Manipulating Spatiotemporal Degrees of Freedom for Photonic Switching Devices : Theoretical and Machine-Learning Approaches = 광스위칭 소자 설계를 위한 시공간 자유도의 조작|RISS 상세보기

다국어 초록 (Multilingual Abstract)

Photonic switching devices are the most basic and essential unit for implementing optical memory and processor, which provide tunable optical responses according to external modulations in analogy with electronic transistors operated by the modulation of gate voltage. When designing such elements, both the spatial and temporal complexities are involved in the operation of photonic switching. For example, one should consider spatial characteristics of light, such as spin and orbital angular momenta and wave vector, as well as time-domain ones such as operating frequency, bandwidth, and the conservation of energy, in terms of the corresponding material and structural properties. In this point of view, the inherent large amount of degrees of freedom arising from the functional multiplicity in photonic active switching devices should be fully considered, while access to them is often blocked by the physical symmetries residing in the structure of devices. Despite the tradeoff between the number of degrees of freedom and the difficulties in terms of theoretical and computational cost, therefore, the necessity of symmetry breaking has been on the rise in recent studies, resolving the complexity with efficient theoretical and data-driven treatments.
Here, I introduce several related topics on numerical, theoretical, and data-driven methods in omnibus format for resolving spatiotemporal complexities in photonic switching or active devices, in terms of C4v-symmetry in photonic crystals and spatiotemporal translational symmetries in photonic disorders. These approaches will pave the way to the photonic design with extremely high complexities and be toolkits for optical computers.

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국문 초록 (Abstract)

광스위칭 (photonic switching) 소자는 일반 전자소자 기반 컴퓨터 내부 트랜지스터 의 동작 원리와 같이, 외부의 변조에 따라 광 응답 (optical response)을 조절할 수 있는 소자로서 광 기억소자 및 광 신호처리 장치의 기본이 된다. 이러한 스위칭 소자를 설계함에 있어, 소자의 동작과 관련된 공간 및 시간적인 복잡도는 매우 중요한 요인이다. 예를 들어, 스핀 및 궤도 각운동량, 파수벡터 등 빛의 공간적인 특성과 함께, 동작 주파수 및 대역, 에너지 보존 등 빛의 시간적인 특성은 관련된 매질 또는 구조의 특성과 연결하여 고려되어야 한다. 이러한 관점에서, 스위칭 소자를 설계할 때는 그 기능적 다양성 및 복잡성으로부터 기인하는 높은 설계 자유도가 요구되지만, 일반적으로 소자의 구조가 가지는 물리적인 대칭성으로부터 그러한 자유도에 통합적으로 접근하는 것은 극히 제한된다. 따라서, 대칭성이 주는 해석의 용이성 및 간결함, 적은 계산 비용에도 불구하고, 의도적인 대칭성 파괴를 통해 폭넓은 시공간적 자유도에 접근하는 것은 최근 연구의 트렌드가 되고 있다.
따라서, 이 논문에서는 스위칭 소자를 설계함에 있어 시공간적 복잡도를 해결하기 위한 수치적, 이론적, 및 데이터 기반의 여러 관련된 방법론들을 소개한다. 특히, 광결정에서의 C4v-대칭성 및 거울 대칭성 붕괴에 기반한 기울어진 디락 (Dirac) 분산관계 및 갭 분리, 시공간적 무질서계에서의 병진 대칭성을 파괴에 의한 빛의 산란특성 제어에 대해 이론적 배경과 함께 심도있게 다루도록 한다.

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광스위칭 (photonic switching) 소자는 일반 전자소자 기반 컴퓨터 내부 트랜지스터 의 동작 원리와 같이, 외부의 변조에 따라 광 응답 (optical response)을 조절할 수 있는 소자로서 광 기억소자 및 광...

목차 (Table of Contents)

1 Introduction 1
1.1 Motivation 1
1.2 Outline of the Dissertation 3
2 Theoretical Background 6
2.1 Photonic crystals 6

1 Introduction 1
1.1 Motivation 1
1.2 Outline of the Dissertation 3
2 Theoretical Background 6
2.1 Photonic crystals 6
2.1.1 k p theory for effective Hamiltonian description 9
2.1.2 Zero-refractive-index materials 11
2.2 Photonic disorders 14
2.2.1 Green's function and Born's approximation 14
2.2.2 Structure factor and τ order metric 18
2.3 Time-varying photonics 21
2.3.1 Temporal boundary 22
2.3.2 Open-system nature 23
3 Engineered Band Structures 28
3.1 Introduction 29
3.2 Effective Hamiltonian description of photonic Dirac cones 30
3.3 Inverse design of tilted Dirac cones 34
3.4 Bandgap opening in tilted PDCs 39
3.5 Discussion 39
4 Engineered Scattering Responses in Spatial Domain 41
4.1 Introduction 42
4.2 Model definition 44
4.3 DNN as a functional regressor 46
4.4 DNN as a material evaluator 51
4.5 Engineered active disorder 55
4.6 Discussion 58
5 Engineered Scattering Responses in Time Domain 60
5.1 Introduction 61
5.2 Temporal scattering 62
5.3 Unidirectional scattering 67
5.4 Engineered time disorder for spectral manipulation 70
5.5 Momentum-selective spectral shaping 73
5.6 Discussion 76
6 Conclusion 79
A Supplementary Information for Chapter 3 81
A.1 Effective wave parameter analysis 81
A.2 Derivation of band anti-crossing near a type-III Dirac point 83
A.3 Perturbative inverse design method 85
A.4 Dipole-based design 85
A.5 Practical implementation and the flat band control 86
A.6 Effect of mirror symmetry breaking 88
B Supplementary Information for Chapter 4 91
B.1 DNN Parameters 91
B.2 Dataset and training information 91
B.3 Normalized intensity profiles 95
B.4 Field distributions calculated by the finite element method 96
B.5 Model performance of R2GNet 97
B.6 Validity of mR2GNet 100
B.7 Plane-wave responses and effective medium approximation 101
B.8 Calculation of the τ order metric 103
B.9 Extended data for the optimization process 105
C Supplementary Information for Chapter 5 108
C.1 Scattering with Born approximation 108
C.2 Causal Green's function 112
C.3 Numerical validation of the Born approximation 114
C.4 Gaussian random generation and the conditions for structure factors 116
C.5 Design of structure factors for target forward and backward scatterings 118
C.6 Estimation of S(ω) for generated realizations 120
C.7 Details of SC(ω) and SP(ω) 121
D Numerical Methods 123
D.1 Plane-wave expansion method 123
D.2 Finite element method 125
D.3 Transfer matrix method 128
Bibliography 131
Abstract (In Korean) 152

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