Vanishing energy Energy in Dispersive Media 07300190021徐小凡
Vanishing Energy ----Energy in Dispersive Media 07300190021 徐小凡
Contradiction · in lecture19: 注意: (1)这里12-50F2指的是纯粹的电场的能量,并没有把“传导电流”携带的机械能量 算上。 )秒色散介,利别12-1bE(叫E讲算分原中磁场的总能量是不对的 否则你就得到负能量这个荒课的结论。色散介质中的能量是个复杂的问题,要得到完整的 答案,请参考 Landar的书 2.良导体在光波段(等离子体中的光波) 在光波段,金属的有效介电常数为(4)≈1-一2,这个模型也被广泛应用
Contradiction • in Lecture 19:
What's a? E(s time-domain expansion)is a response function with following properties time-translation invariant initial condition independent finite causality
What's ε? • ε('s time-domain expansion) is a response function with following properties: • time-translation invariant • initial condition independent • finite • causality
E is consistent with Kramers-Kronig relation Im∈(o) Re∈(o)/∈0=1+-P T [Re∈(o)/∈0-1 Im∈(o)/eo or ’Im∈()/o Re∈(o)/Eo=1+-P T 2 Im E(O)/Eo P [Re∈(o)/∈o-1
• ε is consistent with Kramers-Kronig relation: • or
Provided E/Eo is not alway equal to 1, there exists Im E/Eo, i.e. energy dissipation (proved later) Provided E/Eo is not alway equal to 1. there exists dispersion
• 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
k The imaginary part of E introduces the decay in propagation, i.e. energy absorption
r c k = • The imaginary part of ε introduces the decay in propagation, i.e. energy absorption
Landau: a dispersive medium is also an absorbing medium
• Landau: A dispersive medium is also an absorbing medium
Reference for more details either of Jackson 710 Landau§82 数学物理方法,胡嗣柱,pp138
• Reference for more details: either of • Jackson 7.10 • Landau §82 • 数学物理方法，胡嗣柱，pp138
A simple example Damping is essential for a periodic forced oscillation, or fundamentally speaking, a esponse function
A simple example • Damping is essential for a periodic forced oscillation, or fundamentally speaking, a response function
10 20 x= sin at,x(0)=0,x(0)=0 ∴x 2Sin at+-t
x t t x t x x 1 sin 1 sin , (0) 0, (0) 0 2 = − + = = = 5 1 0 1 5 2 0 2 4 6 8 1 0