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Vanishing Energy

Vanishing Energy. ----Energy in Dispersive Media 07300190021 徐小凡. Contradiction. in Lecture 19:. What's ε?. ε('s time-domain expansion) is a response function with following properties: time-translation invariant initial condition independent finite causality.

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Vanishing Energy

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  1. Vanishing Energy ----Energy in Dispersive Media 07300190021 徐小凡

  2. Contradiction • in Lecture 19:

  3. What's ε? • ε('s time-domain expansion) is a response function with following properties: • time-translation invariant • initial condition independent • finite • causality

  4. ε is consistent with Kramers-Kronig relation: • or

  5. Provided ε/ε0 is not alway equal to 1, there exists Im ε/ε0, i.e. energy dissipation (proved later). • Provided ε/ε0 is not alway equal to 1, there exists dispersion.

  6. The imaginary part of ε introduces the decay in propagation, i.e. energy absorption.

  7. Landau: A dispersive medium is also an absorbing medium.

  8. Reference for more details: either of • Jackson 7.10 • Landau §82 • 数学物理方法，胡嗣柱，pp138

  9. A simple example • Damping is essential for a periodic forced oscillation, or fundamentally speaking, a response function.

  10. Return to Energy • modification upon equation of continuity: instead of considering the temporally non-locality and non-linear operation of energy

  11. analysis of Split the integrand into two equal parts and in one make the substitutions, ω-> -ω', ω'-> -ω, and use the reality constraints to obtain

  12. We now suppose that the electric field is dominated by frequency components in a relatively narrow range compared to the characteristic frequency interval over whichε(ω) changes appreciably. • Thus,

  13. more compactly while and in Lecture 18

  14. Something about μ • Is μ also a similar response function like ε? • Go to Landau §82, and he will show the slight difference.

  15. Thank 林杰

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