Slowly varying envelope approximation

Assume an electromagnetic wave equation:

$\nabla ^{2}E-\mu _{0}\epsilon _{0}{\frac {\partial ^{2}E}{\partial t^{2}}}=0$

Then the Slowly Varying Envelope Approximation (SVEA) refers to the assumption that the pulse envelope varies slowly in time and space compared to a period and wavelength of light. Mathematically:

$E(\mathbf {r} ,t)=E_{0}e^{i(\mathbf {k} \cdot \mathbf {r} -\omega t)}$