Energy flow. Forward ESWs.

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

  Properties

  i) Re κ>0, i.e. the ESW propagation is in +x direction (from left to rigth in animation).

  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 in the same direction as that 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 dielectric medium to MM (-y direction) appear. [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. If we consider that the dielectric medium is vaccum, the dispersion relation can be written as,
  α(ω)=(ω/c) {(ε²(ω)- ε(ω)μ(ω))/(ε²(ω)-1)}^1/2
  where ε(ω) and μ(ω) follow the Drude and Lorentz models respectively,
  ε(ω)=1-ω_p²/(ω²+iωγ)
  μ(ω)=1-F ω²/(ω²-ω₀²+iωγ)
  where ω is the angular frequency, and ω_p and ω₀ are the plasma frequency and the magnetic resonance frequency respectively. Choosing the parameters ω₀/ω_p = 0.4 and F = 0.56, curve ε(μ) falls in region C for 0.52<ω/ω_p<0.6. 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(0.58ω_p) ≈ 1.14 ω/c and a half width Δ = 0.5 {α(0.59ω_p)-α(0.58ω_p)} ≈ 0.014 ω/c.

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