Huygens principle in plane waves

J. A. Romero; L. Hernandez

doi:10.1117/12.591622

21 October 2004 Huygens' principle in plane waves

J. A. Romero, L. Hernandez

Proceedings Volume 5622, 5th Iberoamerican Meeting on Optics and 8th Latin American Meeting on Optics, Lasers, and Their Applications; (2004) https://doi.org/10.1117/12.591622
Event: 5th Iberoamerican Meeting on Optics and 8th Latin American Meeting on Optics, Lasers, and Their Applications, 2004, Porlamar, Venezuela

Abstract

The article presents results corresponding to the mathematical formulation of Huygens' principle for plane waves. We show the deduction of an integral relationship as the basis of the above-mentioned principle. By using this integral formula and the properties of the electrical field vector of the plane waves, a vectorial equation to describe Huygens' Principle is obtained. To corroborate the validity of the solution to problems, which may arise using the vectorial equation, we proved that such solutions fulfil Helmholtz' homogeneous equation. Subsequently the density of energy of the secondary waves was determined. In order to illustrate this method, we found an exact analytical equation that describes relative intensity of the diffracted light as a function of the distance from the center of the aperture. For the first maxima and minima, the intensity behavior is similar to the one predicted by Fresnel's theory. However, for distances near to the aperture, the difference is remarkable. Afterwards, we did a comparative analysis among the results obtained and Fresnel's theory, and new approaches were established. It must also be pointed out that contrary to previous methods; the present formulation is dealt with a vectorial analysis without recurring to any approximations.

Citation Download Citation

J. A. Romero and L. Hernandez "Huygens' principle in plane waves", Proc. SPIE 5622, 5th Iberoamerican Meeting on Optics and 8th Latin American Meeting on Optics, Lasers, and Their Applications, (21 October 2004); https://doi.org/10.1117/12.591622

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KEYWORDS

Diffraction

Electromagnetic radiation

Spherical lenses

Wavefronts

Lanthanum

Laser optics

Dielectrics

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