2003.02.13
1 2 2 (Dielecrics) 4 2.1... 4 2.2... 5 2.3... 6 2.4... 6 3 Maxwell ( ) 9 3.1... 9 3.2 D H... 11 3.3... 13 4 14 4.1... 14 4.2... 14 4.3... 17 4.4... 19 5 22 6 THz 24 6.1... 24 6.2... 25 7 26 7.1 THz... 27 8 30 30 1
1 1.1 Wave length and Frequency of Electromagnetic wave λ Wave length Frequency ν λν=c log10 [m] log10 [Hz] 1000km 6 VLF 3 3 khz 1km 3 LF MF HF 6 3 MHz Radio wave 1m 1cm 1mm 1µm 1nm 1A 1pm 0-3 -6-9 -12 VHF UHF SHF EHF FIR IR UV X-ray 9 12 3 THz Visible 0.77 Light 0.64 15 0.59 0.55 0.49 18 1keV 0.43 0.38 21 3 GHz 30 GHz 1MeV 4.2K 300K µ Red Orange Yellow Green Blue Indigo Violet Micro wave Radiant ray Light γ -ray 1fm -15 1GeV 1.1: 2
3 1.2 10 6 10 9 10 12 10 15 Hz 1km 1m 1cm 1mm 1µm 1nm Radio wave Dielectric Dispersion TDR FIR IR Microwave UV FT-IR THz-TDS Visible Light Low-frequency Raman X-ray Ultrasonic Brillouin Raman Neutron Scattering FT-IR 20 cm -1 ~ 4000 cm -1 Raman 1 cm -1 ~ 4000 cm -1 Brillouin 0.01 cm -1 ~ 10 cm -1 Neutron 1 µev ~ 1000 mev -1 1 cm = 30 GHz 1 mev = 8 cm -1 Dielectric Relaxation 10 µ Hz ~ 10 10 Hz TDR 10 6 Hz ~ 10 10 Hz THz-TDS 0.2 THz ~ 3 THz 1.2: THz
2 (Dielecrics) 2.1 X V Q C 0 C 0 = Q V (2.1) C 0 C 0 = ε 0 S d (2.2) ε 0 S d C = ε S d (2.3) 4
2.2 5 ε r = ε ε 0 (2.4) ε κ 2.2 (dipole moment) d d 2.1: 2.1 P N P = Nq δ q δ
2.3 6 2.3 A δ P ± ± ± ± ± ± ± ± E 2.2: 2.2 2.2 δ A N q e ANδq e =(NAδ)q e =(Aδ)Nq e σ = Nq e δ P σ = P (2.5) 2.4
2.4 7 + _ + _ + _ + _ + _ + _ + _ + _ + _ 2.3: 2.3 P P (r) [1] P P P ( ) P [2] [1] σ n σ = P n (2.6) 2.5
2.4 8 S V ρ Q P σ 2.4: Q 2.4 S ρ σ n S Q Q = P nds = σ ds (2.7) S Q = S ρ dv (2.8) V ρ dv = P nds = P dv (2.9) V S V ρ = P (2.10) ρ ρ ρ ρ = ρ + ρ j = P t (2.11)
3 Maxwell ( ) 3.1 Maxwell M I S m = IS j M 3.1 I M j = M (3.1) M z z S y a z I a x a y x 3.1: m m = IS = Ia x a y = M z (a x a y a z ) I = M z a z 9
3.1 10 a y M z M z + M z a z I 2 M x + M x a z I 1 I 2 a z I 1 M x a x a x a x a y (a) (b) 3.2: 3.2(a) 3.2(b)??(a) I = I 1 I 2 = M z (M z + M z ) = M z a z = M z x a xa z j y = I = M z a x a z x (3.2)??(b) I = I 2 I 1 =(M x + M x ) M x = M x a x = M x z a za x j y = I = M x a z a x z (3.3) j y = M x z M z x (3.4) z j z x j x
3.2 D H 11 j = M (3.5) ( ) 2.10 j j ( 2.11) j j = j + j + j 3.2 D H E B Maxwell E = ρ ε 0 (3.6) E = B t (3.7) B = 0 (3.8) c 2 B = j + E ε 0 t (3.9) ρ j P M ρ = ρ + ρ (3.10) j = j + j + j (3.11) P = ρ P t = j (3.12) M = j (3.13)
