A guided tour of light beams

104 Pages·2016·5.13 MB·English

by  Simon, David S

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A Guided Tour of Light Beams
From lasers to optical knots
A Guided Tour of Light Beams
From lasers to optical knots
David S Simon
Stonehill College and Boston University, USA
Morgan & Claypool Publishers
Copyright ª 2016 Morgan & Claypool Publishers
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system
or transmitted in any form or by any means, electronic, mechanical, photocopying, recording
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contact
Dedicated to Alee, Marcia, Tina, and Jo
Contents
Preface ix
Acknowledgements x
Author biography xi
1 Introduction: From death rays to smartphones 1-1
Bibliography 1-3
2 Optical propagation 2-1
2.1 Electromagnetic fields 2-1
2.2 Helmholtz equation and wave optics 2-2
Bibliography 2-5
3 Gaussian beams and lasers 3-1
3.1 Lasers 3-1
3.2 Gaussian beams 3-5
3.3 Coherent and squeezed states 3-8
3.4 Optical tweezers 3-10
Bibliography 3-13
4 Orbital angular momentum and Laguerre–Gauss beams 4-1
4.1 Polarization and angular momentum in optics 4-1
4.2 Generation and detection of Laguerre–Gauss beams 4-6
4.3 Optical spanners and micropumps 4-8
4.4 Harnessing OAM for measurement 4-9
Bibliography 4-10
5 Bessel beams, self-healing, and diffraction-free propagation 5-1
5.1 Bessel beams 5-1
5.2 Optical petal structures 5-5
5.3 More non-diffracting beams: Mathieu beams 5-6
5.4 Optical tractor beams and conveyor belts 5-9
5.5 Trojan states 5-10
5.6 Localized waves 5-11
Bibliography 5-13
vii
A Guided Tour of Light Beams
6 Airy beams and self-acceleration 6-1
6.1 Airy beams 6-1
6.2 Self-accelerating beams and optical boomerangs 6-2
6.3 Applications 6-4
Bibliography 6-5
7 Further variations 7-1
7.1 Separable solutions 7-1
7.2 Hermite–Gauss beams 7-2
7.3 Ince–Gauss beams 7-4
7.4 Parabolic beams 7-5
7.5 Elegant beams 7-8
7.6 Lorentz beams 7-8
Bibliography 7-9
8 Entangled beams 8-1
8.1 Separability and entanglement 8-1
8.2 Creating entanglement 8-4
8.3 Applications of entangled beams 8-7
Bibliography 8-11
9 Optical knots and links 9-1
9.1 From knotted vortex atoms to knotted light 9-1
9.2 Knotted vortex lines 9-3
Bibliography 9-5
10 Conclusion 10-1
Bibliography 10-2
Appendix Mathematical reference A-1
viii
Preface
It has been over fifty years since the invention of the laser. Since then lasers have
worked their way into every aspect of daily life, from laser pointers and DVD
players to eye surgery and tattoo removal. They have also become an essential tool
in virtually every area of basic scientific research. In addition to their high intensity
and strong coherence properties, the other main defining property of the light
produced by a laser is its high degree of directionality: the light emerges as a well-
defined beam with a definite direction.
In recent years a number of other optical beams have become objects of study
among researchers. Some of these highly-directional solutions to the Maxwell
equations were discussed decades ago and then forgotten; others have been
discovered for the first time in recent years. These newly fashionable beams have
a range of unusual and at times surprising properties. The array of novel features
they present have not only made them interesting subjects for scientific study, but are
also rapidly leading to a number of novel technological applications.
Many of the beams discussed in this book have never appeared in a textbook
before, and information about them is scattered in the original research literature.
The goal here is to collect together in one place the basic properties of many of these
beams, and to cover them in a more or less unified manner, at a level that is
comprehensible to an advanced undergraduate with a background in the physical
and mathematical sciences. This survey may also be useful to graduate students and
researchers wanting a rapid introduction to the area.
The collection of optical beams discussed here will likely play prominent roles at
the forefront of research in a number of fields for years to come, and the hope is that
this book will help the reader gain entry into this world of new discoveries.
David Simon
Easton, MA
ix