The Classical and Quantum Dynamics of the Multispherical Nanostructures

The following sections are included:

• Preface

• Contents

• Introduction

The following sections are included:

• Basic Equations
  • Wave equation
  • Three-dimensional case
  • Electromagnetic waves
  • Potentials of field
  • TM and TE waves
  • Debye potentials
  • Energy of field
  • Metallized sphere
  • Frequency dispersion

• The Variational Principle
  • The Whitham's average variational principle
  • Energy in a layered microsphere

• Multilayered Microsphere

• The Transfer Matrix Method (Solving Equations for a System of Spherical Layers)

• Reflection Coefficient and Impedance of a Spherical Stack

• Conclusion

The following sections are included:

• Experiments with Microspheres

• Lorentz–Mie theory and its extensions
  • Lorentz–Mie theory of elastic scattering
  • Theory of spontaneous emission
  • Mie scattering by concentrically stratified spheres

• Peculiarities of the modes of an open spherical cavity
  • Indexes and order of a whispering-gallery mode
  • The problem of normalization of the whispering-gallery modes

• Quality factor of a whispering-gallery mode
  • Radiative quality factor of an ideal dielectric sphere
  • Effect of light absorption on the quality factor
  • Light scattering on inhomogeneities of the refractive index
  • Effect of a spherical submicrometer-size inclusion
  • Comparison of different WGM-scattering models
  • Q factor of a loaded cavity

The following sections are included:

• Introduction

• Geometry and Basic Equations

• Eigenfrequencies of the Spherical Resonator Coated by the Stack

• Radial Distribution of Fields

• Discussions

• Conclusion

The following sections are included:

• Introduction

• Geometry and Basic Equations

• Results and Discussions

• Conclusion

The following sections are included:

• Introduction

• Basic Equations

• Results and Discussions

• Conclusion

The following sections are included:

• Basic Equations

• Results and Discussions

• Conclusion

The following sections are included:

• Approach to a Non-Uniform Case

• Example. Non-Uniform Electron's Concentration

The investigation and exploitation of the wave properties of atomic matter is of great interest for fundamental as well as applied research and therefore constitutes one of the most active areas in atomic physics and quantum optics. As a consequence of all developments, there is now a vast interest in compact and reliable atom optical setups which not only expand the applicability of atom optics in fundamental research, but also allow for the technological implementation of atom optical measurement systems. A new approach to this challenge lies in the development of miniaturized and integrated atom optical setups based on microfabricated structures [see Birkl et al., 2001 and references therein]…

The following sections are included:

• Transitions under the Action of the Electromagnetic Field

• The Equations for Probability Amplitudes

• Derivation of the Equation for Polarization of TLA: Dielectric Permittivity

• Temporal Dynamics of Polarization and the Probability Amplitudes

The following sections are included:

• Schrödinger Equation

• Matrix Form for Two-Level Atom

The following sections are included:

• Energy of Field

• Structure of Vacuum Field

The following sections are included:

• Equations for the State Vectors

• Equations for Operators
  • Operator's calculations

The following sections are included:

• Equations for Probability Amplitudes in Spherical Coordinates

The following sections are included:

• Introduction

• Basic Equations

• Results and Discussions

• Triple photon state
  • Basic equations
  • Wigner function

• Conclusions

The solution of nonlinear (and sometimes and linear) problems of modern physics requires the investigation of various kinds of models described by a complex set of equations. Often it is impossible to obtain the solution of such a problem in a useful form, involving only the analytical methods. However even if such a solution is found, it may be written in a complicated form, involving infinite series or integrals. Sometimes the problem of evaluating such series or integrals requires efforts commensurable with the numerical solution of the initial task. In such cases it is impossible to produce to some useful result without exploiting the numerical methods or simulation. Such problems deal with the ordinary use of numerical methods and programming. Now one has to reformulate the question by the next way, from which a stage of an investigation it is expedient to exploit the numerical methods more intensively…

The following sections are included:

• Introduction

• The Brief Review of C++ Operators
  • Data
  • Operators
  • Functions
  • Interacting the data of class with member functions
  • Classes
  • Access to members
  • Virtual functions
  • Overloading the mathematical operator

The following sections are included:

• Code

The following sections are included:

• DOS and Visual Programming

• Controls, Events and Handlers

• Graphical User Interface

The following sections are included:

• Introduction

• Code

• Classes

The following sections are included:

• Introduction

• Code

• Classes

The following sections are included:

• Introduction

• Code

• Classes

The following sections are included:

• Introduction

• Code

• Classes

The following sections are included:

• Introduction

• Code

• Classes

The following sections are included:

• Introduction

The following sections are included:

• 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
  • Legendre Polynomials
  • Spherical Functions
  • Bessel Functions
  • Spherical Bessel Functions

• Appendix G: Various Head *.h Files
  • File BGNDefg.h
  • File BGNutil1.h

• Bibliography

• Index