A Simple Analytic Approximation for the Refracted Field at Gaussian Beam Incidence upon a Boundary of Absorbing Medium

Vladimir M. Serdyuk, Joseph A. Titovitsky

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DOI: 10.4236/jemaa.2010.211084                

Abstract

An approximate analytic model is presented to describe spatial structure of refracted electromagnetic field arising at oblique incidence of a Gaussian beam on a plane boundary of an absorbing homogeneous medium. The analytic solution is obtained by asymptotic approximation of a Fourier field integral under the condition of great beam width in comparison with a wavelength (the geometrical-optics approximation). This model can be used also for approximate simulation of refracted field in the cases of beam incidence near the critical angle on transparent or absorbing (amplifying) refracting medium, if one artificially introduces the additional absorption (amplification), whose value is proportional to the ratio of the wavelength and the effective beam width. It is shown that the analytic model reflects the general features of refracted field at total internal reflection.

Keywords

Gaussian Beam; Refraction; Absorbing Medium; Total Internal Reflection

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	C. D. Boyd and J. P. Gordon, “Confocal Multimode Resonator for Millimeter through Optical Wavelength Maser,” Bell System Technical Journal, Vol. 40, No. 2, March 1961, pp. 489-508.
[2]	H. Kogelnik, “Imaging of Optical Modes-Resonators with Internal Lenses,” Bell System Technical Journal, Vol. 44, No. 3, March 1965, pp. 455-494.
[3]	H. Kogelnik, “On the Propagation of Gaussian Beams of Light through Lenslike Media Including Those with a Loss or Gain Variation,” Applied Optics, Vol. 4, No. 12, December 1965, pp. 1562-1569.
[4]	H. A. Haus, “Waves and Fields in Optoelectronics,” Prentice-Hall, Suffolk, 1983.
[5]	S. Solimeno, B. Crosignani and P. DiPorto, “Guiding, Diffraction and Confinement of Optical Radiation,” Academic Press, New York, 1986.
[6]	D. Marcuse, “Light Transmission Optics,” Van Nostrand Reinhold, New York, 1972.
[7]	T. Tamir, “Nonspecular Phenomena in Beam Fields Reflected by Multilayered Media,” Journal of the Optical Society of America A, Vol. 3, No. 4, April 1986, pp. 558-565.
[8]	B. R.Horowitz and T. Tamir, “Lateral Displacement of a Light Beam at a Dielectric Interface,” Journal of the Optical Society of America, Vol. 61, No. 5, May 1971, pp. 586-594.
[9]	C. C. Chan and T. Tamir, “Beam Phenomena at and Near Critical Incidence upon a Dielectric Interface,” Journal of the Optical Society of America A, Vol. 4, No. 4, April 1987, pp. 655-663.
[10]	J. Alda, “Transverse Angular Shift in the Reflection of Light Beams,” Optics Communications, Vol. 182, No. 1-3, August 2000, pp. 1-10.
[11]	W. Szabelak and W. Nasalski, “Transmission of Elegant Laguerre-Gaussian Beams at a Dielectric Interface – numerical simulations,” Bulletin of the Polish Academy of Sciencies, Vol. 57, No. 2, 2009, pp. 181-188.
[12]	Y. Zhang and C-F. Li, “On the Representation of an Inclined Gaussian Beam,” European Journal of Physics, Vol. 27, No. 4, July 2006, pp. 779-786.
[13]	M. Born and E. Wolf, “Principles of Optics,” Pergamon Press, New York, 1968.
[14]	P. Hillion, “Gaussian Beam at a Dielectric Interface,” Journal of Optics, Vol. 25, No. 4, July 1994, pp. 155-164.
[15]	C. W. Hsu and T. Tamir, “Lateral Displacement and Distortion of Beam Incident upon a Transmitting-Layer Configuration,” Journal of the Optical Society of America A, Vol. 2, No. 6, June 1985, pp. 978-988.
[16]	P. Berczynski and Y. A. Kravtsov, “Theory for Gaussian beam diffraction in 2D inhomogeneous medium, based on the eiconal form of complex geometrical optics,” Physics Letters A, Vol. 331, No. 3-4, October 2004, pp. 265-268. M. A. Potenza, D. Brogioli and M. Giglio, “Total internal reflection scattering,” Applied Physics Letters, Vol. 85, No. 14, October 2004, pp. 2730-2732. K. J. Willis, J. B. Schneider and S. C. Hagness, “Amplified Total Internal Reflection: Theory, Analysis, and Demonstration of Existe