Energy flow. Backward ESWs.

• Characteristics of the Poynting vector corresponding to a monocromatic ESW close to a plane interface whose constitutive parameters falls in regions B or D.
  Properties

  i) Re κ>0, i.e. the ESW propagation is in +x direction.

  ii) The complex propagation constant has a small imaginary part, Im κ<0, to represent the slow decaying along the interface of the energy flow.

  iii) The x component of the net energy flow, P_x = ∫_-∞⁰ S_x dy + ∫₀^+∞ S_x dy <0, i.e. P_x is opposed to the direction of wave propagation. [ S_x is the time average of the x component of the Poynting vector]

  iv) A small energy flux, S_y, normal to the interface appears, pointing from MM to dielectric medium (+y direction). [ S_y is the time average of the y component of the Poynting vector]

  v) S_x (thus P_x ) and S_y attenuate in -x direction.

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  • ESW pulse propagation. The sign and magnitude of phase and energy velocity as well the pulse spreading can be derived from the dispersion relation, the relation between the complex ESW wave-vector and the frequency.
  Choosing the parameters ω₀/ω_p = 0.4 and F = 0.56, curve ε(μ) falls in region D for 0.471<ω/ω_p<0.52. To illustrate the ESW’s dispersion characteristics in this region, the video shows the Poynting vector corresponding to a one-dimesional Gaussian wave packet with a spatial harmonic α(0.5ω_p) ≈ 1.41 ω/c and a half width Δ = 0.25 {α(0.49ω_p)-α(0.5ω_p)} ≈ 0.073 .

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