(FBG).7 (OADM)
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- しらん はぎにわ
- 5 years ago
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1
2 (FBG).7 (OADM)
3 FBG B R B R B R OADM AddDrop AddDrop AddDrop
4 PMD PMD PMD PMD PMD 88 PMD
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20 1 1.1 WDMWavelength Division Multiplexing [1] WDM [] OADM(Optical Add Drop Multiplexer) OADM AddDrop [3] OADM AWG(Arrayed Waveguide Grating) OADM (FBG) OADM FBG OADM [4] (FBG) [5] FBG FBG [] 1
21 FBG OADM (FBG) 5 OADM (FBG) OADM. [6,7] Z Z=Zo 13
22 E E x y = A cos( ωt φx).1 A x cos( ωt φy) = y. x y Z=Zo Z=Zo y ExE x y E A x E + A y A x A y cos φ = sin φ.3 x y AxAy tan =-Ay/Ax Ax=Ay=A Ex +Ey =A A Ax Ay=A 0 14
23 15
![.3 [4,6,9] X X Y Y X X Y X Y](/docs-images/84/89837335/images/24-0.jpg "X x Y y PANDA(Polarization")
24 .3 [4,6,9] X X Y Y X X Y X Y X x Y y PANDA(Polarization maintaining AND Absorption reducing Fiber).1.PANDA BO3 16
25 .4. WDM PBS(Polarization Beam Splitter) WDM PBS X Y PANDA.3 PANDA.3PANDA 17
26 18.4
27 .5 [6,11,1] Z Z X Y X E E x y cosθ 1/ =, sin θ j / 1/, j / (.4) E x + E y = 1 (.5) X0 Y0 0 X0 (Circular rotation) (Retardation) R( ) T( ) R( ) 19
28 0 + + = = = ) sin( ) cos( sin cos sin sin cos sin ) sin( ) cos( cos sin sin cos 0 0 cos sin sin cos ) (,0) ( ) ( ), ( j j j j j j e e j j e e e e T R T R φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ (.6) Ω Ω Ω Ω Ω = cos sin sin cos ) ( T (.7) J = Ω = * * ), ( ) ( A B B A R T J φ (.8) ) ) cos( / sin( )cos / cos( Ω + Ω + = φ j A (.9) ) )sin( / sin( )sin / cos( Ω + Ω + = φ j B (.10) = 0 0 y x y x E E J E E (.11).5 X0 0
29 E x e jωt 0 = cosθ 0 (.1) E y e jωt 0 = sinθ0 (.13) t (.11) ExEy t a a E a x 1 E + a y ExEy + cosδ 0 = sinδ 0 a a 1 (.14) { cos ( / ) cos ( θ + Ω) + sin ( / ) cos (φ + Ω θ } 1/ 1 = 0 0 ) { cos ( / ) sin ( θ + Ω) + sin ( / ) sin (φ + Ω θ } 1/ = 0 0 ) cosδ = 0 cos ( / )sin (.15) (.16) { ( θ + Ω) } + sin ( / )sin{ (φ + Ω θ )} 0 a a 1 (.17) (.14) XY (b/a) X ± b a = sin { Ψ (φ + Ω θ )} tan { Ψ ( θ + Ω) } cos 0 0 (.18) 0 tan Ψ = sin cos { ( θ0 + Ω) } + tan ( / )sin{ (φ + Ω θ0) } { ( θ + Ω) } + tan ( / ) cos{ (φ + Ω θ )} 0 0 (.19) 1 Ψ = φ + Ω + ( 1/ ) tan 0 Ps [ tan{ ( θ φ) } ] cos (.0) 1
30 Ps = I I max max I + I min min 1 ( b / a) = 1+ ( b / a) = [ 1 sin sin { ( θ φ) }] 0 (.1) (.0) (.1).5.6 (FBG) [,3,5] (FBG) FBG (GeO) FBG
31 FBG 4 FBG B λ B N = eff Λ (.) Neff.6FBG FBG A B da dz db dz jωexp[ j βz]b = (.3) jω exp[ j βz]a = (.4) z β = β ( π / Λ) (.5) L (.5) A(0)=1B(L)=0 A(z)B(z) 0 { β sinh[ S( z L) ] + js cosh[ S( z L) ]} A( z) exp( j βz) β sinh( SL) js cosh( SL) = (.6) 3
