Subluminal shows how a wave composed of a multitude of frequencies moving at different velocities — all less than or equal to c, the speed of light in a vacuum — can appear to have features moving faster than c.

The grid that crosses the screen is moving with a velocity of c, and no individual frequency outpaces it. However, the total wave (the bottom trace, in white) has its strongest peaks where all the individual frequencies are in phase, and the places where that happens shift with time, at a “speed” that is greater than c. Nothing is actually travelling with these peaks, though; they’re just an artifact of the way the different frequencies are slipping in and out of phase.

This illusion of superluminal motion can only occur when the refractive index of the medium falls as the frequency of the light increases, a situation known as anomalous dispersion. If it falls rapidly enough, the group velocity — the speed at which the overall envelope of the wave seems to move — can even become negative. More details.

Click on the applet to pause or redraw.

to pause or redraw. Use the Change group velocity button to switch between positive and negative group velocities.

button to switch between positive and negative group velocities. Use the Shutter button to lower and raise a shutter in the middle of the screen. Try lowering the shutter just as a “superluminal” pulse crosses the middle of the screen, to see why these pulses can’t be used to send messages faster than light.*

* Note that the response to the shutter shown here is an approximation; the individual frequencies won’t really be chopped off quite as cleanly as this. But whatever the precise shape of the waves that are generated as the shutter is closed, they can’t travel faster than the fastest phase velocity that occurs in the medium (which will not exceed c), so they can’t catch up with a pulse travelling at the group velocity and modify it in any way.

Reference: For an account of how a negative group velocity can be achieved in practice, see LJ Wang, A Kuzmich & A Dogariu, “Gain-assisted superluminal light propagation”, Nature 406, p277 (July 20, 2000).

Applets Gallery / Subluminal / created Tuesday, 15 August 2000 / revised Wednesday, 16 August 2000