a superposition of plane-wave fields. Any contamination introduced by optical elements like mirrors or gratings can persist for only a few wavelengths away from such elements. On the scale of a typical laboratory optical table, this is negligible.

Plane-wave fields propagate at the speed of light in vacuum; they are fundamentally relativistic. The 1905 principle of Einstein is basic: the speed of light is the same in all inertial frames of reference [@einstein]. The mathematical statement of this principle is that any description of a plane-wave field can depend on the spacetime coordinate $x^{\mu}$ only as a scalar product with the propagation 4-vector $k^{\mu}$. The consequence of this projection of the spacetime 4-vector onto the light cone is that any change of gauge must be such as to be confined to the light cone. That is, with the definition$$\varphi\equiv k^{\mu}x_{\mu}, \label{ab}$$ the field 4-vector must be such that $$A_{pw}^{\mu}=A_{pw}^{\mu}\left(  \varphi\right)  , \label{ac}$$ where the subscript *pw* stand for *plane-wave*. When the gauge transformation of Eq. (\[h\]) is applied, the gauge-altered 4-vector potential is confined by the condition (\[ac\]) to the form [@hrgge]$$\widetilde{A}^{\mu}=A^{\mu}+k^{\mu}\Lambda^{\prime}, \label{ad}$$ where the gauge-change generating function can itself depend on $x^{\mu}$ only in the form of $\varphi,$ and 