32 [ S( z L) ] Ωsinh B( z) exp( j βz) β sinh( SL) js cosh( SL) = (.7) S = Ω ) ( β 1/ (.8) 0 { β sinh[ Q( z L) ] + jq cosh[ Q( z L) ]} A( z) exp( j βz) β sinh( QL) jq cosh( QL) = (.9) [ S( z L) ] Ωsinh B( z) exp( j βz) β sinh( QL) jq cosh( QL) = (.30) Q = ( β Ω) 1/ = js (.31) R R = B(0) A(0) (.3) R(L, ) (.6)(.31) Ω sinh ( SL) β sinh ( SL) + S cosh R( L, λ) = Ω sinh ( SL) β Ω cos ( SL) ( SL) ( Ω ( Ω β β < 0) 0) (.33) (.36) B B RB { λ πn L) } π ( π nl / λ ) λb B /( eff + B = (.34) 4
33 R B tanh ( πl nη / λ ) = B (.35) n (.37) FBG L n L cm 100% FBG.7OADM [,13] OADM( ) WDM OADM AWG AWG PLC Planer Lightwave Circuit L AWG AWG.7AWG 5
34 AWG OADM FBG FBG.8 FBG OADM FBG B IN Drop Add B FBG OUT OADM PANDA OADM FBG IN FBG FBG B Drop Add B FBG OUT.8 FBG OADM 6
35 .9 OADM.8 FBG FBG OADM FBG OADM OADM 3. [8,10] W Ge- 7
36 3.3 [8,10] CR PtPc CR CR = Pc 100 Pt + Pc [%] (3.1) 3dB 10dB = 10log( Pi / Po) [db] (3.) Pi Po db dB Ps Ps=0 Ps = 1 0 < Ps < 1 3. Ps =
37 X Ps = { I (0 ) I (90 )} + { I (45 ) I ( 45) } I (0 ) + I (90 ) (3.3) 3.1 Ps X Y (3.3) Ps 1 1 Ψ = tan { I (45 ) I ( 45 )} { I (0 ) I (90 )} (3.4) 3. X slow X [Pxx] 9
38 X fast Y [Pxy] Y slow X [Pyx] Y fast Y [Pyy] Cxy Cyx P xy = 10 log [db] (3.5) Pxx P yx = 10 log [db] (3.6) Pyy (1) 3.4 () (1) (3.6) (3.7) () (3.8) (3.9) (3.10) 3[dB] 1310[nm] 10[dB] 1550[nm] 30
39 31 3.3
40 3.1 3
41 33
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44 CRxCRy X Y 3.4 CRxCRy 1310[nm] 50[%] 3[dB] CRxCRy 1550[nm] 10[%] 10[dB] Ps Ps = 1 Ps = 1 36
45 (3.4) tan 1/ -45< < CxytCxyc t c 1550[nm] CxyCyx 0[dB] Cxy Cyx 15[dB] 0[dB] Ps PANDA (X ) (Y )90 Ps = Ps = 0 X Y X Y =1310nm 5050 =1550nm
![4 (FBG) 4.1 FBG FBG FBG 4. [5] 4..1 FBG FBG 4.](/docs-images/84/89837335/images/46-0.jpg "1 48nm KrF 1 MASKFBG FBG [5] ΛMASK = Λ FBG (4.1) 4.1 4. 4.. FBG FBG 38")
46 4 (FBG) 4.1 FBG FBG FBG 4. [5] 4..1 FBG FBG nm KrF 1 MASKFBG FBG [5] ΛMASK = Λ FBG (4.1) FBG FBG 38
47 Λ = λuv sinθ (4.) uv (44nm) 4.3 FBG nm (SMF) B=1550nmFBG (.) Neff=1.45 B=1550nm (4.) uv=44nm =
48 4.3 FBG 40
49
50 B R 4.3 FBG (FBG1FBG) (S-FBG1S-FBG7) SMF FBG 4.5 ASE FBG 4.5 B 1/ R R = 100 [%] (4.3) ASE FBG FBG FBG S-FBG1 B R B R FBG B R FBG 4
51 4.5. (S-FBG1) 4. S-FBG1 B R B R 4.1 FBG FBG FBG S-FBG S-FBG S-FBG S-FBG S-FBG S-FBG S-FBG
52 B = [nm] 4.6FBG1 4.7FBG B = [nm] 44
53 B = [nm] 4.8S-FBG1 4.9S-FBG B = [nm] 45
54 B = [nm] 4.10S-FBG3 B = [nm] 4.11S-FBG4 46
55 B = [nm] 4.1S-FBG5 4.13S-FBG6 B = [nm] 47
