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GATE 2026 PH – Question 19

Optical Physics · polarization: Jones vectors and matrices for linear, circular and elliptical polarization, birefringence, ray-transfer matrix for mirrors and lenses · 1 mark · Multiple choice

For the electric field of an electromagnetic wave given below, which of the following statements is correct? $$\mathbf E=\hat x E_0\cos(\omega t)+\hat y\,2E_0\cos(\omega t+\pi/2)$$

  1. The electric field is linearly polarised with slope 2.
  2. The electric field is circularly polarised with radius E0.
  3. The electric field is elliptically polarised with a ratio of major to minor axis being 2.
  4. The electric field is unpolarised with the two components being phase shifted by π/2.

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Show answer and explanation

Correct answer: (C) The electric field is elliptically polarised with a ratio of major to minor axis being 2.

Explanation

The field components are
$$E_x=E_0\cos\omega t,\qquad E_y=2E_0\cos(\omega t+\tfrac\pi2)=-2E_0\sin\omega t .$$

The two components have a **phase difference of $\pi/2$** and **unequal amplitudes** ($E_0$ and $2E_0$).

**Eliminate time.** Since $\cos^2\omega t+\sin^2\omega t=1$:
$$\frac{E_x^2}{E_0^2}+\frac{E_y^2}{(2E_0)^2}=1 .$$

This is an **ellipse** with semi-axes $E_0$ and $2E_0$. The ratio of the major to the minor axis is $2E_0/E_0=2$.

The wave is **elliptically polarised with axis ratio 2** (option C).