x E E E e i ω = t + ikx 0 k λ λ 2π k 2π/λ k ω/v v n v c/n k = nω c c ω/2π λ k 2πn/λ 2π/(λ/n) κ n n κ N n iκ k = Nω c iωt + inωx c iωt + i( n+ iκ ) ωx

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つねときいんそん
5 years ago
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1 x E E E e i ω t + ikx k λ λ π k π/λ k ω/v v n v c/n k nω c c ω/π λ k πn/λ π/(λ/n) κ n n κ N n iκ k Nω c iωt + inωx c iωt + i( n+ iκ ) ωx c κω x c iω ( t nx c) E E e E e E e e κ e ωκx/c e iω(t nx/c) I I E E e ωκ x c

2 κ E ωκx/c e x κ α α 1/e xx I () x I (x) α I x I e x α α ωκ c 4πκ λ oth ote D J t + B t EH DBJ J oth D t ote B t D E B H J E ε μ D ε ε E 1 B µ 1 µ H

3 ε μ ε μ 1/c ε ε ε + iε μ EH oth iωε ε E ote H iωµ H ( N ε ) E E N ε N n iκε ε' iε" ε κ n ε nκ κ ε n nκ ε n ( ε ε ) + ( ) κ ε ε ε ε + ε 1 N i λ N i n κ λ ω π/5 4π nωx/c πnx/λ κωx/c πκx/λ κω x c iω t nx c i t i E ( x) E e e ( ) 6. 8 ω Ee e α 4πκ/λ ωκ x c I ( x) E ( x) Ee I e

4 I (x) / I () HB ot ote εε µ ω E ω ε c E ot ote gad dive E E ωn c E dive ( ω N c ) E ( ω ε c ) E ψ ψ 1 ψ ε 1 n E p K H ψ ψ 1 ε (n iκ) z E 1p ψ K K 1 H 1 E p H x y ε 1 n K E H p ε (n iκ) ψ ψ 1 ψ H p z K 1 E 1 H 1p E K x y K K K x 1x x K inψ K inψ K inψ 1 1 inψ inψ K K

5 n 1n K K1 ωn1 c K ωn c inψ inψ ( ωn c) ( ωn c) n n 1 1 ω K1z Kz K coψ ε 1 co ψ c ω Kz K Kx K Kx K K in ψ n n1 in ψ c ψ ψ 1 n 1 K K x K 1 K 1x n K x K ψ δ e i δ p I ( ε ) E R R K K ψ ψ p p e i δ p iδ e x y S

S Ex E co ψ, E y E S E1x E1 co ψ, E1 y E1 S Ex E co ψ,

K E 1 ( ) K coψ + K coψ E K coψ K coψ E 1 p K K coψ K

6 S Ex E co ψ, E y E S E1x E1 co ψ, E1 y E1 S Ex E co ψ, Ey E E 1 E ψ ψ 1 x n 1 E p ψ ψ 1 E 1 p E 1 p coψ 1 H H 1 ψ ψ 1 x H H 1 H y ψ E z y n E p coψ ψ E p coψ E p H ψ z y z E E coψ E coψ 1 H + H H S S S 1 y S H K ωµ E K E + E K E 1 ( ) K coψ + K coψ E K coψ K coψ E 1 p K K coψ K coψ coψ + K coψ K K coψ K coψ coψ + K coψ K K ψ ψ K inψ K inψ

7 K K ( inψ inψ ) coψ coψ in ψ in co in ψ ψ + ψ ψ ψ p K ( inψ inψ ) coψ + K coψ in ψ + in ψ co( ψ ψ )in ψ + ψ K K coψ inψ inψ coψ in ψ ψ K coψ K inψ inψ coψ in ψ + ψ + ( ) tan ψ ψ ( ) tan ( ψ + ψ ) Rp pp tan ( ψ ψ ) tan ( ψ + ψ ) in ψ ψ R in ψ + ψ ψ ψ π/ tan R p ψ ψ ψ p K K K K p coψ in ψ K coψ + K K K in ψ K K K coψ in ψ K coψ + K K in ψ N 1 N K N N N N p 1 1 coψ in ψ ε coψ ε 1 ε ε 1 in ψ N coψ + N1 N N1 in ψ ε coψ + ε1 ε ε1in ψ N N N 1 1 coψ in ψ ε1 coψ ε ε 1 in ψ N1 coψ + N N1 in ψ ε1 coψ + ε ε1in ψ N ε N N1 N N1 coψ in ψ ε coψ ε1 ε ε1in ψ Rp N + N1 N N1 coψ in ψ ε coψ + ε1 ε ε1in ψ N1 N N1 coψ in ψ ε1 coψ ε ε1in ψ R N1 + N N1 coψ in ψ ε1 coψ + ε ε1in ψ