56 B = [nm] 4.14S-FBG7 4.S-FBG1 B R ,581 48
57 4.15 B 4.16 R 49
58 B R FBG1 4.1 B= nm 1550nm R=9.15% =1.087nm 4.6 FBG FBG1 = FBG R=76.34% =0.67nm FBG B= nm B=1539.0nm (.) (4.) = nm S-FBG1S-FBG7 S-FBG1 80% 50
59 70% nm S-FBGS-FBG4 B 1549nmS-FBG5S-FBG7 1553nm S-FBGS-FBG4 S-FBG5 S-FBG7 FBG 4.6. (S-FBG1) B B FBG FBG R 4.7 FBG1 FBG S-FBG1S-FBG7 S-FBGS-FBG4S-FBG5S-FBG7 S-FBG1 B R 5 OADM 5.1 FBG PANDA OADM OADM AddDrop AddDrop OADM 51
60 5. (SMF) (PMF) 1550nm SMF FBG PMF FBG SMF PMF 1FBG OADM 5.11FBG 5. PANDA FBG 5.3 PANDA 5.3PANDA OADM FBG (1) SMF-1 FBG 5050 FBGS-FBG5 4 FBG () SMF FBGS-FBG3 S-FBG4 4 FBG 5
61 (3) PMF-1 FBG (PANDA ) 5050 FBGPANDA FBG B= nm R=99.9% =0.47 (4) PMF- (PANDA ) 5050 FBGPANDA FBG B= nm R=99.9% =0.47 PANDA FBG B= nm R=99.51% = AddDrop 5.4 FBG IN Add OADM AddDrop 5.1 OADM 5. OADM (1) ASE () Drop IN ASE Drop Drop (3) OUT (4) Add Add 1550nm OUT Add (5) RD Drop Drop RD 53
62 R D = Drop 100 [%] (5.1) 5.4OADM AddDrop.9 OADM 54
63 5.1 OADM 5. OADM 55
64 5.3. PMF 1FBG OADM IN Analyzer1Drop (3.3) (3.4) AddDrop 5.1 OADM RD 5. OADM Drop D TAdd A SMF-1 FBG SMF PMF-1 FBG PMF PMF-1 FBG PMF- 5.3 PMF-1 FBG PMF- 5.1 OADM RD [mw] mw R D [%] SMF-1FBG 3.43E E SMF- 4.66E E PMF-1FBG 1.06E E PMF- 4.93E E
65 5. OADM Drop D TAdd A SMF-1FBG Drop Add [nm] nm [nm SMF PMF-1FBG PMF
66 D = [nm] 5.5SMF-1 FBG Drop T = [nm] 5.6SMF-1 FBG 58
67 A = [nm] 5.7SMF-1 FBG Add+ D = [nm] 5.8SMF- Drop 59
68 T = [nm] 5.9SMF- A = [nm] 5.10SMF- Add+ 60
69 D = [nm] 5.11PMF-1FBG Drop T = [nm] 5.1PMF-1 FBG 61
70 A = [nm] 5.13PMF-1 FBG Add+ D = [nm] 5.14PMF- Drop 6
71 T = [nm] 5.15PMF- A = [nm] 5.16PMF- Add+ 63
72 5.3PMF-1 FBG PMF- =1548nm PMF-1FBG Cxy [db] 0.67 Cyx [db] PMF = 1548[nm] 5.17PMF-1FBG PxxPxy 64
73 = 1548[nm] 5.18PMF-1FBG PyyPyx = 1548[nm] 5.19PMF-1FBG 65
74 = 1548[nm] 5.0PMF- PxxPxy = 1548[nm] 5.1PMF- PyyPyx 66
75 = 1548[nm] 5.PMF AddDrop 5.5 SMF-1 FBG Drop FBG 1553nm Drop 5.6 Add 5.7 Add+ Drop FBG Add SMF- PMF-1 FBG PMF- AddDrop OADM AddDrop 5.1 OADM RD SMF PMF 1 FBG FBG IN %FBG 5050 Drop 5% 5. 67
76 FBG 5050 FBG Drop 50% 1 FBG FBG FBG Drop =1550nm 75nm FBG 1 FBG PMF-1FBG Pxx Pyy =1548nm Pxx Pxy 5.18 =1548nm Pyy Pyx PxxPyy FBG Pxy Pyx CxyCyx 0dB PMF-1FBG PMF- PMF-1FBG CxyCyx 15dB PMF OADM PANDA FBG 1550nm =1548nm 1nm 5.6 OADM FBG AddDrop 68
77 1 FBG 1 FBG PANDA OADM OADM FBG B=1550nm FBG FBG1 R FBG R FBG B FBG R FBG OADM PANDA 1 FBG OADM OADM FBG AddDrop 1 FBG 1 FBG 4 FBG FBG AddDrop 69
