光的相干与偏振理论导论

Preface page xi

1. Elementary coherence phenomena 1

1.1 Interference and statistical similarity 1

1.2 Temporal coherence and the coherence time 4

1.3 Spatial coherence and the coherence area 5

1.4 The coherence volume 8

Problems 10

2. Mathematical preliminaries 11

2.1 Elementary concepts of the theory of random processes 11

2.2 Ergodicity 17

2.3 Complex representation of a real signal and the envelope

of a narrow-band signal 19

2.4 The autocorrelation and the cross-correlation functions 22

2.4.1 The autocorrelation function of a finite sum of periodic

components with random amplitudes 24

Preface page xi

1. Elementary coherence phenomena 1

1.1 Interference and statistical similarity 1

1.2 Temporal coherence and the coherence time 4

1.3 Spatial coherence and the coherence area 5

1.4 The coherence volume 8

Problems 10

2. Mathematical preliminaries 11

2.1 Elementary concepts of the theory of random processes 11

2.2 Ergodicity 17

2.3 Complex representation of a real signal and the envelope

of a narrow-band signal 19

2.4 The autocorrelation and the cross-correlation functions 22

2.4.1 The autocorrelation function of a finite sum of periodic

components with random amplitudes 24

2.5 The spectral density and the Wiener-Khintchine theorem 25

Problems 29

3. Second-order coherence phenomena in the space-time domain 31

3.1 Interference law for stationary optical fields. The mutual

coherence function and the complex degree of coherence 31

3.2 Generation of spatial coherence from an incoherent source.

The van Cittert-Zernike theorem 37

3.3 Illustrative examples 46

3.3.1 Michelson's method for measuring stellar diameters 46

3.3.2 Michelson's method for determining energy distribution

in spectral lines 51

3.4 Propagation of the mutual intensity 54

3.5 Wave equations for the propagation of mutual coherence in free space 56

Problems 58

4. Second-order coherence phenomena in the space-frequency domain 60

4.1 Coherent-mode representation and the cross-spectral density

as a correlation function 60

4.2 The spectral interference law and the spectral degree of coherence 63

4.3 An illustrative example: spectral changes on interference 69

4.4 Interference of narrow-band light 73

Problems 76

5. Radiation from sources of different states of coherence 79

5.1 Fields generated by sources with different coherence properties 79

5.2 Correlations and the spectral density in the far field 81

5.3 Radiation from some model sources 88

5.3.1 Schell-model sources 88

5.3.2 Quasi-homogeneous sources 90

5.4 Sources of different states of spatial coherence which generate

identical distributions of the radiant intensity 95

5.5 Coherence properties of Lambertian sources 97

5.6 Spectral changes on propagation. The scaling law 102

Problems 108

6. Coherence effects in scattering 111

6.1 Scattering of a monochromatic plane wave on a deterministic medium 111

6.2 Scattering of partially coherent waves on a deterministic medium 115

6.3 Scattering on random media 118

6.3.1 General formulas 118

6.3.2 Examples 121

6.3.3 Scattering on a quasi-homogeneous medium 123

Problems 127

7. Higher-order coherence effects 129

7.1 Introduction 129

7.2 Intensity interferometry with radio waves 131

7.3 The Hanbury Brown-Twiss effect and intensity interferometry with light 134

7.4 Einstein's formula for energy fluctuations in blackbody radiation

and the wave-particle duality 140

7.5 Mandel's theory of photoelectric detection of light fluctuations 143

7.5.1 Mandel's formula for photocount statistics 143

7.5.2 The variance of counts from a single photodetector 145

7.5.3 Correlation between count fluctuations from two detectors 147

7.6 Determination of statistical properties of light from photocount

measurements 149

Problems 151

8. Elementary theory of polarization of stochastic electromagnetic beams 154

8.1 The 2 _ 2 equal-time correlation matrix of a quasi-monochromatic

electromagnetic beam 154

8.2 Polarized, unpolarized and partially polarized light. The degree

of polarization 158

8.2.1 Completely polarized light 158

8.2.2 Natural (unpolarized) light 160

8.2.3 Partially polarized light and the degree of polarization 161

8.2.4 The geometrical significance of complete polarization. The Stokes

parameters of completely polarized light. The Poincaré sphere 165

Problems 171

9. Unified theory of polarization and coherence 174

9.1 The 2 _ 2 cross-spectral density matrix of a stochastic

electromagnetic beam 174

9.2 The spectral interference law, the spectral degree of coherence

and the spectral degree of polarization of stochastic

electromagnetic beams 175

9.3 Determination of the cross-spectral density matrix from experiments 179

9.4 Changes in random electromagnetic beams on propagation 181

9.4.1 Propagation of the cross-spectral density matrix of a stochastic

electromagnetic beam - general formulas 181

9.4.2 Propagation of the cross-spectral density matrix of an

electromagnetic Gaussian Schell-model beam 183

9.4.3 Examples of correlation-induced changes in stochastic

electromagnetic beams on propagation 186

9.4.4 Coherence-induced changes of the degree of polarization

in Young's interference experiment 191

9.5 Generalized Stokes parameters 194

Problems 197

Appendices 202

I Cells of phase space and the degeneracy parameter 202

(a) Cells of phase space of a quasi-monochromatic light wave (Section 1.4) 202

(b) Cells of phase space of radiation in a cavity (Sections 7.4 and 7.5) 204

(c) The degeneracy parameter 206

II Derivation of Mandel's formula for photocount statistics

[Eq. (2) of Section 7.5.1] 208

III The degree of polarization of an electromagnetic Gaussian

Schell-model source 210

IV Some important probability distributions 212

(a) The binomial (or Bernoulli) distribution and some of its limiting cases 212

(b) The Bose-Einstein distribution 214

Author index 216

Subject index 220

所有的光场都是随机涨落的，有些光场的随机涨落很小，例如许多激光器输出的光；有些光场的随机涨落相当大，例如从热光源辐射的光。描述涨落光场的基础理论是相干理论。部分偏振现象就是涨落的重要表现。实际上，相干理论所能处理的问题不仅限于涨落。与常规的处理方法不同，相干理论是依据可观测量描述光场，并解释这些可观测量，例如光的光谱以及它在传输中如何变化的。
　　《光的相干与偏振理论导论（英文影印版）》给出了光的相干与偏振现象的统一处理方法。适合光通信、激光光束在光纤中和通过湍流大气传输、光学成像，尤其在显微镜成像（例如医学诊断）的物理界和工程界的研究者阅读。

光的相干和偏振是光学中最重要的现象，其应用也极为广泛。《光的相干与偏振理论导论（英文影印版）》的作者是国际光学界的著名学者，在相关的研究取中取得过突破性的进展。也正是因为作者的贡献，本书能够以统一处理方法研究光的相干与偏振这两种现象。对于光通信、光学成像等领域的研究者及研究生，乃至对此领域感兴趣的读者来说，本书是不可多得的优秀读物。