Electromagnetic waves are transverse in nature, meaning the electric field ($\mathbf{E}$), magnetic field ($\mathbf{B}$), and the direction of propagation are mutually perpendicular. The direction of wave propagation is given by the direction of the vector cross product $\mathbf{E} \times \mathbf{B}$ .

Given that the wave propagates along the $+z$-axis (represented by unit vector $\hat{k}$), we must satisfy the condition: Direction of $(\mathbf{E} \times \mathbf{B}) = \hat{k}$.

Let's test the options:

1. $\hat{k} \times \hat{i} = \hat{j}$ (Propagates along $y$-axis). Also, $\mathbf{E}$ cannot be along the direction of propagation.
2. $\hat{j} \times \hat{j} = 0$ (Fields cannot be parallel).
3. $\hat{j} \times \hat{k} = \hat{i}$ (Propagates along $x$-axis).
4. $\hat{i} \times \hat{j} = \hat{k}$ (Propagates along $z$-axis). This matches the given condition.