The answer is negative according to http://www.mathpages.com/home/kmath528/kmath528.htm
It should also be remembered that a perfectly monochromatic wave carries no information, and therefore is not subject to any limitation on the phase velocity.
Can someone clarify?
A monochromatic plane wave is simply:
$$x(t) = A \sin\left(\omega t + \phi\right)$$
where $A$, $\phi$, and $\omega$ are fixed, never-changing quantities. Because the properties of this wave never change, there is no way to use it to transmit information.
Consider this: suppose you point a laser pointer from one building to another, so that you can see the red spot it produces, but you don't have any way to change its brightness ($A$), frequency ($\omega$), or phase ($\phi$). You just have an unchanging spot. How could you use this unchanging spot to transmit information?
Of course, sometimes the existence of a monochromatic wave can tell you something. The red spot tells you that someone installed a laser. Maybe the brightness of the received light really is changing, from fog blowing between the buildings, or perhaps the spot is moving because of relative motion between the source and the receiver. This tells you something about the environment, but it's not the sort of thing that someone is getting at when they say that a monochromatic wave conveys no information.
