Book contents
- Frontmatter
- Contents
- Preface to the Second Edition
- 1 Electromagnetic waves, light, and lasers
- 2 Optical frequency amplifiers
- 3 An introduction to two practical laser systems
- 4 Optical resonators containing amplifying media
- 5 Laser radiation
- 6 Control of laser oscillators
- 7 Optically pumped solid-state lasers
- 8 Gas lasers
- 9 Molecular gas lasers I
- 10 Molecular gas lasers II
- 11 Tunable lasers
- 12 Semiconductor lasers
- 13 Passive optical systems
- 14 Periodic optical systems, resonators, and inhomogeneous media
- 15 The optics of Gaussian beams
- 16 Optical fibers and waveguides
- 17 The optics of anisotropic media
- 18 The electro-optic and acousto-optic effects and modulation of light beams
- 19 Introduction to nonlinear processes
- 20 Wave propagation in nonlinear media
- 21 Detection of optical radiation
- 22 Coherence theory
- 23 Laser applications
- Appendix 1 Optical terminology
- Appendix 2 The ´-function
- Appendix 3 Black-body radiation formulas
- Appendix 4 RLC circuits
- Appendix 5 Storage and transport of energy by electromagnetic fields
- Appendix 6 The reflection and refraction of a plane electromagnetic wave at a boundary between two isotropicmedia of different refractive indices
- Appendix 7 The vector differential equation for light rays
- Appendix 8 Symmetry properties of crystals and the 32 crystal classes
- Appendix 9 Tensors
- Appendix 10 Bessel-function relations
- Appendix 11 Green's functions
- Appendix 12 Recommended values of some physical constants
- Index
- References
22 - Coherence theory
Published online by Cambridge University Press: 05 June 2014
- Frontmatter
- Contents
- Preface to the Second Edition
- 1 Electromagnetic waves, light, and lasers
- 2 Optical frequency amplifiers
- 3 An introduction to two practical laser systems
- 4 Optical resonators containing amplifying media
- 5 Laser radiation
- 6 Control of laser oscillators
- 7 Optically pumped solid-state lasers
- 8 Gas lasers
- 9 Molecular gas lasers I
- 10 Molecular gas lasers II
- 11 Tunable lasers
- 12 Semiconductor lasers
- 13 Passive optical systems
- 14 Periodic optical systems, resonators, and inhomogeneous media
- 15 The optics of Gaussian beams
- 16 Optical fibers and waveguides
- 17 The optics of anisotropic media
- 18 The electro-optic and acousto-optic effects and modulation of light beams
- 19 Introduction to nonlinear processes
- 20 Wave propagation in nonlinear media
- 21 Detection of optical radiation
- 22 Coherence theory
- 23 Laser applications
- Appendix 1 Optical terminology
- Appendix 2 The ´-function
- Appendix 3 Black-body radiation formulas
- Appendix 4 RLC circuits
- Appendix 5 Storage and transport of energy by electromagnetic fields
- Appendix 6 The reflection and refraction of a plane electromagnetic wave at a boundary between two isotropicmedia of different refractive indices
- Appendix 7 The vector differential equation for light rays
- Appendix 8 Symmetry properties of crystals and the 32 crystal classes
- Appendix 9 Tensors
- Appendix 10 Bessel-function relations
- Appendix 11 Green's functions
- Appendix 12 Recommended values of some physical constants
- Index
- References
Summary
Introduction
In this chapter we will put the concept of coherence on a more mathematical basis. This will involve the formal definition of a number of functions that are used to describe the coherence properties of optical fields. These include the analytic signal, various correlation functions, and the degree of coherence for describing both temporal and spatial coherence. We shall see that the degree of temporal coherence is quantitatively related to the lineshape function and that the degree of spatial coherence between two points is determined by the size, intensity distribution, and location of an illuminating source. We will use the wave equation, and special solutions to the wave equation called Green's functions, to show how spatial coherence varies from point to point.
The chapter will conclude with a discussion of how the intensity fluctuations of a source depend on its coherence properties, and we will examine a specific scheme, namely the Hanbury Brown–Twiss experiment, by means of which this relationship is studied. This discussion will involve a discussion of “photon statistics,” namely the time variation of the “detection” of photons from a source. In a quantum-mechanical context, square-law detectors respond to these quantized excitations of the optical field, which we call photons.
In classical coherence theory it is advantageous to represent the real electromagnetic field by a complex quantity, both for its mathematical simplicity and because it serves to emphasize that coherence theory deals with phenomena that are sensitive to the “envelope” or average intensity of the field.
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- Chapter
- Information
- Lasers and Electro-opticsFundamentals and Engineering, pp. 736 - 782Publisher: Cambridge University PressPrint publication year: 2014