78 [1] WDM 00 [] 00 [3] OADM [4] 00 [5] 1996 [6] 00 [7] 1998 [8]Y. Namihira, et al.,"incident polarization angle and temperature dependence of polarization and spectral response characteristics in optical fiber couplers," Applied Optics, Vol.30, No.9, pp ,1991 [9] IECE'77,Vol.60-C, No.7,pp ,1977 [10] OFT [11] 1987 [1] 1998 [13] WDM
79 PMD TPC3 4 TPC4 5 TCN5CN 3 TPC3 4 TPC4 [1] Er EDFA : ErDoped Fiber Amplifier CD : Chromatic Dispersion PDL : Polarization Dependent Loss NL : Nonlinear Effects PMD : Polarization Mode Dispersion DSF : Dispersion Shifted Fiber SMF : Single Mode optical Fiber PMF : Polarization Maintaining optical Fiber PMF PMD PMD 71
80 1. PMD PMD PMF 3 PMD FA : Fixed Analyzer Method PMD FA 4 PMF FA PMD PMD 6 7 7
81 PMD.1 PMD : Polarization Mode Dispersion PMD PMF : Polarization Maintaining optical Fiber. [] z x y E E x y = a = a z y cos( ωt βz + θ ) cos( ωt βt + θ ) θ = θ θ ( π < θ π ) x y y x (.1) (a : z : : t : : : ) ExEy ExEy.1 θ = 0 π π π a x = a y θ = -73-
82 φ : x π π φ χ : π b 0 χ y' tan χ = 4 b x' = 0 = /
83 .3 1 PMD SMF : Single Mode optical Fiber PMD. PMD DWDM : Dense Wavelength Division Multiplexing PMD.4. PMD 1.3 SMF x y.4 FA.4a.4b -75-
84 PMF PMF SMF.3 a b.4-76-
85 .5 PMF [3] PMF PMF.5 [4].5 a b cpanda dbow-tie e.5a.5b.5(b) HE11 x HE11 y.5c d e 1.5(c)(d)(e) x y X x y HE11 x HE11 y PMF PANDA PANDA : Polarization-maintaining AND Absorption-reducing optical Fiber.5c PANDA PANDA SMF PMF 10-4 SMF PMF.1-77-
86 (a) (b) (c) (d) (e).5.1pmf.6 PMD [1,5] x y FA : Fixed Analyzer Method JME : Jones Matrix Eigenanalysis Method SOP : State of Polarization Method. FA FA 3-78-
87 ..7 PMD PMF FA PMD PMD PMD 3.1 PMD PMD FA : Fixed Analyzer Method PMD FA -79-
88 3.PMD PMD : Polarization Mode Dispersion PMD OS CPU OS(CPU) (emulate) OS PMD PMD PMD PMD PMD PMF PMD [1] 3.1 FA /41/4 /1/ 90 / -80-
89 τ = 1 f = 1 1 f π π = N 1 f n 3.1 f : 1 f : 1/ fn : N f f = f n f 1 = c = c λ λn = c λ λ 1 λn λ1 1 n / 1 τ = λ λ N i i+ 1 = f n cn i= 1 λi+ 1λi 3.3 Nn1 N : n : i : c : FA
90 3.1 FA 3.4 PMF x y x y PMF 3. n PMF n En [6] E n = Dn * Rn 1 * En 1 3.4) -8-
91 . Dn Rn-1 n n n1.3.4 D n exp = [ jω( τ / ) ] 0 n exp 0 [ jω( τ / ) ] n 3.5 : n : n R n 1 cosθ n = sinθ n 1 1 sinθ cosθ n 1 n n-1 : n n1 θ θ n 1 n θ θ 1 0 E n E 0 E n = D n * R n-1 * E n-1 D n : R n-1 :
92 3.5 FA [nm]1650[nm]00[nm] Eout Eout ExEy Iout [7] out = Ex cosθ E y sinθ 3.7 I + 45 E E exp = exp ( jωt) ( ) jωt PMD FA PMD FA FA -84-
93 4.1 3 FA : Fixed Analyzer Method [m] PMF : Polarization Maintaining optical Fiber [m] 0.4[m] 3 PMF PMD : Polarization Mode Dispersion 1.34[ps/m] PMF [m] 0.7[m] 1[m] [m] 0.4[m]3 0.3[m] 1[m]
