I would like to know why evanescent waves are not possible in pure vacuum?

Indeed, we have $$ k^2 = (\frac{\omega}{c})^2 $$ in vacuum, so we could have for example : $$ kx^2+ky^2+kz^2=(\frac{\omega}{c})^2 $$ with $$ kz=i kz'' $$ ( $ kx^2+ky^2 > (\frac{ \omega } {c})^2 $ ).

I have read that we need local charges to do it but I dont understand why.

I would like to know why evanescent waves are not possible in pure vacuum?

Indeed, we have $$ k^2 = \left(\frac{\omega}{c}\right)^2 $$

in vacuum, so we could have for example : $$ k_x^2+k_y^2+k_z^2=\left(\frac{\omega}{c}\right)^2 $$

with $ k_z=i k_z'' $ and $ k_x^2+k_y^2 > \left(\frac{ \omega } {c}\right)^2$.

I have read that we need local charges to do it but I don't understand why.

I would like to know why evanescent waves are not possible in pure vacuum  ?

Indeed, we have $ k^2 = (\frac{\omega}{c})^2 $ in vacuum, so we could have for example : $ kx^2+ky^2+kz^2=(\frac{\omega}{c})^2 $ with $ kz=i kz'' $ ( $ kx^2+ky^2 > (\frac{ \omega } {c})^2 $ ).

I have read that we need local charges to do it but I dont understand why.

Thank you.

I would like to know why evanescent waves are not possible in pure vacuum?

Indeed, we have $$ k^2 = (\frac{\omega}{c})^2 $$ in vacuum, so we could have for example : $$ kx^2+ky^2+kz^2=(\frac{\omega}{c})^2 $$ with $$ kz=i kz'' $$ ( $ kx^2+ky^2 > (\frac{ \omega } {c})^2 $ ).

I have read that we need local charges to do it but I dont understand why.