## Natural Focusing and Fine Structure of Light: Caustics and Wave DislocationsA new kind of optics has grown up during the last 25 years. Geometrical optics has been studied for centuries (the law of reflection was known to the ancient Greeks) and wave optics (heralded by Huygens' Treatise on Light) has been studied for more than 300 years. But in the mid 1970s it began to be understood that when natural processes focus light, as when sunlight is reflected from the sea at sunset, the light caustics that are produced have a systematic behavior previously unrecognized. Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations provides a definitive account of how classical optics has been reconstructed in a modern way by emphasizing the hierarchy of singularities that exists in light fields. The book discusses the singularities of geometrical optics and their systematization by catastrophe theory. It explores the diffraction patterns associated with caustics that are dominated by wave dislocations, line singularities of the phase, and analogous to crystal dislocations. The book is a perfect blend of mathematics and physics, combining theory, computer simulation, and beautiful experimental photographs of the phenomena studied. |

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### Contents

Natural Focusing | 9 |

Folds and Cusps in Three Dimensions | 41 |

Caustics of Codimension Three | 59 |

General analysis of trajectory patterns in pair creation | 90 |

Diffraction | 123 |

Higher Caustics as Organizing Centres | 157 |

Producing D | 184 |

Network Patterns of Catastrophes | 237 |

Statistics of Caustics and Twinkling | 249 |

Caustics within a General Refracting Medium | 261 |

Singularities in Paraxial Electromagnetic Waves | 271 |

Singularities in Waves Travelling in Many Directions | 293 |

Retrospect | 307 |

319 | |

### Common terms and phrases

Airy Airy function amplitude angle approximation axes axis beak-to-beak event beam Berry catastrophe theory centre Chapter circular circular polarization codimension component constant contour control space control variables coordinates corresponding curvature curved cusp line cuspoids defined diagram diffraction catastrophe diffraction pattern direction disclination dislocation lines distance elliptic umbilic equation example foci focusing fold catastrophe fold caustic fringes function geometrical optics height higher catastrophes hyperbolic umbilic infinity initial wavefront intersecting lens linear monochromatic monstar non-generic observation parabolic umbilic parallel parameter paraxial paraxial approximation perpendicular perturbation phase screen plane wave polarization ellipse potential principal curvature produce propagation quadratic rainbow refraction result rotated saddle point scalar screw dislocation seen shape shows singularities standard form stationary structurally stable surface swallowtail symmetry tangential three dimensions triple junction two-dimensional umbilic focus umbilic point unfolding Upstill vector water drop wave dislocations wave field wavelength zero