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.

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

13. 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

14. 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,

15. more compactly while and in Lecture 18

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

17. Thank 林杰