94
95 4.3 PMF 3 PMD FA : Fixed Analyzer Method PMF PMF PMF 1 PANDA PANDA : Polarization-maintaining AND Absorption-reducing PANDA 30 3 PMF PMD 4.1 PMF PMD PMD [ps] 00.05[ps] [7] PMD PMD -87-
96 4.4 FA FA PMD PMD PMD 5.1 FA : Fixed Analyzer Method PMD : Polarization Mode Dispersion PMD PMD 0.61[ps/m] PMD [] PMF : Polarization Maintaining optical Fiber 0.[m] 10 5.PMD PMD PMD PMD Maxwell Maxwell y x exp σ = Ax A : 5.1 : -88-
97 5.1 PMF PMD Maxwell 1000 PMD 5. PMD PMD PMD PMD Maxwell 3000 PMD Maxwell PMD PMD Maxwell PMD Maxwell Maxwell 5.1 A PMD 0.9[ps] [ps] [ps]39 0.8[ps] [ps] PMD 5.3 PMD PMF PMD 1.1[ps]0.61[ps/m] PMD PMD [m] PMD 1.51[ps/m]PMF PMD FA 5. PMD 5. PMD PMD 1.0[ps] 1.1[ps]
98 PMD Maxwell Maxwell Maxwell Maxwell Maxwell Maxwell Maxwell PMD Maxwell 1 PMD PMD PMD PMF PMF PMD PMD PMD PMD 1.51[ps/m]PMF0.[m]10 1.1[ps]PMD [m]pmd FA PMD PMD PMD PMD [m]PMF -90-
99 10 PMF 4 PMF PANDA.4 PMD PMD 5.5 FA PMD 1.1[ps] PMD PMD [m] 1 EDFA EDFA PMD PMD PMF PMD 3 PMD FA PMD PMD 4 PMF PMD Maxwell 9 PMD 0.91[ps] PMD PMF
100 N = PMD 500 N = PMD
101 N = PMD 000 N = PMD
102 N = PMD 3000 N = PMD
103 N = PMD 3000 N = PMD
104 N = PMD
105 (PMD = 0.91 [ps]) (PMD = 1.73 [ps]) -97-
106 5.1 9 (PMD =.41 [ps]) (PMD =.6 [ps]) -98-
107 (PMD = 3.11 [ps]) -99-
108 5.PMD 5.PMD -100-
109 5.14PMD 5.15PMD -101-
110 [1] : DWDM 001 URL : [] : pp [3] : pp.0-00 [4] : p [5] : 1994 KDD : [6] Y. Suetsugu Y. Terasawa S. Tanaka : Effect of Fiber Splicing on Polarization Mode DispersionOFMC 93 [7] K. Mochizuki : Degree of Polarization in Jointed Fibers : The Lyot Depolarizer Applied OpticsVol.3No
111 FTTH(Fiber To The Home) DWDM( ) Gbit/s 800 Gbit/s DWDM OTNet DWDM OADM:Optical Add Drop Multiplexer AWG: Arrayed Wavegude Grating OADM H14 WDM B WDM WIC (FBG:Fiber Bragg Grating) H14 FBG FBG FBG 44nm 1550nm 1310nm FBG -103-
112 OADM OADM -104-
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- i - - i - Application of All-Optical Switching by Optical Fiber Grating Coupler Yasuhiko Maeda Abstract All-optical switching devices are strongly required for fast signal processing in future optical
e a b a b b a a a 1 a a 1 = a 1 a = e G G G : x ( x =, 8, 1 ) x 1,, 60 θ, ϕ ψ θ G G H H G x. n n 1 n 1 n σ = (σ 1, σ,..., σ N ) i σ i i n S n n = 1,,
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1 3 1.1.......................... 3 1............................... 3 1.3....................... 5 1.4.......................... 6 1.5........................ 7 8.1......................... 8..............................
