1. For a plane electromagnetic wave, the direction of propagation is given by

and the three vectors $\vec{E}, \vec{B}, \vec{k}$ are mutually perpendicular.

2. The wave is propagating along the $y$-direction. Therefore:

• $\vec{E}$ must be perpendicular to $\hat{y}$
• $\vec{B}$ must be perpendicular to $\hat{y}$
• and $\vec{E} \times \vec{B}$ must be along $\pm \hat{y}$

So neither $\vec{E}$ nor $\vec{B}$ can have a $y$-component.

3. Check each option:

Option A: $E_x, B_z$ or $E_z, B_x$

• If $\vec{E} = E_x \hat{i}$ and $\vec{B} = B_z \hat{k}$, then

which is along the $y$-axis.

• If $\vec{E} = E_z \hat{k}$ and $\vec{B} = B_x \hat{i}$, then

again along the $y$-axis.

So this option is possible.

Option B: $E_x, B_y$ or $E_y, B_x$

Here one of the fields has a $y$-component, i.e. along the direction of propagation. That is not allowed for a plane EM wave in free space.

So option B is incorrect.

Option C: $E_y, B_y$ or $E_z, B_z$

• In the first case, both have $y$-component, impossible.
• In the second case, both are along $z$; then they are parallel, but $\vec{E}$ and $\vec{B}$ must be perpendicular.

So option C is incorrect.

Option D: $E_y, B_x$ or $E_x, B_y$

Again one field has a $y$-component, which is not allowed.

So option D is incorrect.

4. Therefore, the only valid pair is: