Abstract
The use of optimization theory to describe light propagation phenomena through optical media with different optical properties and geometries is an area of great theoretical interest. This methodology concerns optimized design of arbitrary optical media for which an a priori characterization of significant parameters would be required. The problem of characterizing the output of a system from partial input data is defined as a control theoretical problem. The mathematical theory of adaptive control processes was first introduced by Bellman [1] and has been applied to wide variety of problems in Engineering, Physics, Biology, Economics and even Medicine [1–5]. The problem is usually stated as the minimization of a functional equation. An approach to solving this problem is a technique called dynamic programming which will be introduced in this chapter.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. E. Bellman, Dynamic Programming, Pinceton Univ Press, Princeton NJ, (1957)
S.E Dreyfus, Dynamic Programming and the calculus of variations, Academic Press, NY, (1965)
S.E. Dreyfus and A.M Law, The art and theory of dynamic programming, Academic Press, NY, (1977)
R.E. Bellman, and S.E. Drefus, Applied dynamic programming, Princeton Univ Press, Princeton, NJ, (1962)
R.E. Bellman and R. Vasudevan, Wave propagation, Reidal. Derdrecht, Netherlands (1986)
M.L. Calvo, and V. Lakshrninarayanan, Light propagation in optical waveguides: a dynamic programming approach, J. Opt. Soc. Am. A, 14:872, (1997)
V. Lakshminarayanan, S. Varadarajam, ML Calvo, A note on the applicability of dynamic programming to wave guide problems, in Photonics 96: Proceedings of the international conference on photonics and fiber optics, ed. J.P. Raina, P.R. Vaya, Tata Mc Graw Hill, New Delhi, Vol. 1, Pp. 209–216, (1997)
V. Lakshminarayanan, S. Varadharajan, Dynamic Programming, Fermat’s principle and the Eikonal equation — revisited, J. Optimization Theory and Applications, 95, 713, (1997)
M.L. Calvo and V. Lakshminarayanan, Optimal design using dynamic programming: Applications to gain guided segmented planar waveguides, in Optics and Optoelectronics: Theory, Devices and Applications, Vol. 2, eds. O.P. Nijhawan, A. K. Gupta, A.K. Musla and K. Singh, Springer-Narosa, New Delhi, pages 1206–1214, (1999)
M.L. Calvo and V. Lakshminarayanan, Spatial pulse characterization in periodically segments wave guides by using dynamic programming approach. Optics Communications, 169:223, (1991)
R.K. Laghu, and R.V. Ramaswamy, A variational finite difference method for analyzing channel waveguides with arbitrary index profiles, IEEE J. Quant. Electron. QE-22, 968, (1986)
A. Sharma, P. Bindal, Variational analysis of diffused planar and channel waveguides and directional couplers, J. Opt. Soc. Am. A, 11, 2244, (1994)
B.D. Stone, G.W. Forbes, Optical interpolants for Runge Kutta ray tracing in inhomogeneous media, J. Opt. Soc. Am A, 7, 248, (1990)
J. Puchalsky, Numerical determination of continuos ray tracing: The four component method, Appl. Opt. 33, 1900, (1994)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Lakshminarayanan, V., Ghatak, A.K., Thyagarajan, K. (2002). An Introduction to Dynamic Programming and Applications to Optics. In: Lagrangian Optics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1711-5_9
Download citation
DOI: https://doi.org/10.1007/978-1-4615-1711-5_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-7582-1
Online ISBN: 978-1-4615-1711-5
eBook Packages: Springer Book Archive