m(ẍ + γẋ + ω 0 x) = ee (2.118) e iωt P(ω) = χ(ω)e = ex = e2 E(ω) m ω0 2 ω2 iωγ (2.119) Z N ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.120)
2.6 2.6.1 mẍ + γẋ + ω 0 x) = ee 2.118) e iωt Pω) = χω)e = ex = e2 Eω) m ω0 2 ω2 iωγ 2.119) Z N ϵω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j 2.120) Z ω ω j γ j f j f j f j sum j f j = Z 2.120 ω ω j, γ ϵω) ϵ
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光ネットワーク用デバイス
Optical Devices for Photonic Networks WDM OADM OXC 140 Gbps Abstract This paper describes optical devices required for rapidly evolving large-capacity photonic networks and introduces some optical devices
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145 13 13.1 13.1.1 0 m mg S 13.1 F 13.1 F /m S F F 13.1 F mg S F F mg 13.1: m d2 r 2 = F + F = 0 (13.1) 146 13 F = F (13.2) S S S S S P r S P r r = r 0 + r (13.3) r 0 S S m d2 r 2 = F (13.4) (13.3) d 2
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
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211 ( 4 2 1. 3 1.1............................... 3 1.2 1- -......................... 13 1.3 2-1 -................... 19 1.4 3- -......................... 29 2. 37 2.1................................ 37
4 2 Rutherford 89 Rydberg λ = R ( n 2 ) n 2 n = n +,n +2, n = Lyman n =2 Balmer n =3 Paschen R Rydberg R = cm 896 Zeeman Zeeman Zeeman Lorentz
2 Rutherford 2. Rutherford N. Bohr Rutherford 859 Kirchhoff Bunsen 86 Maxwell Maxwell 885 Balmer λ Balmer λ = 364.56 n 2 n 2 4 Lyman, Paschen 3 nm, n =3, 4, 5, 4 2 Rutherford 89 Rydberg λ = R ( n 2 ) n
18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α
18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α 2 ), ϕ(t) = B 1 cos(ω 1 t + α 1 ) + B 2 cos(ω 2 t
50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq
49 2 I II 2.1 3 e e = 1.602 10 19 A s (2.1 50 2 I SI MKSA 2.1.1 r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = 3 10 8 m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq F = k r
[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s
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Chap9.dvi
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4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5.
A 1. Boltzmann Planck u(ν, T )dν = 8πh ν 3 c 3 kt 1 dν h 6.63 10 34 J s Planck k 1.38 10 23 J K 1 Boltzmann u(ν, T ) T ν e hν c = 3 10 8 m s 1 2. Planck λ = c/ν Rayleigh-Jeans u(ν, T )dν = 8πν2 kt dν c
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chap1.dvi
1 1 007 1 e iθ = cos θ + isin θ 1) θ = π e iπ + 1 = 0 1 ) 3 11 f 0 r 1 1 ) k f k = 1 + r) k f 0 f k k = 01) f k+1 = 1 + r)f k ) f k+1 f k = rf k 3) 1 ) ) ) 1+r/)f 0 1 1 + r/) f 0 = 1 + r + r /4)f 0 1 f
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OHO.dvi
1 Coil D-shaped electrodes ( [1] ) Vacuum chamber Ion source Oscillator 1.1 m e v B F = evb (1) r m v2 = evb r v = erb (2) m r T = 2πr v = 2πm (3) eb v
[ ] (Ising model) 2 i S i S i = 1 (up spin : ) = 1 (down spin : ) (4.38) s z = ±1 4 H 0 = J zn/2 i,j S i S j (4.39) i, j z 5 2 z = 4 z = 6 3
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4.2 4.2.1 [ ] (Ising model) 2 i S i S i = 1 (up spin : ) = 1 (down spin : ) (4.38) s z = ±1 4 H 0 = J zn/2 S i S j (4.39) i, j z 5 2 z = 4 z = 6 3 z = 6 z = 8 zn/2 1 2 N i z nearest neighbors of i j=1
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AC Modeling and Control of AC Motors Seiji Kondo, Member 1. q q (1) PM (a) N d q Dept. of E&E, Nagaoka Unive
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= hυ = h c λ υ λ (ev) = 1240 λ W=NE = Nhc λ W= N 2 10-16 λ / / Φe = dqe dt J/s Φ = km Φe(λ)v(λ)dλ THBV3_0101JA Qe = Φedt (W s) Q = Φdt lm s Ee = dφe ds E = dφ ds Φ Φ THBV3_0102JA Me = dφe ds M = dφ ds
IA hara@math.kyushu-u.ac.jp Last updated: January,......................................................................................................................................................................................