Tài liệu Động lực học cổ điển và lượng tử cấu trúc nano đa lớp

1.1.3 Electromagnetic waves 6
1.1.4 Potentials of field . 7
1.1.5 TMand TE waves 10
1.1.6 Debye potentials . 13
1.1.7 Energy of field . 22
1.1.8 Metallized sphere . 28
1.1.9 Frequency dispersion . 30
1.2 The Variational Principle . 32
1.2.1 TheWhitham’s average variational principle 34
1.2.2 Energy in a layeredmicrosphere . 36
1.3 MultilayeredMicrosphere . 37
1.4 The Transfer Matrix Method (Solving Equations for a
System of Spherical Layers) . 37
1.5 Reflection Coefficient and Impedance of a Spherical Stack . 43
1.6 Conclusion . 48
xi
xii Contents
2. Electromagnetic Field in Homogeneous Microspheres
Without Surface Structures 50
2.1 Experiments withMicrospheres . 50
2.2 Lorentz–Mie theory and its extensions 57
2.2.1 Lorentz–Mie theory of elastic scattering 58
2.2.2 Theory of spontaneous emission . 62
2.2.3 Mie scattering by concentrically stratified spheres . 65
2.3 Peculiarities of the modes of an open spherical cavity . 65
2.3.1 Indexes and order of a whispering-gallery mode 65
2.3.2 The problem of normalization of the
whispering-gallerymodes . 66
2.4 Quality factor of a whispering-gallerymode . 69
2.4.1 Radiative quality factor of an ideal dielectric sphere 69
2.4.2 Effect of light absorption on the quality factor . 72
2.4.3 Light scattering on inhomogeneities of the refractive
index 72
2.4.4 Effect of a spherical submicrometer-size inclusion . 76
2.4.5 Comparison of different WGM-scattering models . 77
2.4.6 Q factor of a loaded cavity 79
3. Electromagnetic Eigen Oscillations and Fields in a
Dielectric Microsphere with Multilayer Spherical Stack 81
3.1 Introduction 81
3.2 Geometry and Basic Equations 84
3.3 Eigenfrequencies of the Spherical Resonator Coated
by the Stack 86
3.4 Radial Distribution of Fields . 91
3.5 Discussions . 95
3.6 Conclusion . 99
4. Transmittance and Resonance Tunneling of the Optical
Fields in the Microspherical Metal-Dielectric Structures 101
4.1 Introduction 101
4.2 Geometry and Basic Equations 103
4.3 Results and Discussions 106
4.4 Conclusion . 112
Contents xiii
5. Confinement of Electromagnetic Oscillations in a
Dielectric Microsphere Coated by the Frequency
Dispersive Multilayers 113
5.1 Introduction 113
5.2 Basic Equations 114
5.3 Results and Discussions 116
5.4 Conclusion . 120
6. Oscillations in Microspheres with an Active Kernel 121
6.1 Basic Equations . 122
6.2 Results and Discussions . 123
6.3 Conclusion 129
7. Transfer Matrix Approach in a Non-Uniform Case 130
7.1 Approach to a Non-UniformCase . 131
7.2 Example. Non-UniformElectron’s Concentration 134
II The Quantum Phenomena in Microspheres
8. Coupling of Two-Level Atom with Electromagnetic Field 145
8.1 Transitions under the Action of the
Electromagnetic Field 147
8.2 The Equations for Probability Amplitudes 148
8.3 Derivation of the Equation for Polarization of TLA:
Dielectric Permittivity . 150
8.4 Temporal Dynamics of Polarization and the
Probability Amplitudes . 153
9. Classical Field 157
9.1 Schr¨odinger Equation 157
9.2 Matrix Formfor Two-Level Atom . 158
10. Quantization of Electromagnetic Field 161
10.1 Energy of Field . 162
10.2 Structure of VacuumField . 166
xiv Contents
11. Schr¨odinger and Interaction Pictures 168
11.1 Equations for the State Vectors 168
11.2 Equations for Operators 171
11.2.1 Operator’s calculations . 172
12. Two-Level Atom (The Matrix Approach, a Quantized Field) 173
12.1 Equations for Probability Amplitudes in
Spherical Coordinates 178
13. Dynamics of Spontaneous Emission of Two-Level Atom
in Microspheres: Direct Calculation 182
13.1 Introduction . 182
13.2 Basic Equations . 185
13.3 Results and Discussions . 190
13.4 Triple photon state . 200
13.4.1 Basic equations . 200
13.4.2 Wigner function . 207
13.5 Conclusions . 211
III Numerical Methods and Object-Oriented
Approach to the Problems of Multilayered
Microsystems
14. Use of Numerical Experiment 217
14.1 Introduction . 221
14.2 The Brief Review of C++ Operators . 222
14.2.1 Data . 222
14.2.2 Operators 225
14.2.3 Functions 230
14.2.4 Interacting the data of class with
member functions 237
14.2.5 Classes 239
14.2.6 Access to members . 240
14.2.7 Virtual functions 243
14.2.8 Overloading the mathematical operator 247
Contents xv
15. Exception Handling 250
15.1 Code . 252
16. Visual Programming: Controls, Events and Handlers 254
16.1 DOS and Visual Programming . 254
16.2 Controls, Events and Handlers . 255
16.3 Graphical User Interface 259
17. Quantum Electromagnetic Field 260
17.1 Introduction . 260
17.2 Code . 261
17.3 Classes 264
18. Root Finding for Nonlinear and Complex Equations 270
18.1 Introduction . 270
18.2 Code . 271
18.3 Classes 275
19. Evaluation of Complex ODE 284
19.1 Introduction . 284
19.2 Code . 285
19.3 Classes 290
20. The Complex Vectorial and Matrix Operations 293
20.1 Introduction . 293
20.2 Code . 294
20.3 Classes 305
21. Spontaneous Emission of Atom in Microsphere 324
21.1 Introduction . 324
21.2 Code . 327
21.3 Classes 327
22. Electromagnetic Oscillations in Layered Microsphere 340
22.1 Introduction . 340
xvi Contents
Appendix A: Calculation of Field’s Energy in a Sphere 349
Appendix B: Calculation of Surface Integral 352
Appendix C: Continuity of Tangential Fields 353
Appendix D: Integral on Bessel Functions 354
Appendix E: Surface Integrals for Dipole 355
Appendix F: Some Mathematical Formulas 357
Appendix G: Various Head *.h Files 360
Bibliography 364
Index 377