Overview
- Provides both new and well-known results, giving the reader a balanced overview of the state of the art
- Makes connections between liquid crystal optics and multiple areas of mathematics, such as dynamical systems
- Provides specific open directions of research related to lens design and imaging with liquid crystals
Part of the book series: Springer Tracts in Modern Physics (STMP, volume 294)
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About this book
Freeform lens design has numerous applications in imaging, aerospace, and biomedicine. Due to recent advancements in precision cutting and grinding, the manufacturing of freeform optical lenses with very high precision is now possible. However, there is still a significant lack of mathematical literature on the subject, and essentially none related to liquid crystals. Liquid crystals are appealing for use in imaging due to their flexibility and unique electro-optical properties.
This book fills a gap in mathematical literature and attracts focus to liquid crystals for freeform lens design. It provides a rigorous mathematical perspective on liquid crystal optics, focusing on ray tracing in the geometric optics regime. A mathematical foundation is set to study lens design and ray tracing problems in liquid crystals.
Additionally, it addresses absolute instruments, which are devices that image without any optical aberrations. These instruments cannot be designed through transformation optics, and until recently, only a handful of examples were known. Mathematically, this is a largely untapped area of research, yet the applications are profound.
Finally, the book describes several open directions, revealing the richness of the intersection of liquid crystal optics and mathematical analysis. The content of this book will prove invaluable for researchers of mathematical optics as well as those interested in liquid crystal theory, in addition to those mathematics graduate students aiming to understand the physical basis of light propagation in liquid crystals
Keywords
- Snell's Law
- geodesics
- Finsler Space
- aberrations
- absolute instruments
- variational methods
- broken extremals
- liquid crystals
- Fermat Principle
- lens design
- effective refractive index
- extraordinary rays
- geometric optics
- Euler-Lagrange equation
Authors and Affiliations
About the author
Eric Stachura
Kennesaw State University
Department of Mathematics
Marietta, GA
United States of America
Bibliographic Information
Book Title: Mathematical Methods in Liquid Crystal Optics and Lens Design
Authors: Eric Stachura
Series Title: Springer Tracts in Modern Physics
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Hardcover ISBN: 978-3-031-46613-7Due: 13 June 2024
Softcover ISBN: 978-3-031-46616-8Due: 13 June 2024
eBook ISBN: 978-3-031-46614-4Due: 13 June 2024
Series ISSN: 0081-3869
Series E-ISSN: 1615-0430
Edition Number: 1
Number of Pages: X, 190
Number of Illustrations: 10 b/w illustrations, 18 illustrations in colour