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- なお こうじょう
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1 Research on interference-filter-stabilized external cavity diode lasers with narrow linewidth
2
3 ECDL IFLD ECDL IFLD IFLD Cateye Cateye ABCD Cateye IFLD IFLD PDH
4 Pseudo-Voigt fitting I-P A LD 81 B PD 83 C 85 D IFLD Cateye
5 Bose-Einstein BEC:Bose-Einstein Condensation 1925 Einstein [1] BEC BEC [2, 3] BEC 70 BEC 1960 T. H. Maiman [4] 1975 T. W. Hänsch A. L. Schawlow [5] 1985 S. Chu Na [6] 1987 E. L. Raab [7] 1995 BEC Rb [8] Na [9] Li [10] E. A. Cornell C. E. Wieman W. Ketterle R. G. Hulet E. A. Cornell C. E. Wieman W. Ketterle Sr [11] Yb [12] BEC [13] 2 1 C. A. Regal BCS-BEC [14] Mott [15]
6 6 1 BEC MHz khz MHz [16, 17, 18] 1.2 LD(Laser Diode) AR(Anti Reflection) ECDL(External Cavity Diode Laser) IFLD(Interference-Filter-stabilized external cavity Diode Laser) L D LD khz PZT Piezoelectric Transducer PZT PZT nm PZT 3
7 1.3 7 PZT ECDL IFLD IFLD ECDL BEC BEC ECDL IFLD IFLD ECDL IFLD IFLD IFLD ECDL IFLD 1.4 ECDL IFLD ECDL 1.1 ECDL LD 0 1 LD 1
8 8 1 LD ECDL ECDL LD [16] 1 LD [17] 1.2 ECDL 1.1 ECDL LD PZT 1.2 ECDL 2 LD PZT
9 1.4 ECDL IFLD 9 ECDL PZT 1.3 ECDL [19, 20] LD eagleyard AR LD EYP- RWE SOT Edmund Optics Newport U100-P LD PZT Noliac CMAP09 Agilent Torrseal ECDL LD 1.3 ECDL IFLD 1.3 ECDL ECDL 25mm LD
10 IFLD IFLD IFLD 1.4 IFLD IFLD LD Cateye 2.2 Cateye ECDL LD ECDL ECDL IFLD 1.4 IFLD LD PZT IFLD 2
11 1.4 ECDL IFLD IFLD PZT 65mm
12
13 13 2 IFLD IFLD Cateye 2.1 Cateye Cateye IFLD IFLD [18] 1 LD(Laser Diode) AR(Anti Reflection) eagleyard AR LD EYP-RWE SOT IFLD D 2.1 Cateye Cateye 1 ECDL IFLD 1 Cateye 2.2 Cateye Cateye ECDL
14 14 2 IFLD 2.1 IFLD IFLD L = 65mm FSR Free Spectral Range 2.3GHz 4.1 ν c MHz IFLD = FSR ν c 4.0 Cateye nm 0.3 ( PSM30-15C /800) Cateye Thorlabs AR ( C280TMD-B f = 18.4mm) 2 Cateye Cateye 2 LD ECDL Cateye ECDL Cateye 1 LD ECDL Cateye
15 2.1 Cateye Cateye IFLD Cateye 2 f = 18.4mm ABCD Cateye Cateye Cateye ABCD ABCD θ sinθ θ ( ) r r θ θ ( ) r, θ A B r, θ r 1, θ 1, r 2, θ 2 C D ( r 2 θ 2 ) = ( A C ) ( B D r 1 θ 1 ) (2.1) ( ) A B r, θ C D ABCD d ABCD r 2 = r 1 + d θ 1 θ 2 = θ 1
