Ray and energy propagation in graded-index media
JOSA, Vol. 65, Issue 2, pp. 169-173 (1975)
http://dx.doi.org/10.1364/JOSA.65.000169
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Abstract
We have studied the validity of the eikonal equation for an inhomogeneous medium. The propagation of an electromagnetic wave in a medium that is characterized by a parabolic dielectric constant variation in the transverse direction, has been studied in detail. The general path of a ray has been calculated and the irradiance distribution near the focal point has been analytically obtained.
Citation
A. K. Ghatak and K. Thyagarajan, "Ray and energy propagation in graded-index media," J. Opt. Soc. Am. 65, 169-173 (1975)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-65-2-169
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References
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- It may be added that this failure is not due to the particular form of ∊(γ) chosen, which is unbounded as γ→∞. Even for the case in which ∊(x)=∊_{e} + ∊_{2}a^{2}/cosh^{2}x/a, which is bounded, the term (1/k^{2}_{0}ψ_{0})∇^{2}ψ_{0} is finite and equal to ∊_{2}a^{2} tanh^{2}x/a.
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- A two-dimensional analysis is given here for simplicity.
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- This implies that the neglect of terms O(1/k_{0}) in β_{mn} and ∂^{2}A/∂z^{2} in Ref. 13, is equivalent to paraxial approximation.
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