3.2 D H 12 3.6 3.12 E = ρ + ρ ε 0 = ρ P ε 0 (3.14) (ε 0 E + P )=ρ (3.15) D D = ε 0 E + P Maxwell D = ρ (3.16) E D 3.9 3.11 3.12 3.13 ε 0 c 2 B = j + M + P t + (ɛ 0E) t (3.17) (ɛ 0 c 2 B M) = j + (ɛ 0 E + P ) t (3.18) H = ɛ 0 c 2 B M H B = µ 0 ( H + M) ɛ 0 µ 0 = 1 c 2 H 3.9 H = j + D t (3.19) j H D t H B H 0 H 3.9 B
3.3 13 3.3 E ρ P P = ρ χ P = χɛ 0 E (3.20) D = ε 0 E + P D =(1+χ)ε 0 E = ɛε 0 E (3.21) ɛ χ = ɛ 1 (3.22)
4 4.1 P E D P = χε 0 E =(ε 1) ε 0 E D ε 0 E + P = ε 0 E + χε 0 E =(1+χ) ε 0 E = εε 0 E ε 1= P ε 0 E = χ (4.1) χ ( ) ε χ ε = = = (polar molecule) H 2 O (non-polar molecule) 4.2 14
4.2 15 r 0 4.1 4.1: 4.1 E x Gauss q e x q e ( x r 0 ) 3 q e 4πε 0 x 2 = q2 e x = k 4πε 0 r0 3 e x (4.2) k e = q2 e 4πε 0 r 3 0 (4.3) k e x = q e E (4.4) p e α p e = q e x = αε 0 E α =4πr 3 0 (4.5)
4.2 16 m e m e d 2 x dt 2 = k ex k e = q2 e 4πε 0 r 3 0 (4.6) ω e ( ) ke q 2 1/2 e ω e = = (4.7) m e 4πε 0 r0m 3 e q e e a B r 0 = ab = 4πε 0 m e e 2 = 0.53 10 10 m ( 0.5 A ) (4.8) ω e = 4.1 10 16 s 1 λ =2πc/ω e = 460 A F = q e E x ( d 2 x m e dt + γ dx ) 2 dt + ω2 e x = q e E (4.9) m e γ ω 2 ex E = E 0 e iωt x = x 0 e iωt x = q 2 e/m e (ω 2 e ω 2 )+iγω E (4.10) p el p el = q e x = ε 0 αe
4.3 17 α(ω) = q 2 e/m e ε 0 (ω 2 e ω 2 )+iγω (4.11) χ el α P el P el = Np el = Nq 2 e /m e (ω 2 e ω2 )+iγω E = ε 0χ el E N ε(ω) ε(ω) 1=χ el (ω) = Nq 2 e /m eε 0 (ω 2 e ω 2 )+iγω ε (ω) =1+ ω2 e (ε 1) (ω 2 e ω 2 )+iγω (4.12) ε ε =1+ Nq2 e ε 0 m e ωe 2 =1+χ el (0) (4.13) µ =1) ε (3.12) Imε ωε ωε ω = ω e ω e 4.3 NaCl Na + Cl F = q 0 E
4.3 18 X ( ) d 2 X M dt +Γdx 2 dt + ω2 0 X = q 0 E (4.14) M Γ ω 2 0 x ω 0 q 0 E = E 0 e iωt X = X 0 e iωt X = q 0 /M (ω 2 0 ω 2 )+iγω E (4.15) p ion p ion = q 0 X = q 2 0 /M (ω 2 0 ω2 )+iγω E N P ion P ion = Np ion = Nq 2 0 /M (ω 2 0 ω2 )+iγω E = ε 0χ ion E (4.16) χ ion P P = P el + P ion =(χ el + χ ion ) ε 0 E =(ε(ω) 1) ε 0 E (4.17) ω 0 ω e ω 0 χ el (0) ε (ω) = (1 + χ el (0)) + χ ion = ε + Nq 2 0/Mε 0 (ω 2 0 ω 2 )+iγω (4.18) ε (ω) =ε + ε(0) ε (ω 2 0 ω 2 )+iγω = ε (ω) iε (ω) (4.19)
4.4 19 ε (ω) ε + (ε(0) ε )(ω 2 0 ω2 ) (ω 2 0 ω 2 ) 2 +Γ 2 ω 2 (4.20) ε (ω) (ε(0) ε )Γ 2 ω 2 (ω 2 0 ω 2 ) 2 +Γ 2 ω 2 (4.21) ε(0) ε Na Na g 10 23 M K 30 Nm 1 M 20 6 10 23 g 3 10 26 kg ω 0 K 30 M 3 10 3 26 1013 s 1 (4.22) ω e = 3 10 13 s 1 λ =2πc/ω e = 60µm 4.21 ωε ωε ω = ω 0 ω 0 4.4
