Contents

Preface

1 Scalar Partially Coherent Sources: Theoretical Foundations

1.1 Review of Scalar Diffraction Theory

     1.1.1 Maxwell’s Equations and the Scalar Wave Equation

     1.1.2 Solution of the Scalar Wave Equation and the Plane Wave Spectrum

     1.1.3 Fresnel and Fraunhofer Diffraction

1.2 First-Order Field and Irradiance Statistics

     1.2.1 Thermal and Pseudo-Thermal Light

     1.2.2 Probability Density Function of the Irradiance

1.3 Second-Order Field Statistics

     1.3.1 Mutual Coherence Function

     1.3.2 Cross-Spectral Density Function

     1.3.3 Propagation of the Cross-Spectral Density Function

     1.3.4 Coherent-Modes Representation

     1.3.5 Superposition Rule

     1.3.6 Models of the Cross-Spectral Density Function

     1.3.7 The van Cittert–Zernike Theorem

1.4 Second-Order Irradiance Statistics

     1.4.1 Covariance of Irradiance

     1.4.2 Statistics of Integrated Irradiance

     1.4.3 Intensity Interferometry

References

2 Simulating Random Scalar Fields

2.1 Coherent-Modes Representation

     2.1.1 Simulation Methods

     2.1.2 Gaussian Schell-Model Source

     2.1.3 I_m-Bessel Correlated Source

2.2 Superposition Rule: Pseudo-Modes

     2.2.1 Simulation Methods

     2.2.2 Schell-Model Sources

     2.2.3 Self-Focusing Non-uniformly Correlated Sources

2.3 Superposition Rule: Thermal and Pseudo-Thermal Light

     2.3.1 Simulation Method

     2.3.2 Schell-Model Sources

     2.3.3 Self-Focusing Non-uniformly Correlated Sources

References

3 Electromagnetic Partially Coherent Sources: Theoretical Foundations

3.1 Review of Electromagnetic Theory

     3.1.1 Electromagnetic Plane Wave Spectrum

     3.1.2 Polarization Ellipse

     3.1.3 Jones Vectors, Stokes Parameters, and the Poincaré Sphere

3.2 First-Order Field and Irradiance Statistics

     3.2.1 Partially Polarized Thermal and Pseudo-Thermal Light

     3.2.2 Probability Density Functions of Stokes Parameters

3.3 Second-Order Field Statistics

     3.3.1 Beam Coherence-Polarization Matrix

     3.3.2 Cross-Spectral Density Matrix

     3.3.3 Propagation of the Cross-Spectral Density Matrix

     3.3.4 Coherent-Modes Representation

     3.3.5 Superposition Rule

     3.3.6 Models of the Cross-Spectral Density Matrix

3.4 Second-Order Irradiance Statistics

     3.4.1 Covariance of Irradiance

References

4 Simulating Random Electromagnetic Fields

4.1 Coherent-Modes Representation: Bimodal Expansions

     4.1.1 Simulation Method

     4.1.2 Electromagnetic Gaussian Schell-Model Source

4.2 Superposition Rule: Pseudo-Modes

     4.2.1 Simulation Method

     4.2.2 Electromagnetic Schell-Model Sources

     4.2.3 Electromagnetic Self-Focusing Non-uniformly Correlated Sources

4.3 Superposition Rule: Thermal and Pseudo-thermal Light

     4.3.1 Simulation Method

     4.3.2 Electromagnetic Schell-Model Sources

     4.3.3 Electromagnetic Self-Focusing Non-uniformly Correlated Sources

References

5 Application Examples

5.1 Young’s Experiment

     5.1.1 Theory

     5.1.2 Simulation

5.2 Michelson Interferometer

     5.2.1 Theory

     5.2.2 Simulation

5.3 The van Cittert–Zernike Theorem

     5.3.1 Beam Shaping with Random Scalar Fields

     5.3.2 Polarization Control with Random Electromagnetic Fields

5.4 The Hanbury Brown and Twiss Effect

     5.4.1 Theory

     5.4.2 Simulation

5.5 Imaging with Partially Coherent Light

     5.5.1 Theory

     5.5.2 Simulation

References

6 Pulsed Partially Coherent Fields

6.1 Review of Basic Theory

     6.1.1 Coherent-Modes Representation

     6.1.2 Superposition Rule

6.2 Superposition Rule: Thermal and Pseudo-Thermal Light

     6.2.1 Schell-Model Pulsed Beams

     6.2.2 Non-uniformly Correlated Pulsed Beams

     6.2.3 Spatiotemporal Coupling: Twisted Space-Time Beams

References

Appendix A Numerical Diffraction Using the Collins Formula

A.1 The Collins Formula

A.2 Sampling Analysis

A.3 Example

References

Appendix B Simulating Spatially Incoherent Sources

B.1 Theory

B.2 Example

References

Appendix C MATLAB® Code

C.1 Chapter II

C.2 Chapter IV

C.3 Chapter V

C.4 Chapter VI

C.5 Appendix A

C.6 Appendix B

References

Index