Abstract
A generalized refractive index in the form of optic eikonal is defined through comparing frame definitions of left-handed and right-handed sets and indicates the sign of the refractive index covered by the quadratic form of the eikonal equation. Fermat’s principle is generalized, and the general refractive law is derived directly. Under this definition, the comparison between Fermat’s principle and the least action principle is made through employing path integral and analogizing L. de Broglie’s theory.
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References
Born M, Wolf E. Principle of Optics (in Chinese). Beijing: Science Press, 1978
Guo H, Deng X M. Differential geometrical study of Fermat’s principle and static light beam transmission (in Chinese). Sci China Ser A-Math Phys Astron, 1995, 25(3): 273–279
Cao Q, Deng X M, Guo H. A generalization of Fermat’s principle (in Chinese). Sci China Ser A-Math Phys Astron, 1996, 26(5): 437–442
She W L, Wu S S, Guo H, et al. Further generalization of Fermat’s principle (in Chinese). Sci China Ser A-Math Phys Astron, 1999, 29(7): 667–672
Pendry J B, Smith D R. Reversing light: Negative refraction. Phys Today, 2004, 57(2): 37–44
Veselago V G. About the wording of Fermat’s principle for light propagation in media with negative refraction index. arXiv:cond-mat/0203451, http://arXiv.org
Planck M. Einfuhrung in die Theoretische Physik: Theoretische OptiK (in Chinese). Beijing: Higher Education Press, 1959
Guenther R D. Modern Optics. New York: John Wiley & Sons, 1990
Wang M G. Geometrical Theory of Diffraction (in Chinese). Xi’an: Xidian University Press, 1994
Kirilyuk P. 75 years of matter wave: Louis de Broglie and renaissance of the causally complete knowledge. arXiv:quant-ph/9911107, http://arXiv.org
Xu L. The Principle of Least Action and the Development of Physics (in Chinese). Chengdu: Sichuan Education Press, 2001
Jackson J D. Classical Electrodynamics. 3rd ed. New York: Wiley, 1999
Zeng J Y. Quantum Mechanics Vol. II (in Chinese). Beijing: Science Press, 1995
Zhou S X. A Course of Quantum (in Chinese). Beijing: People Education Press, 1981
Zeng J Y. Quantum Mechanics Vol. I (in Chinese). Beijing: Science Press, 1981
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Supported by the National Natural Science Foundation of China (Grant No. 60601028)
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Tan, K., Liang, C. & Shi, X. Optic eikonal, Fermat’s principle and the least action principle. Sci. China Ser. G-Phys. Mech. Astron. 51, 1826–1834 (2008). https://doi.org/10.1007/s11433-008-0190-7
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DOI: https://doi.org/10.1007/s11433-008-0190-7