ar X iv : p hy si cs / 0 10 40 05 2 A pr 2 00 1 Poynting vector , energy density and energy velocity in anomalous dispersion medium

The Poynting vector, energy density and energy velocity of light pulses propagating in anomalous dispersion medium (used in WKD-like experiments) are calculated. Results show that a negative energy density in the medium propagates along opposite of incident direction with such a velocity similar to the negative group velocity while the direction of the Poynting vector is positive. In other words, one might say that a positive energy density in the medium would propagate along the positive direction with a speed having approximately the absolute value of the group velocity. We further point out that neither energy velocity nor group velocity is a good concept to describe the propagation process of light pulse inside the medium in WKD experiment owing to the strong accumulation and dissipation effects. PACS numbers: 42.50.Gy, 42.25.Bs Wang, Kuzmich and Dogaiu claim that they have observed the superluminal light propagation by sending the probe laser pulses through the particularly prepared atomic caesium vapour and measuring the deviation of the refractive index of the medium from that of the vacuum and the arrival time of the pulses[1, 2]. Their main conclusion is that the light pulse propagates through the medium with group velocity about −c/310. Some comments on the WKD experiment have been made [3–6] in different ways. Recently, we analyse the negative group velocity and distortion of light pulse in the anomalous dispersion medium with two gain lines and show that although the shape of the light pulses seems to be almost preserved in a specific view, the distortion is still too large to use the concept of the group velocity to describe the propagation of the light in the medium[7]. In the present letter, we shall study the Poynting vector, energy density and energy velocity of light pulse in the anomalous dispersion medium. Without loss of generality, let the incident light pulse go to the medium at z = 0 from vacuum in z < 0. The electric and magnetic fields E(r, t) and H(r, t) of the light pulse propagating in the medium in the z-direction can be expanded by complex Fourier series as E(z, t) = 1 2 √ 2π (∫ dωE(z, ω)e−i(ω+ωc)t + c.c. ) (1)