# I Plasma self-focusing index of refraction < 1?

1. Apr 24, 2017

### 2sin54

Hi. After reading about self-focusing in plasmas I came across the relative index of refraction that a light wave experiences during the interaction with plasma. Namely $$n = \sqrt{1-\frac{{\omega_p}^2}{{\omega}^2}}$$ where $$\omega_p$$ is the plasma frequency and $$\omega$$ is the light (for example laser) frequency. Clearly this is smaller than 1 but how can that be? What does it imply? What's the speed of light due to this self-focusing?

2. Apr 28, 2017

### jasonRF

This just means that the phase velocity of electromagnetic waves in the plasma is faster than c (just like for EM waves in a waveguide) However, the group velocity is smaller than c so there is no violation of special relativity.