16 16 2 IFLD ( ) ( ) A B 1 d = C D 0 1 ( ) ( ) A B 1 0 ABCD = C D 1/f 1 r 1 = r 2 1/a+1/b = 1/f ( ) ( ) n 1 n 2 ABCD A B 1 0 = C D 0 n 1 /n 2 Cateye ( ) 3 ABCD r 0 θ 0 ABCD d d r, θ r 0, θ 0 r, θ r = 0 ( r θ ) = ( 1 d 0 1 ) ( /n mir ) ( 1 d 0 1 ) ( 1 0 1/f 1 ) ( r 0 θ 0 ) (2.2) f = 18.4mm 2 n mir = 1.51 d 2 d = 5mm θ 0 = 0 d 15.1mm 2 d + d = 20.1mm 2 1.7mm mm d Cateye 2.5 Cateye SM1TM09 Cateye 2 LD
17 2.1 Cateye ABCD θ 0 = 0, r = 0, f = 18.4mm, d = 5.0mm, n mir = 1.51 PZT 2.4 ABCD PZT 15mm 14mm 10mm Z10H14x15C-SYX(C-82) Agilent TorrSeal IFLD Cateye Cateye 2 780nm ECDL Cateye
18 18 2 IFLD 2.5 Cateye 2 Cateye Cateye PZT 2 f = 18.4mm 0.3 PZT 780nm 1 PZT Cateye Thorlabs 2.6 Cateye Cateye Cateye 2.7 IFLD Cateye LD LD AR LD Cateye
19 Cateye Cateye 2.2 IFLD 1 IFLD LASER OPTIK ( B AR B S ) IFLD
20 20 2 IFLD 2.7 IFLD Cateye LD Cateye mm θ n θ d = 2nd cosθ = 2nd 1 (sinθ/n) 2 mλ = 2nd 1 (sinθ/n) 2 (2.3) m = 1, 2, 3, (2.3) 1 m θ = 0 λ 0 λ = λ 0 1 (sinθ/n) 2 (2.4)
21 IFLD θ = 0 λ 0 = 781.5nm θ = 6 λ = 780.0nm n 1.7 n λ 0 θ λ 2.8 θ θ d n (2.4) LD LD L = 1 mλ L m 1 2 IFLD f L = 1m c 2 f c f = c 2L
22 22 2 IFLD f FSR(Free Spectral Range) IFLD L = 65mm f 2.3GHz 2.3GHz (2.4) f θ f = f (sinθ/n) 2 f 0( (sinθ n )2 ) (2.5) df dθ = f 0 sinθ cosθ (2.6) n2 f 0 = c/λ 0 (2.5) (sinθ/n) 2 1 (2.6) θ sinθ,cosθ 2 df dθ f 0 n θ (2.7) 2 f θ θ Rb D2 f 385THz θ = 6 df/dθ n = 1.7 c = m/s λ 0 = 781.5nm df dθ 14THz/rad 240GHz/ (2.8) 2.3GHz θ = θ Rb D Cateye Torrseal
23 Thorlabs ϕ1/2 20mm TR20/M M4 M IFLD 0.01 MOGLabs IFLD mm θ 3 dl r 2b sinθ θ dl/r (2.9)
![2mm 2 2 dl [ ]/360 IFLD r](/docs-images/84/89055571/images/24-1.jpg "6mm θ=0.01 dl 1um 0.")
24 24 2 IFLD D M6 1 3 M mm 2 2 dl [ ]/360 IFLD r 6mm θ=0.01 dl 1um 0.2mm 1/
25 2.3 IFLD r 3 dl IFLD LD Cateye M6 M IFLD LD LD
26 26 2 IFLD IFLD IFLD Z-MAX FPH AC RS: IFLD TAKACHI BDN IFLD Thorlabs TEMPERATURE CONTROLLER( TED200C) IFLD IFLD TorrSeal IFLD IFLD IFLD A 15.7V 55.6W IFLD
27 2.3 IFLD IFLD IFLD IFLD- IFLD-
28
29 29 3 IFLD IFLD IFLD ECDL 3.1 IFLD Rb D2 3.4 IFLD IFLD ECDL IFLD IFLD IFLD 3.1 λ=780nm ECDL 1 ECDL 1 ECDL 2 ECDL ECDL LD ECDL IFLD IFLD ECDL ECDL ECDL
![30 3 IFLD ECDL IFLD Power [mw] 40 30 20 red:ifld blue:ecdl(p-polarized) green:ecdl(s-polarized) 10 0 0 20 40 Current [ma] 60 80 3.1 λ=780nm IFLD I = (14.6 ± 0.7)mA ECDL I = (20.5 ± 0.](/docs-images/84/89055571/images/30-0.jpg "4)mA ECDL I = (42 ± 2)mA IFLD (0.62 ± 0.01)W/A ECDL (0.398 ± 0.005)W/A ECDL (0.51 ± 0.02)W/A 3.2 ECDL IFLD ECDL ECDL IFLD ECDL ECDL 0.2 0.03 IFLD 0.3 0.8 1 0.3 0.8 2 0.8 ECDL 1 0.2 = 0.")
