GATE 2017 EC – Question 63
An optical fiber is kept along the $\hat{z}$ direction. The refractive indices for the electric fields along $\hat{x}$ and $\hat{y}$ directions in the fiber are $n_x = 1.5000$ and $n_y = 1.5001$, respectively ($n_x \neq n_y$ due to the imperfection in the fiber cross-section). The free space wavelength of a light wave propagating in the fiber is 1.5 $\mu$m. 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 ________.
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Correct answer: 0.37 to 0.38
Explanation
A circularly polarized wave has its two components 90° out of phase. To become linear, the phase difference between the two components must change by another quarter wavelength, so the extra phase must be $\frac{\pi}{2}$. The phase difference builds up as $\frac{2\pi}{\lambda}\Delta n\,L$, so $L = \frac{\lambda}{4\Delta n} = \frac{1.5\ \mu\text{m}}{4 \times 10^{-4}} = 3750\ \mu\text{m} = 0.375$ cm.