Directional change of beams undergoing partial reflection*

Ian A. White; Allan W. Snyder; Colin Pask

doi:10.1364/JOSA.67.000703

Journal of the Optical Society of America
Vol. 67,
Issue 5,
pp. 703-705
(1977)
•https://doi.org/10.1364/JOSA.67.000703

Directional change of beams undergoing partial reflection

Ian A. White, Allan W. Snyder, and Colin Pask

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Ian A. White, Allan W. Snyder, and Colin Pask, "Directional change of beams undergoing partial reflection*," J. Opt. Soc. Am. 67, 703-705 (1977)

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Abstract

When a beam of finite width is partially reflected at a planar dielectric interface, there is in general a shift in the reflected beam direction away from that predicted by the simple application of the geometrical optics relfection law. We give a simple derivation of this shift, clarifying the underlying physical mechanism. The Gaussian beam is studied in detail.

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Spatial beam profile	Relative power distribution of component rays	Angular shift in beam direction
Gaussian baam
$exp {[- (\frac{X_{i}}{W_{0}}) 2]}^{- 1}$	$exp [- {(\frac{(sin α - sin α_{i}) k_{1} W_{0}}{2 cos α_{i}})}^{2}]$	$\frac{2 cos α_{i}}{{(k_{1} W_{0})}^{2}} \frac{{\| R (sin α_{i}) \|}^{'}}{\| R (sin α_{i}) \|}$
Lorentzian beam
${[1 + {(\frac{X_{i}}{W_{0}})}^{2}]}^{- 1}$	$exp (- \| \frac{(sin α - sin α_{i}) k_{1} W_{0}}{cos α_{i}} \|)$	0
Exponential beam
$exp [- \| \frac{X_{i}}{W_{0}} \|]$	${(1 + {\| \frac{(sin α - sin α_{i}) k_{1} W_{0}}{cos α_{i}} \|}^{2})}^{- 1}$	$\frac{cos α_{i}}{2 {(k_{1} W_{0})}^{2}} \frac{{\| R (sin α_{i}) \|}^{'}}{\| R (sin α_{i}) \|}$

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