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Resonance: Long-Lived Waves, a new volume in the
Interface Transmission Tutorial Book series, introduces long-life resonance properties for telecommunications. The book's authors review the general analysis methods of interface transmission, giving many examples and applying these methods to telecommunications systems (materials and devices). Each chapter introduces and defines the long-lived resonances, their path states and phase shifts, and applications.
This book is suitable for materials scientists and engineers in academia and R&D, and may also be appropriate for applied physicists.
List of contents
Preface xi
Acknowledgments xiii
1 State phase, rules, and theorems 1
1.1 Introduction
1
1.2
Finite, semi-infinite, and infinite systems 2
1.3
State and resonance 2
1.4 State phase
3
1.4.1 State phase shift
4
1.4.2 General state phase
5
1.4.3 Discrete final states
6
1.4.4 Bulk state phase shift
7
1.4.5 Comments
7
1.5 General rules and theorems
8
1.5.1 Eigenfunction continuity rules
8
1.5.2 General theorems
9
1.6 Outlook
9
References
10
2 Photonic open loops 11
2.1 Introduction
11
2.2 Open loops
12
2.2.1 Open-loop basic elements
12
2.2.2 One finite open loop
17
2.2.3 Two finite open loops
20
2.2.4
N finite open loops
25
2.3 Comb systems
30
2.3.1 A finite comb system with two teeth and three teeth at its two ends
31
2.3.2 A finite comb system with
N teeth at
M equidistant interface points
35
2.3.3 Long-lived resonances: comb with two teeth per port
38
2.4 Outlook
51
References
52 3 One photonic closed loop 53
3.1 Introduction
53
3.2 One closed loop and stubs
53
3.2.1 Basic closed-loop elements
53
3.2.2 One closed loop
L and one stub
L3
55
3.2.3 One closed loop
L and several stubs
70
3.3 Simultaneous cross transmissions and disentanglement
79
3.4 Outlook
79
Acknowledgments
79
References
79
4 Two photonic closed loops 81
4.1 Introduction
81
4.2 Two tangent closed loops
81
4.2.1 General results
81
4.2.2 Two identical tangent loops
L 83
4.2.3 Two tangent closed loops
L1 and
L2
86
4.3 Two tangent closed loops and stubs
89
4.3.1 Two closed loops
L1 and
L2 and two stubs
L1
/4 and
L2
/4
89
4.3.2 Two closed loops
L +
¿ and
L ¿
¿ and two stubs
L/4 +
¿/4 and
L/4 ¿
¿/4
93
4.3.3 Two closed loops
L +
¿1 and
L¿
¿1 and two stubs
L/2+
¿2 and
L/2 ¿
¿2
96
4.4 Outlook
98
References
99
5 Photonic two-port closed loop 101
5.1 Introduction
101
5.2 Closed-loop states
102
5.3 Final system states
104
5.3.1 BIC and SIBIC states
104
5.3.2 Bulk state phase shift and state densities
105
5.4 Transmission
108
5.4.1 The transmission coefficient and the hybrid long-lived resonances
108
5.4.2 Transmission phase and phase time
111
5.5 States and transmission
113
5.6 Stub hybrid resonances
115
5.6.1 A general system
115
5.6.2 Identical stubs
L3 =
L4
117
5.7 Cross-transmission
125
5.7.1 Cross-transmissions for any symmetric two-port system
125
5.7.2 Cross-transmissions for the two-port closed loop
125
5.7.3 Stub improved cross-transmissions
129 5.8 Outlook
129
Acknowledgments
130
References
130
6 Photonic spheres 133
6.1 Introduction
133
6.2 States of a two interface point sphere
134
6.3
N closed loops: two tangent interface points and one port
135
6.3.1 BIC and SIBIC states
136
6.3.2 Long-lived transmission resonances in function of
N 136
6.4 Long-lived transmission resonances for
N = 2: one port
137
6.4.1 Two closed loops of length
L 137
6.4.2 Two closed loops
L1 =
L +
¿,
L2 =
L ¿
¿ and stubs
L1
/4,
L2
/4
138
6.4.3 Two closed loops (4 different parts): one
L/4 stub
142
6.4.4 Two closed loops (4 different parts): stubs
L/4 and
L/8
144
6.5
N closed loops: two tangent interface points and two ports
145
6.5.1 BIC and quasi-SIBIC states
147
6.5.2 Long-lived transmission resonances as functions of
N 148
6.6 Long-lived transmission resonances for
N = 2: two ports
149
6.7 Outlook
152
References
152
7 Photonic triangular pyramid 153
7.1 Introduction
153
7.2 Triangular pyramid states
154
7.2.1 Response function elements
154
7.2.2 States of the pyramid
155
7.3 The pyramid with two leads: one port
156
7.3.1 BIC and SIBIC states
156
7.3.2 Transmission, transmission phase, and state phase shift
157
7.3.3 The one port long-lived resonances
160
7.4 The pyramid with two leads: two ports
167
7.4.1 BIC and SIBIC states
169
7.4.2 Transmission, transmission phase, and state phase shift
169
7.4.3 The two-port long-lived resonances
174
7.5 Outlook
181
References
182
8 Square pyramid: one summit port 183
8.1 Introduction
183
8.2 Square pyramid states
184
8.2.1 Response function: interface elements
185
8.2.2 States of the square pyramid
186 8.3 The pyramid with one summit port
187
8.3.1 BIC and SIBIC states
188
8.3.2 Transmission, state phase shift, and VADOS
188
8.3.3 Transmission phase and phase time
191
8.3.4 The long-lived resonances
193
8.4 State and particle shifts, collapses, and sensing
199
8.5 Outlook
202
References
203
9 Generalizations 205
9.1 Introduction
205
9.2 Other simple system geometries
206
9.2.1 Open-loop chains
206
9.2.2 Closed-loop chains
206
9.2.3 Hexagons
206
9.2.4 Squares and cubes
207
9.2.5 Square pyramids
207
9.2.6 Many-port systems
207
9.3 Other generalizations
207
9.3.1 Composite material systems
207
9.3.2 Long-wavelength electronic waves
208
9.3.3 Plasmonic waves
209
9.3.4 Elastic waves
209
9.3.5 Polaritonic waves
209
9.3.6 Spin waves
209
9.3.7 Atomic and continuous material edge states
209
9.3.8 Simulations and state number conservations
209
9.3.9 Exact models versus small deformation ones
210
9.3.10 The attenuation effects
210
9.4 Outlook
210
References
210
Index 213
About the author
Léonard Dobrzyński is Emeritus Research Professor at CNRS, Lille University, France. His research interests focus on interface science, phononics, magnonics, and resonance.
Housni Al-Wahsh is Professor of Theoretical Physics and Head of the Engineering, Mathematics, and Physics Department, Faculty of Engineering, Benha University, Cairo, Egypt. He is primarily interested in the physical properties of electronic, plasmonic and magnonic crystals.
Abdellatif Akjouj is Professor at the University of Lille in France. His scientific activities deal with theory and modelling of wave propagation and elementary excitations in nanostructured materials, more particularly: nanoplasmonics, photonics, magnonics, phononics and optomechanics.
