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Kirchhoff's Theory for Optical Diffraction, Its Predecessor and Subsequent Development: The Resilience of an Inconsistent Theory

Buchwald, Jed Z. and Yeang, Chen-Pang (2016) Kirchhoff's Theory for Optical Diffraction, Its Predecessor and Subsequent Development: The Resilience of an Inconsistent Theory. In: Gustav Robert Kirchhoff's Treatise “On the Theory of Light Rays” (1882). World Scientific Publishing , Hackensack, NJ, pp. 63-123. ISBN 9789813147133. http://resolver.caltech.edu/CaltechAUTHORS:20170912-083447481

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Abstract

Kirchhoff's 1882 theory of optical diffraction forms the centerpiece in the long-term development of wave optics, one that commenced in the 1820s when Fresnel produced an empirically successful theory based on a reinterpretation of Huygens' principle, but without working from a wave equation. Then, in 1856, Stokes demonstrated that the principle was derivable from such an equation albeit without consideration of boundary conditions. Kirchhoff's work a quarter century later marked a crucial, and widely influential, point for he produced Fresnel's results by means of Green's theorem and function under specific boundary conditions. In the late 1880s, Poincaré uncovered an inconsistency between Kirchhoff's conditions and his solution, one that seemed to imply that waves should not exist at all. Researchers nevertheless continued to use Kirchhoff's theory — even though Rayleigh, and much later Sommerfeld, developed a different and mathematically consistent formulation, which, however, did not match experimental data better than Kirchhoff's theory. After all, Kirchhoff's formula worked quite well in a specific approximation regime. Finally, in 1966 Marchand and Wolf employed the transformation of Kirchhoff's surface integral that had been developed by Maggi and Rubinowicz for other purposes. The result yielded a consistent boundary condition that, while introducing a species of discontinuity, nevertheless rescued the essential structure of Kirchhoff's original formulation from Poincaré's paradox.


Item Type:Book Section
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https://doi.org/10.1142/9789813147157_0004 DOIArticle
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Additional Information:© 2017 World Scientific Publishing Co Pte Ltd.
Record Number:CaltechAUTHORS:20170912-083447481
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170912-083447481
Official Citation:Kirchhoff's Theory for Optical Diffraction, Its Predecessor and Subsequent Development: The Resilience of an Inconsistent Theory, by Jed Z. Buchwald (Caltech) and Chen-Pang Yeang (Univ. of Toronto) Gustav Robert Kirchhoff's Treatise “On the Theory of Light Rays” (1882). October 2016, 63-123
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81341
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Sep 2017 18:40
Last Modified:12 Sep 2017 18:40

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