Are there materials that just change the speed of light?

Maxwell’s equations in medium without charges read
begin{align}
0&=nablacdot D,,\
0&=nablacdot B,,\
0&=nablatimes E + dot B,,\
0&=nablatimes H – dot D,.
end{align}
Here, $D = varepsilon E$ and $mu H = B$, with $varepsilon$ and $mu$ the relative permittivity and permeability of the medium.

One may derive wave equations for $E$ and $B$ of the form
begin{align}
0&=square E,,\
0&=square B,,
end{align}
if $varepsilon$ and $mu$ are constant. However, when they vary in space, derivatives of $mu$ and $varepsilon$ spoil this nice relationship. Even so, if the medium is slowly changing as a function of space, we can usually neglect derivatives of $mu$ and $varepsilon$, leading to the interpretation of $1/sqrt{muvarepsilon}$ as the effective speed of light. My question is whether there are inhomogeneous media for which this interpretation is exact, i.e. for which changing $mu$ and $varepsilon$ may be exactly interpreted as changing $c$ in the wave equation.