The dark side of light: negative frequency photons

The impact of something we thought couldn't exist has now been detected.

A team of physicists has shown that light with a negative frequency (thought to be a quirk of the equations) actually, in some sense, exists.

The equations in question are Maxwell's, and they describe the propagation of light. When describing the propagation of light, the equations require that we describe the light field as having both positive and negative frequencies. A negative frequency would indicate a wave made up of photons that have a negative energy, something that doesn't necessarily make a lot of sense.

A team of researchers has shown that, in some sense, negative frequencies can be observed through the generation of radiation with a positive frequency.

...the solutions to Maxwell's equations are rather weird. Remember, every light field is described mathematically by a positive and a negative frequency. If we just consider the positive frequency component, then there are four solutions to the equation. These correspond to light waves that have positive and negative frequencies, and waves that are travelling in the same and opposite direction to the initial pulse of light.

The researchers ignore the two solutions corresponding to waves travelling in the opposite direction to the input pulse because they are not amplified. Any pulse that travels in the opposite direction does not overlap with the input pulse for very long, and there is no time to transfer much energy to the generated pulse.

Of the remaining two solutions, one has a positive frequency and travels with the generating pulse, allowing it to be amplified. This is commonly observed. The last solution corresponds to a negative frequency, also travelling with the input pulse. This solution, which should produce photons with negative energy, was thought to be an artifact of the equations and did not correspond to anything physical.

But that field itself consists of positive and negative frequencies. And (believe it or not) the negative frequency component of the negative frequency solution is a positive frequency. Or, you might think of it like this: the negative frequency element of the input pulse also generates four solutions that have both positive and negative frequencies. [emphasis mine]