# 32 833 charges are sources of dielectric displacement

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ω 2 − i − nv 1 τ τ 3 ε 0m (8.28) 1 e2 with ω = ω − 3 nv ε m 0 2 1 2 0 Separation: ε(ω) =ε1(ω) + iε2(ω) (8.29) nv e 2 ω12 − ω 2 ε1 (ω ) = 1 + ε 0 m (ω12 − ω 2 ) 2 + ω 2 / τ 2 (8.30) nv e 2 ω /τ ε 2 (ω ) = ε 0 m (ω12 − ω 2 ) 2 + ω 2 / τ 2 (8.31) 8-11 Maxwell equations for solid divB = 0 ⇔ ∫∫ Bd A = 0 divD = ρ ⇔ ∫∫ Dd A = Q (no magnetic monopoles) (8.32) (8.33) (charges are sources of dielectric displacement field) & curl ( = - B ⇔ & ∫ ( d r = − ∫∫ Bd A (8.34) (law of induction) & curl H = j + D ⇔ & ∫ H d r = I + ∫∫ Dd A (8.35) (current or charge in flux cause curled magnetic field) & (8.35) ⇒ curl H = j + D = σ ( + ε 0ε (& ⇒ & = − µ H = curl( ⇒ µ curl H = curl curl ( & & (8.34) ⇒ − B 0 0 − 1 curl curl ( = σ (& + ε 0ε (&& 23 µ 0 14 4 curl curl ( = ∇ × (∇ × ( ) = ∇ (∇( ) − ∇ ( 2 ∇( = 0 if ρ = 0 inside the sample ⇒ 2 ∇ ( = ε 0εµ 0(&& + µ 0σ (& Wave equation for nonmagnetic solid (µ ≈ 1) 8-12 (8.36) 2 ∇ ( = ε 0εµ 0 (&& + µ 0σ (& (8.36) Solution by damped wave ansatz: ε = ε 0e ~ i ( k ⋅ r −ω t ) ~ 2 εω 2 ω k = 2 + iσ c ε 0c 2 (8.37) in (8.37) ⇒ c = 1 / µ 0ε 0 , ⇒ (8.37) speed of light in vacuum ~ω σ ω~ k= =n ε +i c ε 0ω c ~ Complex refractive index n = n + iκ (8.38) (8.39) n: refractive index, κ: absorbtion coefficient ~ω ω k = n+i κ ⇒ c c (8.40) Plane wave propagating in z-direction: ω κω i n z −ωt z − (8.37) c c ⇒ ε = ε 0e e2 13 14 4 23 (8.40) damping in direction plane wave of propagation c in vacuum → c/n in solid 8-13 (8.41) Damping of amplitude by e Damping of intencity by e K= − − κω z c ⇒ 2κω z c 2κω : absorbtion constant c (8.42) Relation to ε(ω) =ε1(ω) + iε2(ω) ~ n 2 = ( n + iκ ) 2 = ε (ω ) = ε 1 (ω ) + iε 2 (ω ) (8.43) ε1(ω) = n2 - κ2 = ε (8.44) σ ε 0ω (8.49) ε 2 (ω ) = 2nκ = σ ~ n2 = ε +i ↑ (8.38) ⇒ ε 0ω 8-14 Fig. 8.5 General form of ε1(ω) and ε2(ω) for a dipole oscillator according to equations (8.30) and (8.31). ε2(ω) ≈ 0 outside resonance maximum Width of maximum: 1/τ ε2(ω) ≈ 0 ⇒ n ≈ ε 1 (ω ) e2 1 Resonance frequency: ω1 = ω 0 − 3 nv ε m < ω 0 0 ω0: resonance frequency of αel(ω) ω1 < ω0 due to effect of local field. Classical harmonic oscillator: ω 0 = 8-15 f /m Quantum mechnics: resonances are absorbtion frequencies due to electronic tansitions ⇒ always several resonance maxima in atom mainly in 1016 s-1 range (UV). Solid: also interband and intraband transitions Intraband transitions: between filled and empty states of conduction band in metals and semiconductors. ω < ω1 : ε1(ω) > 1 ⇒ n ≈ ε1 (ω ) > 1 lim ε 1 (ω ) = ε (0) ω →0 ε(0): statistic dielectric constant (already holds for visible range). ω > ω1 : ε1(ω) < 1 ⇒ n < 1 e.g. for X-rays lim ε1 (ω ) = 1 ω →∞ 8-16...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online