Theoretical Study of Electromagnetic Wave Propagation: Gaussian Bean Method


In this work, we present the study of electromagnetic wave propagation through a medium with a variable dielectric function using the concept of Gaussian Beam. First of all, we start with wave equation with which we obtain the solution in terms of the electric field and intensity distributions approximate to Gaussian Function, . With this, we analyze the dependency of r on Gaussian beam distribution spread, the distant from the axis at which the intensity of the beam distribution begins to fall at a given estimate of its peak value. The influence of the optimum beam waist wo and the beam spread on the intensity distribution will also be analyzed.

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Ugwu, E. , Ekpe, J. , Nnaji, E. and Uguru, E. (2013) Theoretical Study of Electromagnetic Wave Propagation: Gaussian Bean Method. Applied Mathematics, 4, 1466-1470. doi: 10.4236/am.2013.410198.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] A. Siegman, “Lasers Sensitization,” C.A University Sciences Books, 1986.
[2] S. A. Self, “Focusing of Spherical Gaussian Beam,” Applied Optics, Vol. 22, No. 5, 1983, pp. 658-661.
[3] H. Sun, “Thin Lens Equation for a Real Laser Beam with Weak Lens Aperture Truncation,” Optical Engineering, Vol. 37, No. 11, 1998, pp. 2903-2913.
[4] J. W. Ra, H. L. Bertoni and L. B. Felsen, “Reflection and Transmission of Beam at Dielectric Interface,” SIAM Journal on Applied Mathematics, Vol. 24, No. 3, 1973, pp. 396-413.
[5] M. McGuirik and C. K. Carniglia, “An Angular Spectrum Representation Approach to the Goos-Hanchen Shift,” Journal of the Optical Society of America, Vol. 67, No. 1, 1977, pp. 103-107.
[6] R. P. Riesz and R. Simon, “Reflection of a Gaussian Beam from a Dielectric Slab,” Journal of the Optical Society of America A, Vol. 2, No. 11, 1985, pp. 558-565.
[7] T. Tamir, “Nonspecular Phenomena in Beam Field Reflected by Multilayered Media,” Journal of the Optical Society of America A, Vol. 3, No. 4, 1986, pp. 586-594.
[8] S. Z. Zhang and C. C. Fan, “Nonspecilar Phenomena on Gaussian Beam Reflection at Dielectric Interface,” Journal of the Optical Society of America A, Vol. 5, No. 9, 1988, pp. 1407-1411.
[9] F. Pampaloni and J. Enderlein, “Gaussian, HermiteGaussian, and Laguerre Gaussian Beam: A Primer,” 2004, 29p.
[10] J. Ralton, “Gaussian Beams and the Propagation of Singularity, Studies in Partial Differential Equations,” MAA Studies in Mathematics, Vol. 23, 1982, pp. 206-248.

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