Rosen coordinates

I would like to express this spacetime interval for a spacetime with a monochromatic electromagnetic wave for which I believe $|E|=frac{q}{omega}sin(u)$ expressed in Rosen coordinates:

$ds^2=-2dudv+C^2left( frac{q^2}{omega^2},2frac{q^2}{omega^2},omega uright )left(dx^2+dy^2 right )tag{1}$

In Cartesian coordinates.

I can’t really find out what exactly Rosen coordinates are but I believe they work as follows:

$u=-t+ztag{2}$

$v=frac{-1}{2}(t+x)tag{3}$

So that I retrieve $ds^2=-dt^2+dx^2+dy^2+dz^2$ in the limit of $omega$ going to zero.

Is this correct?