Consider a graded index medium characterized by the following refractive index
distribution
(100)
Substitute in Eq.(32) and integrate to obtain
(101)
Notice that the periodic length
is independent of the launching angle (see Fig. 3.32) and all rays rigorously take the same amount of time in propagating through a distance zp in the z – direction.
[Hint: While carrying out the integration, make the substitutionFig 3.40
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