4.4 20 τ 1/τ 1/τ P or (t) P d (t) P (t) P (t) =P d (t)+p or (t) (4.23) t t 4.2: 4.2 P d (t) P d (t) P or (t) P d (t) =ε 0 χ d E(t) (4.24)
4.4 21 dp or (t) dt = 1 τ (ε 0χ or E(t) P or (t)) (4.25) τ χ d =χ el +χ ion E(t) =E 0 e iωt P or (t) =P 0 e iωt iωp or = 1 τ (ε 0χ or E P or ) (4.26) P or = ε 0χ or 1+iωτ (4.27) P ( P = ε 0 χ d + χ ) or E 1+iωτ = ε 0 (ε(ω) 1) E (4.28) χ or ε(ω) = (1 + χ d )+ 1+iωτ ε(0) ε( ) = ε( )+ 1+iωτ (4.29) = ε (ω) iε (ω) (4.30) ε (ω) ε( )+ ε(0) ε( ) 1+ω 2 τ 2 (4.31) ε (ω) = (ε(0) ε( )) ωτ 1+ω 2 τ 2 (4.32) Debye ε (ω) 1/τ ωε (ω) Debye 4.25
5 χ(ω) ε(ω) Debye 5.1 C. J. F. Böttcher and P. Bordewijk Theory of electric polarization, vol. II [1] ε(0) ε( ) ε ε (ω) 1/τ ω ω 5.1: 22
23 5.1 ε( ) ε(0) ε
6 THz 6.1 5.1 ω(q) THz THz-TDS 24
6.2 25 overdamped limit narrowing limit THz THz 1 cm 1 (90 GHz) 6.2 [2] (displacive) (order-disorder : OD ) k (critical slowing down)
7 (KH 2 PO 4 KDP) KDP PO 4 1.8 [3][4] OD [5][6][7] [1] PO 4 C 2 [2] [3] [4] KDP x(yx)y PO 4 PO 4 PO 4 [5] KDP DKDP(KD 2 PO 4 ) KDP DKDP 26
7.1 THz 27 PO 4 [6] KDP DKDP 1/1.37 1.37 O-H O-D O-H [7] KDP DKDP KDP DKDP [8] KDP PO 4 H D [8] H D 7.1 THz THz [2] [3] [4] KDP Kaminow Damen [9] Kaminow Damen x(yx)y log 7.1
7.1 THz 28 7.1: KDP T=295K x(yx)y log 180 cm-1 B2(z) 180 cm 1 Kaminow Damen x(yx)y 180 cm 1 D 2d B 2 (z) KDP D 2d x(yx)y B 2 (z)
7.1 THz 29 KDP x(yx)y A 1 ( ) B 2 (z) factorized form [10] PO 4 H 2 PO 4 A 1 B 2 (z) PO 4 A 1 PO 4 PO 4 [11]
8 THz THz THz THz-TDS THz 30
[1] C. J. F. Böttcher and P. Bordewijk, Theory of electric polarization, vol. II. Elsevier, second ed., 1978. 22 [2], p.14.,, 1988. 25 [3] R. Blinc J. Phys. Chem. Solids,vol. 13, p. 204, 1960. 26 [4], 7 I,p. 206, 1973.,, 1973 26 [5] and, vol. 18,p. 725, 1983. 26 [6], vol. 39, p. 520, 1984. 26 [7] and, vol. 40,p. 26, 1998. 26 [8] H. Sugimoto and S. Ikeda Phys. Rev. Lett., vol. 67, p. 1306, 1991. 27 [9] I. P. Kaminow and T. C. Damen, Phys. Rev. Lett. vol. 20,p. 1105, 1968. 27 [10] Y. Tominaga, A. Agui and S. Shin, Ferroelectrics vol. 152, p. 397, 1994. 29 [11] Y. Tominaga, H. Urabe and M. Tokunaga, Solid State Commun. vol. 48, p. 265, 1983. 29 31