GATE EC 2017 Set 1 — Question 53
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Electromagnetics → Plane Waves → Light Propagation in Fibers
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Question
An optical fiber is kept along the direction. The refractive indices for the electric fields along and directions in the fiber are and , respectively ( due to the imperfection in the fiber cross-section). If the free space wavelength of a light wave propagating in the fiber is . If the lightwave is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimetres, is ______.
Correct answer
0.36 to 0.38
Solution
The fiber is birefringent with refractive indices and . The difference in refractive indices is .
The free space wavelength is cm.A circularly polarized wave has a phase difference of (or ) between its orthogonal components ( and ). For the wave to become linearly polarized, the total phase difference must become an integer multiple of (e.g., ).The additional phase difference introduced by the fiber over a distance is given by:
To change from circular polarization (initial phase difference ) to linear polarization (target phase difference ), the minimum additional phase shift required is :
cm.
The free space wavelength is cm.A circularly polarized wave has a phase difference of (or ) between its orthogonal components ( and ). For the wave to become linearly polarized, the total phase difference must become an integer multiple of (e.g., ).The additional phase difference introduced by the fiber over a distance is given by:
To change from circular polarization (initial phase difference ) to linear polarization (target phase difference ), the minimum additional phase shift required is :
cm.
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