Preface
The main aim of this book is to describe light propagation in linear media by expanding on diffraction theories a little beyond what is available in the optics books that we love and admire (such as Born and Wolf, Jenkins and White, Goodman, Hecht, Brooker, or Akhmanov and Nikitin). This book can possibly be used as a technical reference book by professional scientists and engineers interested in light propagation and as a supplemental text for upper-level undergraduate or graduate courses in optics. The first two chapters of the book, written at a more introductory level, are included for the sake of completeness and perhaps can be used as a refresher to the subject.
The general flow of chapters and topics in the book is illustrated in Table 0.1. Chapters 1 and 2 provide background information and descriptive explanations of the fundamentals of light and physical optics. Chapter 1 provides a background of the origins of light, our historical understanding of it, and a brief explanation of both classical and quantum mechanical models for the creation of light. Chapter 2 describes light as electromagnetic waves and provides a mathematical description of the fundamentals of linear physical optics. It is assumed that the light is traveling through a single, homogeneous, isotropic medium. Chapter 3 continues the topic of light traveling within a single unbounded medium. However, the medium is now an anisotropic crystal. Calculations of walk-off angles in both biaxial and uniaxial crystals, which are of particular importance in nonlinear optical applications, are emphasized in this chapter.
Chapters 4 and 5 present mathematical models for what happens when light encounters planar boundaries between different media. In Chapter 4 the behavior of the electromagnetic fields when they encounter a single planar boundary between two different optical media is described, whereas Chapter 5 presents light propagation within a slab waveguide bounded by two different media. In Chapter 6 we derive and explain the propagation of Gaussian beams through homogeneous media, through slabs and lenses, and mathematical models for higher order Hermite and Laguerre-Gaussian beams.
In Chapters 7–10 we discuss various diffraction models for the propagation of light through regions where sizes of apertures and optical components can affect the propagation of the light via diffraction. In Chapter 7 we present various scalar and vector diffraction theories for light fields within and beyond a planar aperture, with the results of calculation for several scenarios illustrated in Chapter 8. Chapter 9 expands the vector diffraction theory to propagation
TABLE 0.1
General flow of chapters and topics.
across curved surfaces. In Chapter 10 we describe the diffraction of Gaussian beams by spatially limiting apertures or obstacles.
In Chapter 11 we present an application of diffraction theory: spatially confining (trapping) cold atoms within localized light intensity patterns. We present a few methods to trap atoms using a variety of propagating light fields including a scalar light-atom interaction, a vector light-atom interaction, and projecting a near-field diffraction pattern to trap atoms located in what would be considered to be a “far-field” location.
Significant portions of this book have been compiled from several sources: research work performed by Shekhar Guha and Glen Gillen at the Air Force Research Laboratory, research performed by Glen and Katharina Gillen at California Polytechnic State University, and adaptations of in-class lecture notes of Glen and Katharina Gillen from a variety of courses in physics and optics they have taught.
Acknowledgments
Glen D. Gillen would like to thank his college professors at Denison University, Granville, OH, for providing him the academic and analytical training that has served as a strong foundation for a scientific and academic career. Glen would also like to thank Shekhar Guha for the wonderful opportunity to have worked with him at the Air Force Research Labs, Dayton, OH, right out of graduate school, and all of his guidance and support while pursuing a career in academia. Last, but certainly not least, Glen thanks his family and loving wife for their love and support throughout the years.
Katharina (“Kat”) Gillen would like to thank Shekhar Guha for giving her the opportunity to collaborate on research and to participate in the writing of this book. She would like to acknowledge useful discussions with Ivan Deutsch, Marianna Safronova, and her friend and colleague Thomas Gutierrez. Most importantly, she would like to thank her research students for all their hard work and enthusiasm. In particular, she appreciated helpful discussions with Travis Frazer, and the joint research project with Bert D. Copsey, the results of which have been included in this book. On a personal level, Kat is thankful for all her mentors along the way, from her high school math and physics teachers Jutta Bremken and Ludwig Weisgerber, who believed in her talents, to her Ph.D. advisor Greg Lafyatis, to her faculty mentor Paula Turner, who helped give her a good start in to the college teaching world. Finally, she would like to express her deepest gratitude for her friends and colleagues at Cal Poly, and her friends and family back home for supporting her and inspiring her. Last, but not least, she thanks her collaborator Glen Gillen for being patient when she wasn’t writing the book, and her husband Glen for when she was. She could not have accomplished this without the love and support of her family.
Shekhar Guha would like to take this opportunity to thank his collaborators, Profs. Glen and Katharina Gillen for embarking on this venture and for skilfully bringing it to completion despite demanding academic and family responsibilities. Also he would like to gratefully acknowledge his high school physics teacher, Anjan Baran Das Gupta, for instilling in him the love of learning physics, for continuing to provide guidance and inspiration throughout his college days, and for providing many precious books as gifts. Working on this book reminded him of those days of long ago. Shekhar would also like to thank his colleague Dr. Leonel Gonzalez not only for the everyday discussions and keen insight that must have permeated this book but also for reviewing and helping with much of this manuscript. He also thanks the Air Force Research Laboratory for providing him the facilities and the stimulating work environment that made this book possible. Lastly and mostly, he thanks his family for their patience, support, and love.