8 N 1 in i R pr R p n R R p R pr N i1. R pr R p R p R p R R p R pr ψ ψ 1 $ $ K K N N $ p $ K + K N + N ε ε1 ε + ε1 N i N n iκ

9 N $ n i 1 R i N + + κ 1 n + i + exp ( θ ) 1 κ 1 R θ R ε 1 ( 1 n) + κ ε n κ + κ θ tan 1 n + κ 1 1 R n 1+ R R coθ R inθ κ 1 + R R coθ Z 1 Z $ Z Z 1 Z1 + Z ε μ Z µ ε μ ε ε 1 $ ε ε1 ε + ε1 p co ψ ψ i i ( + ) exp ( ) tanψ exp ( ) co ψ ψ p p ψ Δ δ p δ p ψ Δ ΨΔ ε' ε'' nκ ( ) in ψ tan ψ co ψ in ψ in ε 1+ in ψ co in ψ tan ψ in 4ψ in ε 1+ in ψ co + in ψ ε' ε'' nκ n ε + ε κ ε ε ε ε + ε ΨΔ

10 ω ω ω f(ω) f'(ω) if"(ω) f'(ω) f"(ω) π f ( ω) ω ( ω) π f xf ( x) dx x ω ( x) f dx x ω f(ω) f"(ω) f'(ω) f ( ω ) 1 π x + ω d ln x ω dx f x dx ln x + ω d x ω f'(ω) f"(ω) x x ω dx f ( x ) x ω ω ε' ε'' (ω) R 1/ (ω) e iθ (ω) ln (ω) (1/) lnr (1/) lnr f'(ω) iθ f"(ω) θ ω ω π ln R x x ω R (ω) θ (ω) R (ω) θ (ω) n κ f (x) x x f x x f' ( x) f' (x)f" ( x) f" (ω) iπ f x f x φ dx x ω f (ω) f' (ω) if"(ω) ω ω f ω t t Im (x) x ω Re (x) x

11 E u u m * τ m d u d + ( m τ ) du dt qe Eu e iωt Nqu D ε ε E ε E ε 1 Nq m ε ω 1+ i ωτ 1 ω ω ω i τ { } + { } ω p N 1/ q /m * ε ε ε' iε'' ε 1 ω ω + 1 τ ε ω ωτ ω + 1 τ hω p h τ ω ω (ω p 1/τ ) 1/ n ε 1/ hω p ε ''

12 ε'ε'' R hω p h τ hω hω ε'ε'' ε'' ε''/3 ε' hω ε '' E F E F E F E E F u m * τ m d u dt + ( m τ ) du dt + m ω u qe ω Eu e iωt u N b N bqu

13 ε 1 ω ω + ω τ ω b i ( ) ω b N bq /m * ε { } ( ) + ( ) ε 1 ω ω ω ω ω ω τ b {( ) + } ε ω ω τ ω ω ω τ b hω h τ ε " ε ' E F ε'ε'' k hω hω p h τ hω ε ' ε ' h τ hω p hω ε'ε'' ε '' ε ' R hω ω

14 ε ε ' ω ω p' ( ) ω ω ε 1 τ 1 hω p h ω p u M d dt u + Mω u qe M q ω N Nqu d dt Nq + ω E M e iωt ikx Nq ( ω ω ) + E M Nq 1 ε 1+ 1 ε E Mε ω ω ω ω i/τ K oth D iω ε E + t ote B iωµ H t H ω + ( ω c K ) E

15 ω ω ω Nq M ω c K 4 Nq ω ω + c K Mε ε ω + ωc K ε ω K Nq ω ω ωup ω + Mε ω ω up ω ω ck K

ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 +

2.6 2.6.1 ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.121) Z ω ω j γ j f j