Preface -- Contents -- Introduction -- I Classical Dynamics -- 1. Maxwell Equations -- 1.1 Basic Equations -- 1.1.1 Wave equation -- 1.1.2 Three-dimensional case -- 1.1.3 Electromagnetic waves -- 1.1.4 Potentials of field -- 1.1.5 TM and TE waves -- 1.1.6 Debye potentials -- (i) TM case -- (ii) TE case -- (iii) Uniform dispersive medium -- 1.1.7 Energy of field -- 1.1.8 Metallized sphere -- 1.1.9 Frequency dispersion -- 1.2 The Variational Principle -- 1.2.1 The Whitham's average variational principle -- 1.2.2 Energy in a layered microsphere -- 1.3 Multilayered Microsphere -- 1.4 The Transfer Matrix Method (Solving Equations for a System of Spherical Layers) -- 1.5 Reflection Coefficient and Impedance of a Spherical Stack -- 1.6 Conclusion -- 2. Electromagnetic Field in Homogeneous Microspheres Without Surface Structures -- 2.1 Experiments with Microspheres -- 2.2 Lorentz-Mie theory and its extensions -- 2.2.1 Lorentz-Mie theory of elastic scattering -- 2.2.2 Theory of spontaneous emission -- 2.2.3 Mie scattering by concentrically stratified spheres -- 2.3 Peculiarities of the modes of an open spherical cavity -- 2.3.1 Indexes and order of a whispering-gallery mode -- 2.3.2 The problem of normalization of the whispering-gallery modes -- 2.4 Quality factor of a whispering-gallery mode -- 2.4.1 Radiative quality factor of an ideal dielectric sphere -- 2.4.2 Effect of light absorption on the quality factor -- 2.4.3 Light scattering on inhomogeneities of the refractive index -- 2.4.4 Effect of a spherical submicrometer-size inclusion -- 2.4.5 Comparison of different WGM-scattering models -- 2.4.6 Q factor of a loaded cavity -- 3. Electromagnetic Eigen Oscillations and Fields in a Dielectric Microsphere with Multilayer Spherical Stack -- 3.1 Introduction -- 3.2 Geometry and Basic Equations.

3.3 Eigenfrequencies of the Spherical Resonator Coated by the Stack -- 3.4 Radial Distribution of Fields -- 3.5 Discussions -- 3.6 Conclusion -- 4. Transmittance and Resonance Tunneling of the Optical Fields in the Microspherical Metal-Dielectric Structures -- 4.1 Introduction -- 4.2 Geometry and Basic Equations -- 4.3 Results and Discussions -- 4.4 Conclusion -- 5. Confinement of Electromagnetic Oscillations in a Dielectric Microsphere Coated by the Frequency Dispersive Multilayers -- 5.1 Introduction -- 5.2 Basic Equations -- 5.3 Results and Discussions -- 5.4 Conclusion -- 6. Oscillations in Microspheres with an Active Kernel -- 6.1 Basic Equations -- 6.2 Results and Discussions -- 6.3 Conclusion -- 7. Transfer Matrix Approach in a Non-Uniform Case -- 7.1 Approach to a Non-Uniform Case -- 7.2 Example. Non-Uniform Electron's Concentration -- II The Quantum Phenomena in Microspheres -- 8. Coupling of Two-Level Atom with Electromagnetic Field -- 8.1 Transitions under the Action of the Electromagnetic Field -- 8.2 The Equations for Probability Amplitudes -- 8.3 Derivation of the Equation for Polarization of TLA: Dielectric Permittivity -- 8.4 Temporal Dynamics of Polarization and the Probability Amplitudes -- 9. Classical Field -- 9.1 Schrodinger Equation -- 9.2 Matrix Form for Two-Level Atom -- 10. Quantization of Electromagnetic Field -- 10.1 Energy of Field -- 10.2 Structure of Vacuum Field -- 11. Schrodinger and Interaction Pictures -- 11.1 Equations for the State Vectors -- 11.2 Equations for Operators -- 11.2.1 Operator's calculations -- 12. Two-Level Atom (The Matrix Approach, a Quantized Field) -- 12.1 Equations for Probability Amplitudes in Spherical Coordinates -- 13. Dynamics of Spontaneous Emission of Two-Level Atom in Microspheres: Direct Calculation -- 13.1 Introduction -- 13.2 Basic Equations -- 13.3 Results and Discussions.

13.4 Triple photon state -- 13.4.1 Basic equations -- 13.4.2 Wigner function -- 13.5 Conclusions -- III Numerical Methods and Object-Oriented Approach to the Problems of Multilayered Microsystems -- 14. Use of Numerical Experiment -- 14.1 Introduction -- 14.2 The Brief Review of C++ Operators -- 14.2.1 Data -- Arrays -- Structures -- 14.2.2 Operators -- Increments and Decrements -- Conditional Statements -- Switch Statements -- Iteration Statements for Loops -- While Loops -- Do-while Loops -- 14.2.3 Functions -- Function Declarations and Definitions -- Return Values -- Recursive Functions -- Overloading -- Function Types -- Passing Functions as Argument -- 14.2.4 Interacting the data of class with member functions -- 14.2.5 Classes -- 14.2.6 Access to members -- 14.2.7 Virtual functions -- 14.2.8 Overloading the mathematical operator -- 15. Exception Handling -- 15.1 Code -- 16. Visual Programming: Controls, Events and Handlers -- 16.1 DOS and Visual Programming -- 16.2 Controls, Events and Handlers -- 16.3 Graphical User Interface -- 17. Quantum Electromagnetic Field -- 17.1 Introduction -- 17.2 Code -- 17.3 Classes -- 18. Root Finding for Nonlinear and Complex Equations -- 18.1 Introduction -- 18.2 Code -- 18.3 Classes -- 19. Evaluation of Complex ODE -- 19.1 Introduction -- 19.2 Code -- 19.3 Classes -- 20. The Complex Vectorial and Matrix Operations -- 20.1 Introduction -- 20.2 Code -- 20.3 Classes -- 21. Spontaneous Emission of Atom in Microsphere -- 21.1 Introduction -- 21.2 Code -- 21.3 Classes -- 22. Electromagnetic Oscillations in Layered Microsphere -- 22.1 Introduction -- Appendix A: Calculation of Field's Energy in a Sphere -- Appendix B: Calculation of Surface Integral -- Appendix C: Continuity of Tangential Fields -- Appendix D: Integral on Bessel Functions -- Appendix E: Surface Integrals for Dipole.

Appendix F: Some Mathematical Formulas -- F.1 Legendre Polynomials -- F.2 Spherical Functions -- F.3 Bessel Functions -- F.4 Spherical Bessel Functions -- Appendix G: Various Head *.h Files -- G.1 File BGNDefg.h -- G.2 File BGNutil1.h -- Bibliography -- Index.