Resonance

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.

• Preface xiAcknowledgments xiii1 State phase, rules, and theorems 11.1 Introduction 11.2 Finite, semi-infinite, and infinite systems 21.3 State and resonance 21.4 State phase 31.4.1 State phase shift 41.4.2 General state phase 51.4.3 Discrete final states 61.4.4 Bulk state phase shift 71.4.5 Comments 71.5 General rules and theorems 81.5.1 Eigenfunction continuity rules 81.5.2 General theorems 91.6 Outlook 9References 102 Photonic open loops 112.1 Introduction 112.2 Open loops 122.2.1 Open-loop basic elements 122.2.2 One finite open loop 172.2.3 Two finite open loops 202.2.4 N finite open loops 252.3 Comb systems 302.3.1 A finite comb system with two teeth and three teeth at its two ends 312.3.2 A finite comb system with N teeth at M equidistant interface points 352.3.3 Long-lived resonances: comb with two teeth per port 382.4 Outlook 51References 523 One photonic closed loop 533.1 Introduction 533.2 One closed loop and stubs 533.2.1 Basic closed-loop elements 533.2.2 One closed loop L and one stub L3 553.2.3 One closed loop L and several stubs 703.3 Simultaneous cross transmissions and disentanglement 793.4 Outlook 79Acknowledgments 79References 794 Two photonic closed loops 814.1 Introduction 814.2 Two tangent closed loops 814.2.1 General results 814.2.2 Two identical tangent loops L 834.2.3 Two tangent closed loops L1 and L2 864.3 Two tangent closed loops and stubs 894.3.1 Two closed loops L1 and L2 and two stubs L1/4 and L2/4 894.3.2 Two closed loops L +δ and L −δ and two stubs L/4 +δ/4 and L/4 −δ/4 934.3.3 Two closed loops L +δ1 and L− δ1 and two stubs L/2+ δ2 and L/2 −δ2 964.4 Outlook 98References 995 Photonic two-port closed loop 1015.1 Introduction 1015.2 Closed-loop states 1025.3 Final system states 1045.3.1 BIC and SIBIC states 1045.3.2 Bulk state phase shift and state densities 1055.4 Transmission 1085.4.1 The transmission coefficient and the hybrid long-lived resonances 1085.4.2 Transmission phase and phase time 1115.5 States and transmission 1135.6 Stub hybrid resonances 1155.6.1 A general system 1155.6.2 Identical stubs L3 = L4 1175.7 Cross-transmission 1255.7.1 Cross-transmissions for any symmetric two-port system 1255.7.2 Cross-transmissions for the two-port closed loop 1255.7.3 Stub improved cross-transmissions 1295.8 Outlook 129Acknowledgments 130References 1306 Photonic spheres 1336.1 Introduction 1336.2 States of a two interface point sphere 1346.3 N closed loops: two tangent interface points and one port 1356.3.1 BIC and SIBIC states 1366.3.2 Long-lived transmission resonances in function of N 1366.4 Long-lived transmission resonances for N = 2: one port 1376.4.1 Two closed loops of length L 1376.4.2 Two closed loops L1 = L +δ, L2 = L −δ and stubs L1/4, L2/4 1386.4.3 Two closed loops (4 different parts): one L/4 stub 1426.4.4 Two closed loops (4 different parts): stubs L/4 and L/8 1446.5 N closed loops: two tangent interface points and two ports 1456.5.1 BIC and quasi-SIBIC states 1476.5.2 Long-lived transmission resonances as functions of N 1486.6 Long-lived transmission resonances for N = 2: two ports 1496.7 Outlook 152References 1527 Photonic triangular pyramid 1537.1 Introduction 1537.2 Triangular pyramid states 1547.2.1 Response function elements 1547.2.2 States of the pyramid 1557.3 The pyramid with two leads: one port 1567.3.1 BIC and SIBIC states 1567.3.2 Transmission, transmission phase, and state phase shift 1577.3.3 The one port long-lived resonances 1607.4 The pyramid with two leads: two ports 1677.4.1 BIC and SIBIC states 1697.4.2 Transmission, transmission phase, and state phase shift 1697.4.3 The two-port long-lived resonances 1747.5 Outlook 181References 1828 Square pyramid: one summit port 1838.1 Introduction 1838.2 Square pyramid states 1848.2.1 Response function: interface elements 1858.2.2 States of the square pyramid 1868.3 The pyramid with one summit port 1878.3.1 BIC and SIBIC states 1888.3.2 Transmission, state phase shift, and VADOS 1888.3.3 Transmission phase and phase time 1918.3.4 The long-lived resonances 1938.4 State and particle shifts, collapses, and sensing 1998.5 Outlook 202References 2039 Generalizations 2059.1 Introduction 2059.2 Other simple system geometries 2069.2.1 Open-loop chains 2069.2.2 Closed-loop chains 2069.2.3 Hexagons 2069.2.4 Squares and cubes 2079.2.5 Square pyramids 2079.2.6 Many-port systems 2079.3 Other generalizations 2079.3.1 Composite material systems 2079.3.2 Long-wavelength electronic waves 2089.3.3 Plasmonic waves 2099.3.4 Elastic waves 2099.3.5 Polaritonic waves 2099.3.6 Spin waves 2099.3.7 Atomic and continuous material edge states 2099.3.8 Simulations and state number conservations 2099.3.9 Exact models versus small deformation ones 2109.3.10 The attenuation effects 2109.4 Outlook 210References 210Index 213