30 30 3 IFLD ECDL IFLD Power [mw] red:ifld blue:ecdl(p-polarized) green:ecdl(s-polarized) Current [ma] λ=780nm IFLD I = (14.6 ± 0.7)mA ECDL I = (20.5 ± 0.4)mA ECDL I = (42 ± 2)mA IFLD (0.62 ± 0.01)W/A ECDL (0.398 ± 0.005)W/A ECDL (0.51 ± 0.02)W/A 3.2 ECDL IFLD ECDL ECDL IFLD ECDL ECDL IFLD ECDL = 0.8
31 ECDL = 0.97 IFLD ECDL ECDL 3.1 ECDL IFLD ECDL ECDL ECDL IFLD IFLD ECDL ECDL Cateye 2 Cateye LD Cateye ECDL Cateye IFLD ECDL IFLD ECDL IFLD IFLD ECDL 3.3 IFLD I=70.25mA ADVANTEST TQ8325 dλ/dθ
32 32 3 IFLD Power [mw] wavelength [nm] I=70mA LD 3.3 λ 750nm IFLD λ 750nm 2 λ=750nm 28 IFLD 28 0 IFLD λ=781.5nm IFLD 750nm 781.5nm K Rb K D1 D2 λ=770nm 767nm Rb D1 D2 λ=795nm 780nm 1 IFLD 795nm 3.3 LD 3.1.2
33 IFLD 3.4 ECDL ECDL nm 775nm 770nm 3.3 LD
34 34 3 IFLD 0.8 peak 0.84 transmittance FWHM=0.48 nm wave length [nm] nm ( 18 ) peak A y = y 0 + (x x 0 ) 2 +B 0.8 peak 0.83 transmittance FWHM = 0.43 nm wave length [nm] nm ( 13 ) peak A y = y 0 + (x x 0 ) 2 +B
35 peak 0.82 transmittance FWHM = 0.42 nm wave length [nm] nm ( 6 ) peak y = A y 0 + (x x 0 ) 2 +B
36 36 3 IFLD MHz 1MHz ω D = 2 ln2 u c ω 0 (3.1) ω 0 u = u = 2kB T M (3.2) M 1 u Rb T = 300K 500MHz Probe Pump ω 0 Probe Pump v 0 Pump Probe Pump Probe PD Pump Probe Probe v 0 ω ω 0 Probe Pump Probe Probe
37 ω 01 ω 02 ω = 1 2 (ω 01 + ω 02 ) Probe Pump Probe δω = +kv Pump δω = kv kv = 1 2 (ω 01 ω 02 )(k ) Probe ω 01 Pump ω 02 Probe EOM EOM 3.8 Rb CH1 CH2 Rb 87 Rb F=2-F =1,2,3 85 Rb F=3-F =2,3,4 CH PDH IFLD PZT PD
38 38 3 IFLD Pound-Drever-Hall PDH [21] 0 PZT PDH Electro-Optic Phase Modulator EOM Probe ( 3.11 ) Probe E = E 0 e iωt (3.3) EOM Mixer V f = V 0 sinω t (3.4) ω 2π 15MHz EOM 3.3 E EOM = E 0 e i(ωt+δ sinω t) = E 0 e iωt (1 + iδ sinω t) = E 0 e iωt (1 + δ 2 (eiω t e iω t )) (3.5) V 0 EOM π δ 1 Rb F (ω) E cell = F (ω)e EOM = E 0 (F (ω)e iωt + δ 2 F (ω + ω )e i(ω+ω )t δ 2 F (ω ω )e i(ω ω )t ) (3.6)
