Chapter 6. Conclusion 140

Appendix A. Finite element analysis of radiation characteristics of guided waves generated by magnetostrictive patch-type transducers 143
A.1. Appendix overview 143
A.2. Finite element formulation for general MPTs 147
A.2.1 Linearized magnetostrictive modeling for general MPTs 147
A.2.2 Time-harmonic wave simulation for general MPTs 152
A.2.3 Overall finite element analysis procedure 159
A.3. Verification of the proposed analysis and numerical observations 161
A.3.1 Verification of the proposed finite element analysis 161
A.3.2 Numerical observations for elastic wave generation in MPTs 172
A.4. Conclusion 175

References 178
Abstract (Korean) 192
Acknowledgements 194
dc.format.extent33538822 bytes-
dc.publisher서울대학교 대학원-
dc.subjectHyperbolic equi-frequency curve-
dc.subjectElastic hyperlens-
dc.subjectSub-wavelength resolution-
dc.subjectElastic metamaterial-
dc.titleSub-wavelength Resolution in Ultrasonic waves by hyperbolic metamaterials-
dc.title.alternative하이퍼볼릭 메타물질을 응용한 초음파의 회절한계 이상 해상도 구현-
dc.contributor.AlternativeAuthorJoo Hwan Oh-
dc.citation.pagesx, 194-
dc.contributor.affiliation공과대학 기계항공공학부-
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College of Engineering/Engineering Practice School (공과대학/대학원)Dept. of Mechanical Aerospace Engineering (기계항공공학부)Theses (Ph.D. / Sc.D._기계항공공학부)
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