Now the author tries to sum up the analytical technology in the electromagnetic field theory that has taken place in these several ten years, which includes the papers and materials not only from author but also from other authors. All of those have been listed in the bibliography and have been mentioned in each chapter. Obviously, the problems... are so complicated which cannot be analyzed by means of the traditional analysis, but to set up a new system to analyze the electromagnetic field based on the functional analysis. Nowadays, the functional analysis has been displaced everywhere on the high level magazine to analyze the complicated boundary value problem in the theory of electromagnetic field. However, "the functional analysis" and "the electromagnetic field theory" is still separated into two causes in USA and Canada...
We have discussed the nonlinear phenomena in single mode fiber such as the Stimulated Raman Scattering, the Stimulated Brillouin Scattering, the Self-Focus Phenomenon, the Kerr Effect, the Four-Photon Mixture , the Nonlinear Absorption and the Soliton Transmission in a single-mode fiber. From the mathematic point of view, we have discussed the characteristic method, the per-turbation approach, the function transformation method and the inverse scattering transformation method to transform the nonlinear equations into the linear equations to get the solutions.
Now, the numerical method has been widely used in the microwave devices and optical devices to do the calculation by computer. However, the analytical technology still is a powerful tool in the computer aided design. For instance, a very powerful computer aided design program named "EESOF" from EESOF Inc. and the "Advanced Design System" (ADS) from Agilent Inc. are mostly based on the analytical solutions. Now this software has been used widely in the world to settle down a big project with a small amount of computer time compared with that from the purely numerical method. Meanwhile, the analytical technology can provide the medelling, analytical technology and the physical meaning for the analytical solution, which encourages us to learn more analytical technology.
In this book, the author:
1. Introduces the principle of functional analysis
2. Analyzes the complicated boundary value problems of the electromagnetic field based on the functional analysis. Namely, making use of the vector
spaces and the operator theory to analyze the boundary value problem of the electromagnetic field in:
(a) An inhomogeneous dynamic medium
(b) A discrete medium and anisotropic medium
(c) A nonlinear medium
3. Examines the electromagnetic field in a non-orthogonal coordinates system
4. Evaluates the electromagnetic field in an anisotropic multi-waveguides system
5. Follows the complex function to explain the conformal transformation and the Weiner-Hopf technology to analyze the field in the micro-strip waveguide and dielectric waveguide.