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Theory of wave propagation in inhomogeneous complex media including Dirac materials, bi-isotropic metamaterials, and plasmas

초록/요약

In this thesis, we investigate the wave propagation in inhomogeneous complex media, including Dirac materials, bi-isotropic metamaterials, and plasmas theoretically, using the invariant imbedding method (IIM). We pursue to find phenomena that are well-known in one's field but unconventional in the other's field, comparing two different kinds of waves that have similarities in the forms of the wave equation. In order to investigate the wave propagation in various materials, we generalize IIM. At first, we investigate the surface wave excitation in the interface between a metal/a bi-isotropic medium, and bi-isotropic/bi-isotropic media. We also derive the dispersion relation of surface waves. The results obtained using IIM agree with those obtained from the dispersion relation perfectly. We generalize the concept of a conjugate matched pair to bi-isotropic media and obtain several conditions under which the omnidirectional total transmission, which we call the super-Klein tunneling, occurs through conjugate matched pairs consisting of Tellegen media and of chiral media. We find that these conditions are closely linked to those for the omnidirectional excitation of surface waves. Secondly, we investigate the mode conversion of transverse electromagnetic waves into longitudinal plasma oscillations in chiral media and magnetized plasma. We verify the conditions where mode conversion occurs and find the conditions where mode conversion enhanced. We explain the giant over-reflection as the inverse process of perfect absorption. Lastly, we investigate the Anderson localization phenomena of electromagnetic waves in anisotropic media and matter waves in pseudospin-1/2, -1 Dirac materials. By applying the perturbation expansion method to the invariant imbedding equations, we derive concise analytical expressions for the localization length, which are extremely accurate in the weak and strong disorder regimes. From analytical considerations, we provide an interpretation of the delocalization of waves at a special incident angle, as a phenomenon arising when the wave impedance is effectively uniform. Similarly, the ordinary Brewster effect of EM waves, the Klein tunneling of massless pseudospin-N particles and the super Klein tunneling of massless pseudospin-1 particles which are the total transmission phenomena of waves at a condition, is interpreted as an impedance matching phenomenon.

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목차

1 Introduction 1
2 Invariant imbedding theory of wave propagation in arbitrarily inhomogeneous stratified bi-isotropic media 8
2.1 Introduction 8
2.2 Coupled wave equations in stratified bi-isotropic media 10
2.3 Invariant imbedding equations 11
2.4 Conservation of energy 15
2.5 Applications 17
2.5.1 Uniform chiral slab 18
2.5.2 Surface waves in Tellegen media 19
2.5.3 Mode conversion in inhomogeneous Tellegen media 22
2.6 Conclusion 24
3 Excitation of surface waves on the interfaces of general biisotropic media 29
3.1 introduction 29
3.2 Dispersion relation for surface waves in general bi-isotropic media 31
3.3 Invariant imbedding method 33
3.4 Numerical results 35
3.5 Conclusion 48
4 Omnidirectional excitation of surface waves and super-Klein tunneling at the interface between two different bi-isotropic media 52
4.1 Introduction 52
4.2 Dispersion relation for surface waves 56
4.3 Omnidirectional excitation of surface waves and super-Klein tunneling 58
4.4 Invariant imbedding method 62
4.5 Numerical results 70
4.5.1 Generic case 70
4.5.2 Cases I and II 72
4.5.3 Cases III and IV 77
4.5.4 Case III or IV 79
4.5.5 Cases V and VI 83
4.5.6 Cases VII and VIII 85
4.5.7 Case VII or VIII 88
4.6 Conclusion 92
5 Anderson localization and Brewster anomaly of electromagnetic waves in randomly-stratified anisotropic media 98
5.1 Introduction 98
5.2 Model 99
5.3 Invariant imbedding method 100
5.3.1 Model I 101
5.3.2 Model II 102
5.4 General considerations on the existence condition of the Brewster anomaly and the properties of localization 103
5.4.1 Argument based on the impedance matching condition 103
5.4.2 Argument based on the Fresnel formula 107
5.5 Analytical expressions for the localization length in the weak disorder regime 108
5.6 Numerical results 109
5.7 Conclusion 114
6 Resonant absorption and amplification of circularly-polarized waves in inhomogeneous chiral media 119
6.1 Introduction 119
6.2 Method 121
6.3 Numerical result 123
6.4 Conclusion 130
7 Perfect absorption and giant over-reflection induced by the mode conversion of MHD waves 136
7.1 Introduction 136
7.2 model 138
7.3 Invariant imbedding method 141
7.4 Time-reversed partner 142
7.5 Numerical result 144
7.6 Conclusion 148
8 Anderson localization and delocalization of massless two dimensional Dirac electrons in random one-dimensional scalar and vector potentials 151
8.1 Introduction 151
8.2 Model 154
8.3 Invariant imbedding method 156
8.4 Interpretation of Klein tunneling and related delocalization phenomena using the concept of wave impedance 159
8.4.1 Effective wave impedance 159
8.4.2 Generalized Klein tunneling in inhomogeneous potentials 161
8.4.3 Delocalization condition in the presence of random scalar and vector potentials 163
8.4.4 Alternative derivation of the delocalization condition using the Fresnel formula 165
8.4.5 Counterintuitive delocalization in the strong disorder limit 165
8.5 Analytical expression for the localization length in the weak and strong disorder regimes 166
8.5.1 Weak disorder regime 166
8.5.2 Strong disorder regime 169
8.6 Numerical Results 171
8.6.1 Incident angle dependence 171
8.6.2 Disorder dependance 178
8.6.3 Energy dependence 181
8.6.4 Total transmission through a disordered region 184
8.7 Conclusion 185
9 Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a correlated random one-dimensional scalar potential 191
9.1 Introduction 191
9.2 Model 195
9.3 Invariant imbedding method 198
9.3.1 δ-correlated random potential 199
9.3.2 Short-range correlated dichotomous random potential 201
9.4 Analytical expressions for the localization length in the weak and strong disorder regimes 203
9.4.1 Weak disorder regime in a δ-correlated random potential 203
9.4.2 Weak disorder regime in a short-range correlated dichotomous random potential 205
9.4.3 Strong disorder regime in a short-range correlated dichotomous random potential 209
9.5 Numerical results 212
9.5.1 Incident angle dependence 212
9.5.2 Disorder correlation length dependence 216
9.5.3 Disorder strength dependence 216
9.5.4 Energy and wavelength dependence 220
9.6 Conclusion 226
10 Conclusion 232
A Invariant imbedding method 236

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