39 PD V E cell 2 V E cell 2 δ 2 (F (ω)f (ω + ω ) e iω t + F (ω) F (ω + ω )e iω t ) δ 2 (F (ω)f (ω ω ) e iω t + F (ω) F (ω ω )e iω t ) + Const δ2 4 g(2ω ) = δ[cosω t Re(F (ω)f (ω + ω ) F (ω) F (ω ω )) + i sinω t Im(F (ω)f (ω + ω ) F (ω) F (ω ω ))] + Const δ2 4 g(2ω ) (3.7) 2ω g(2ω ) 250kHz δ 1 Mixer PD Mixer ϕ Mixer V Mixer = V V 0 sin(ω t + ϕ) δv 0 4i (e2iω t+iϕ e 2iω t iϕ 2i sinϕ)re(f (ω)f (ω + ω ) F (ω) F (ω ω )) iδv 0 4 (e2iω t+iϕ + e 2iω t iϕ 2 cosϕ)im(f (ω)f (ω + ω ) F (ω) F (ω ω ))] (3.8) 5MHz 2ω V lowpass δv 0 2 [sinϕ Re(F (ω)f (ω + ω ) F (ω) F (ω ω )) cosϕ Im(F (ω)f (ω + ω ) F (ω) F (ω ω ))] (3.9) ω ω F (ω)f (ω + ω ) F (ω) F (ω ω ) = ω [F (ω) F (ω + ω ) F (ω) + F (ω) F (ω) F (ω ω ) ] = ω d F ω ω (ω) 2 dω (3.10)
40 40 3 IFLD 3.9 V lowpass δv 0ω sinϕ 2 d dω F (ω) 2 (3.11) V 3.9 CH1 CH2 Rb CH3 PDH Rb F=2-F =1,2,3 PDH IFLD PZT Lock C Lock IFLD PZT Lock Lock 3.9 0
41 CH1 CH2 Rb CH3 PDH 87 Rb F=2-F =3 ( 3.9 ) Ch2 1 IFLD Rb IFLD
42 42 3 IFLD 3.11 Ramp 100Hz 10V EOM Mixer 15MHz 9.6V 5MHz m Rb Rb D2 85 Rb 87 Rb 2 Rb 85 Rb 87 Rb Rb Rb 85 Rb 87 Rb Rb GHz FSR IFLD FSR 2.3GHz 2.3GHz
43 IFLD Rb PD B IFLD PZT Rb D2 Rb D2 87 Rb F=2-F =1,2,3 85 Rb F=3-F =2,3,4 2GHz FSR 2.3GHz IFLD 3.4 IFLD 1 1 IFLD ECDL
44 44 3 IFLD IFLD ECDL IFLD ECDL V/1g g
45 V/1g 3.16 g 30 IFLD 0.05g 0.04g 0.06g
46 46 3 IFLD IFLD 1/2 IFLD ECDL ECDL IFLD 30 g y = 1 1 exp b(x u) +1 u IFLD ECDL MHz MHz Rb 6MHz MHz IFLD THz [22]
47 [23] IFLD B [22] 3.17 B B IFLD PZT IFLD ECDL B 3.18 B PD B PD [24] ν ν = πd2 < V 2 > B (3.12) [24] 0 < f < B Voltage Controlled Oscillator(VCO) <V 2 > B Acousto Optic Modulator(AOM) < e i(ϕ ϕ) > 3.12 D VCO f V B [24]
48 48 3 IFLD 3.12 <V 2 > B RP f RBW R = 50Ω P [W] f RBW D B F V B D PD B FSR B PZT f t B B B V t B f t V t t f = V f (3.13) B D ν = π[ f t ( V t ) 1 ] 2 RP (3.14) f RBW B FSR 1GHz B B PD B 0V B PD
49 B PD 3.17 B FSR 1.0GHz PD DC B AC PD B DC AC DC B AC DC AC 21 AC 47Ω 50Ω 3.14 P 2 2 A 3.14 A = ( 1 47[Ω] + 50[Ω] H) 2 (3.15) 21 50[Ω] H 200kHz-1MHz H H = 1.15 A A
