# Gain medium and the speed of light

I am currently studying optics, and when taking a closer look at refractive indices, I stumbled across gain mediums. On Wikipedia it states that gain mediums can have a refractive index of $n<0$. But how can this be? According to $v_{ph}=\frac{c}{n}$ the wave would have to propagate faster than the speed of light. Doesn’t this clash with the assumption no information can travel faster than the speed of light?

• Can you add a link to what you have read? – eranreches Nov 18 '17 at 17:59
• @eranreches sure, just added it – BluNova897 Nov 18 '17 at 18:07
• It's $k<1$. This is the imaginary part of $n$. – Andrei Geanta Nov 18 '17 at 18:14
• @Arthur It clearly states that n can be smaller than one though. – BluNova897 Nov 18 '17 at 18:27
• @BluNova897, Yes, $n$ can be smaller than $1$, but the refractive index measures the phase velocity of light, which does not carry information. So there is not contradiction with special relativity. – Andrei Geanta Nov 18 '17 at 18:33

## 1 Answer

The refractive index cannot be less than one in standard materials, and is defiantly not < 1 in most (all) Laser gain materials. What I think you are getting confuse about is the imaginary part of the complex refractive index, which describes the absorption coefficient, can be less than 1. The refractive index (which is really an amalgamation of different properties) is not in this case, and not usually, less than 1.