Lagrangian Optics

Authors: Lakshminarayanan, V., Ghatak, Ajoy, Thyagarajan, K.

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About this book

Ingeometrical optics, light propagation is analyzed in terms of light rays which define the path of propagation of light energy in the limitofthe optical wavelength tending to zero. Many features oflight propagation can be analyzed in terms ofrays,ofcourse, subtle effects near foci, caustics or turning points would need an analysis based on the wave natureoflight. Allofgeometric optics can be derived from Fermat's principle which is an extremum principle. The counterpart in classical mechanics is of course Hamilton's principle. There is a very close analogy between mechanics ofparticles and optics oflight rays. Much insight (and useful results) can be obtained by analyzing these analogies. Asnoted by H. Goldstein in his book Classical Mechanics (Addison Wesley, Cambridge, MA, 1956), classical mechanics is only a geometrical optics approximation to a wave theory! In this book we begin with Fermat's principle and obtain the Lagrangian and Hamiltonian pictures of ray propagation through various media. Given the current interest and activity in optical fibers and optical communication, analysis of light propagation in inhomogeneous media is dealt with in great detail. The past decade has witnessed great advances in adaptive optics and compensation for optical aberrations. The formalism described herein can be used to calculate aberrations ofoptical systems. Toward the end of the book, we present application of the formalism to current research problems. Of particular interest is the use of dynamic programming techniques which can be used to handle variational/extremum problems. This method has only recently been applied to opticalproblems.

Table of contents (9 chapters)

  • Introduction

    Lakshminarayanan, Vasudevan (et al.)

    Pages 1-14

  • Fermat’s Principle

    Lakshminarayanan, Vasudevan (et al.)

    Pages 15-32

  • The Optical Lagrangian and the Ray Equation

    Lakshminarayanan, Vasudevan (et al.)

    Pages 33-53

  • Ray Paths in Media with Spherical and Cylindrical Symmetry

    Lakshminarayanan, Vasudevan (et al.)

    Pages 55-76

  • Ray Paths in Bent Waveguides

    Lakshminarayanan, Vasudevan (et al.)

    Pages 77-91

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-1-4615-1711-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-0-7923-7582-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-1-4613-5690-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Lagrangian Optics
Authors
Copyright
2002
Publisher
Springer US
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4615-1711-5
DOI
10.1007/978-1-4615-1711-5
Hardcover ISBN
978-0-7923-7582-1
Softcover ISBN
978-1-4613-5690-5
Edition Number
1
Number of Pages
X, 227
Topics