Vanishing Energy Energy in Dispersive Media 07300190021 Contradiction

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

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

• Provided ε/ε 0 is not alway equal to 1, there exists Im ε/ε 0, i. e. energy dissipation (proved later). • Provided ε/ε 0 is not alway equal to 1, there exists dispersion.

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

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

• Reference for more details: either of • Jackson 7. 10 • Landau § 82 • 数学物理方法，胡嗣柱，pp 138

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

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

• 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

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

• more compactly while and in Lecture 18

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