radiation caustic waveguide

I am a begginer and I want to get a thorough understanding on the geometrical theory of diffraction. Can anybody help?

Regards

You should read this book :
Geometrical Theory of Diffraction of V.A. Borovikov And B. Ye. Kinber

Editorial preface
Preface

1. Introduction
2. Fundamendals of the geometrical theory of diffraction
2.1 - Laws of geometrical optics
2.2 - Postulates of the geometrical theory of diffraction
2.3 - Diffraction by slit: representation of edge waves in terms of Diffraction coefficients
2.4 - Diffraction by slit: explicit expressions for edge diffracted waves
2.5 - Reconstruction of antenna radiation pattern by its nearfield measurements
2.6 - Compensation of diffraction effects in antenna synthesis
2.7 - GTD applicability limits
3. Ray fields and reflections from smooth bodies
3.1 - Ray expansions
3.2 - Eikonal equation and transport equations
3.3 - Applicability limits for ray expansions: crossing caustics
3.4 - Ray expansions of simple fields
3.5 - Asymptotic solutions of reflection problems
3.6 - Transformation of ray fields by smoothly curved diffraction gratings
3.7 - Ray fields in irregular flaring waveguides
3.8 - Smooth junction between regular waveguides
4. Caustic and focal expansions
4.1 - Uniform asymptotic expansions
4.2 - Relationships between wavefronts and caustics
4.3 - Systems of co-ordinates near caustics
4.4 - Caustic expansions
4.5 - Field near asymptote of a caustic
4.6 - Focal expansions
4.7 - Diffraction integral
5. Diffracted waves
5.1 - Classification
5.2 - Diffraction of plane wave by halfplane: penumbra fields
5.3 - Cylindrical wave diffraction by halfplane; diffraction by wedge
5.4 - Penumbra fields in slit diffraction
5.5 - 2-D diffraction of arbitrary wave by curved wedge
5.6 - 3-D edge diffraction
5.7 - Diffraction of toroidal wave by bicone
5.8 - Canonic wave expansions
5.9 - Reflection of penumbra field from smooth surface
5.10 - Diffraction of penumbra field by wedge
5.11 - Radiation pattern of slotted-guide antenna
5.12 - Wedge diffraction of field with caustic in inhomogeneous medium
6. GTD or physical optics methods?
6.1 - Approximations of Kirchhoff and physical theory of diffraction
6.2 - High-frequency asymptotics in Kirchhoff approximation and physical theory of diffraction
6.3 - Radiation of reflector antenna
6.4 - Diffraction by corner point of edge
6.5 - Diffraction by arbitrary aperture
6.6 - Side radiation of parabolic antenna with noncircular edge
6.7 - Applicability limits of GTD formulations: Fresnel zones
6.8 - Field-forming region and applicability criterion of geometrical optics
7. Diffraction by bodies of complex geometry
7.1 - Phase structure of solutions
7.2 - Successive diffraction method
7.3 - Diffraction by strip: recursion expressions for edge diffracted waves
7.4 - Method of self-consistent field
7.5 - Accuracy of successive diffraction and self consistent field methods
8. Diffraction at open end of waveguide
8.1 - Waveguide penumbra fields
8.2 - Open-ended waveguide: nonuniform asymptotic
8.3 - Waveguiding problems: slotted waveguide, reflector in waveguide bend
8.4 - Open-ended waveguide: asymptotic uniform over observation angle
8.5 - Open-ended waveguide: asymptotic uniform over angles of incidence and observation
8.6 - Mode conversion in waveguide-horn junction
8.7 - Asymptotic of excitation and reflection coefficients of horn modes in a waveguide-horn junction
9. Methods and results of asympotic diffraction theory
9.1 - Sommerfield integral method
9.2 - Method of canonical waves
9.3 - Boundary layer method: edge diffraction by bicone
9.4 - Nonstationary problems
9.5 - Diffraction by cone
10. Appendix
10.1 - Generalised Fresnel integral
10.2 - Expressions for radiation pattern of reflector antenna
10.3 - Calculation of sums of integrals
10.4 - Field of system of equidistant sources
11. References
Index

The book is quite detailed. I need intial understanding than go to the details.

Does anybody have a start up breig explanation for the GTD theory?

Try this excellent book

Geometrical Theory of Diffraction for Electromagnetic Waves de
Graeme L. James

http://books.google.com.br/books?id=...cd=1#PPA187,M1

Added after 10 minutes:

Other sources:
- Chapter 13 - GTD
Advanced Engineering Electromagnetics
Constantine A. Balanis
- Paper:
J.B. Keller, "Geometrical Theory of Difraction", J. Opt. Soc. Amer., Vol.52, n.2,
pp. 116-130, February 1962.

You need to read some books and summarize by yourself.