50 50 3 IFLD 3.14 ν = π[ f t ( V t ) 1 ] 2 RP (3.16) f RBW B PZT B 3.18 t 3.18 PZT PZT [25] 2 PZT t B t 1+ t t 1 = 3.32ms t 2 = 3.76ms t t = t 1+ t 2 2 = (3.5 ± 0.2)ms B FSR 1.0GHz f = 1.0GHz B PZT f t f t = (2.8 ± 0.2) 1011 [Hz/s] V t V t 0V 3.19 ±0.02V 3.20 b = (4200 ± 200)V/s V B t V kHz 3.14 P P P P = ( ± 0.02)dBm = (1.042 ± 0.006) 10 8 W RBW 30kHz R = 50Ω IFLD
51 ν = (2.6 ± 0.4)kHz 3.18 B CH1 B CH2 PD B 2 PZT B 2 2 V = 0 t 1 t = t 1+ t 2 2 Beat 1 IFLD IFLD 1 IFLD ν = (14 ± 2)kHz IFLD 2 IFLD IFLD LD 1 IFLD 2 IFLD 1 IFLD <0.2 µa(10hz 10MHz) 2 IFLD <1.5 µa(10hz 10MHz) 2 1 3kHz
52 52 3 IFLD 3.19 B CH1 B CH2 PD B 2 ch2 0V 0V ±0.02V y=a+bx a = ± b = 4200 ± 100 Voltage [V] x x time [s] CH2 0V ±0.02V b V t
53 B 40 RBW 30kHz 200kHz-1MHz IFLD B CH1 B CH2 PD B t 1 = 3.56ms t 2 = 3.16ms B FSR 1GHz f t = (3.0 ± 0.2) 1011 Hz/s
54 54 3 IFLD IFLD B CH1 B CH2 PD B 2 ch2 0V 0V ±0.02V y=a+bx a = 0.57 ± 0.01 b = 3910 ± 90 Voltage [V] x x time [s] CH2 0V ±0.02V b V t
55 IFLD B 40 RBW 30kHz 400kHz-1MHz H = 1.08 P P = ( ± 0.03)dBm = (4.47 ± 0.02) 10 8 W
56 56 3 IFLD THz PD 1 E 1 (t) = E 1 e i(ω 1t+ϕ) (3.17) P (τ) P (τ) =< E(t) E(t + τ) > = E 2 1e iω 1τ < e i(ϕ ϕ) > (3.18) ϕ E(t + τ) <> 3.18 τ < e i(ϕ ϕ) > e τ τ 1 (3.19) P (τ) P (ω) P (ω) = + dτp (τ)e iωτ = E e i(ω 1 ω)τ τ τ 1 = 2 1 τ 1 (ω 1 ω) τ 2 1 (3.20) 2 τ 1 2 PD E(t) = E 1 (t) + E 2 (t) = E 1 e i(ω 1t+ϕ 1 ) + E 2 e i(ω 2t+ϕ 2 ) (3.21) PD PD PD V P D V P D (t) E 1 (t) + E 2 (t) 2 = const + 2E 1 E 2 cos[(ω 2 ω 1 )t + (ϕ 2 ϕ 1 )] (3.22)
57 PD V P D V P D(t) 2E 1 E 2 cos[(ω 2 ω 1 )t + (ϕ 2 ϕ 1 )] (3.23) V P D (t) < V P D(t) V P D(t + τ) > 4E 2 1E 2 2 < cos[(ω 2 ω 1 )t + (ϕ 2 ϕ 1 )] cos[(ω 2 ω 1 )(t + τ) + (ϕ 2 ϕ 1)] > = 2E 2 1E 2 2 < cos[(ω 2 ω 1 )(2t + τ) + (ϕ 2 ϕ 1 ) + (ϕ 2 ϕ 1)] + cos[(ω 2 ω 1 )τ + (ϕ 2 ϕ 1) (ϕ 2 ϕ 1 )] > (3.24) < cos[(ω 2 ω 1 )τ + (ϕ 2 ϕ 1) (ϕ 2 ϕ 1 )] > = 1 2 [ei(ω 2 ω 1 )τ < e i(ϕ 2 ϕ 2) e i(ϕ 1 ϕ 1) > + e i(ω 2 ω 1 )τ < e i(ϕ 2 ϕ 2) e i(ϕ 1 ϕ 1) >] (3.25) e