If $$\vec{E}$$ and $$\vec{K}$$ represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by: ($$\omega$$ - angular frequency)

The magnetic field vector $$\vec{B}$$ of an electromagnetic wave can be expressed in terms of the electric field $$\vec{E}$$ and the propagation vector $$\vec{K}$$. From Faraday’s law for a plane wave one obtains $$\vec{B} = \frac{1}{c}(\hat{k} \times \vec{E}),$$ where $$c$$ is the speed of light and $$\hat{k}$$ is the unit vector in the propagation direction.

The propagation vector $$\vec{K}$$ has magnitude $$|\vec{K}| = k = \omega/c$$, so that $$\vec{K} = \frac{\omega}{c}\,\hat{k}$$. Hence $$\hat{k} = \frac{c}{\omega}\,\vec{K}$$, and substituting this into the expression for $$\vec{B}$$ yields $$\vec{B} = \frac{1}{c}\cdot\frac{c}{\omega}(\vec{K} \times \vec{E}) = \frac{1}{\omega}(\vec{K} \times \vec{E}).$$ Therefore, the magnetic field can be written as $$\frac{1}{\omega}\,\vec{K}\times\vec{E}\,.$$