i(ϕ 2 ϕ 2) e i(ϕ 1 ϕ 1) < e i(ϕ 2 ϕ 2) e i(ϕ 1 ϕ 1) > =< e i(ϕ 2 ϕ 2) >< e i(ϕ 1 ϕ 1) > = e τ τ 2 e τ τ 1 (3.26) < e i(ϕ 2 ϕ 2) e i(ϕ 1 ϕ 1) > =< e i(ϕ 2 ϕ 2) >< e i(ϕ 1 ϕ 1) > 3.24 = e τ τ 2 e τ τ 1 (3.27) < V P D(t) V P D(t + τ) > 2E 2 1E 2 2cos(ω 2 ω 1 )τ e ( 1 τ τ 2 ) τ (3.28) S(ω) S(ω) = + + dτ < V P D(t) V P D(t + τ) > e iωτ dτ(e i( ω ω)τ ( 1 τ τ 2 ) τ + e i( ω+ω)τ ( 1 τ τ 2 ) τ ) (3.29)
58 58 3 IFLD ω = ω 2 ω 1 2 ω > 0 S(ω) 2( 1 τ τ 2 ) ( ω ω) 2 + ( 1 τ τ 2 ) 2 (3.30) 2( 1 τ τ 2 ) PD Pseudo-Voigt fitting /f
59 Beat RBW 10kHz 40 [27] Voigt [18, 26, 27, 30] Pseudo-Voigt [28] Pseudo-Voigt Γ G Γ L Γ η 1 η f P V (x) = ηf L (x) + (1 η)f G (x) (3.31) Pseudo-Voigt f P V = y 0 + A[η( 2 πh ( x x ) + (1 η) 2 0 H/2 )2 H ln2 π exp( 4 ln2 (x x 0 H )2 )] (3.32) H H Γ y 0 A Pseudo-Voigt
60 60 3 IFLD 1.0 HL/H, HG/H blue HG/H=(K0+K1x+K2x^2+K3x^3)^0.5 K0 = 1 K1 = ± 0.02 K2 = ± 0.04 K3 = ± 0.03 red HL/H=K1x+K2x^2+K3x^3 K1 = 0.71 ± 0.02 K2 = 0.18 ± 0.04 K3 = 0.12 ± eta Voigt Pseudo-Voigt η Γ G Γ Γ L Γ η 3 H H G H L Γ Γ G Γ L Γ G Γ Γ L Γ 2 H A [29] Γ G Γ Γ L Γ η (1) Voigt (2) Pseudo-Voigt η Γ (3) Γ Γ G Γ Γ L Γ η (4) η 3.28 η η < 1 η 3 η = 0 Γ = Γ G η = 1 Γ = Γ L K0 Γ G Γ 1 Γ L Γ 0 Voigt Pseudo-Voigt η Γ Γ G Γ = (1 0.73η 0.19η2 0.08η 3 ) 1 2 Γ L Γ = 0.71η η η 3 (3.33)
61 Γ G Γ L Pseudo-Voigt 2 IFLD dbm W f beat = 10log[(y 0 + A[η( 2 πh ( x x ) + (1 η) 2 0 H/2 )2 H ln2 π exp( 4 ln2 (x x 0 H )2 )]) ] (3.34) dbm y 0 A 3.33 Γ G Γ L Γ G = (430 ± 6)kHz Γ L = (16.9 ± 0.9)kHz Γ G Γ L 1MHz IFLD Pseudo-Voigt η Pseudo-Voigt < e i(ϕ ϕ) > 2
62 62 3 IFLD dv(lor)=(16.9±0.9)khz dv(gauss)=(430±6)khz A = ± H = 439 ± 6 eta = ± x0 = ± 4 y0 = -4e-11 ± 2e-11 dbm Freq [khz] 35x Pseudo-Voight Beat Pseudo-Voight 3.34 A Pseudo-Voigt H Pseudo-Voigt IFLD IFLD IFLD 4 3
63 PD IFLD ECDL2 IFLD1 ECDL1 ECDL2 2 ECDL ECDL1 (120 ± 20)kHz ECDL2 (13 ± 1)kHz ECDL1 ECDL2 ECDL2 IFLD1 ECDL1 IFLD1 3 3 ECDL Pseudo-Voigt ν(ifld1) ν(ecdl1) ν(ecdl2) 3.33 ν(ifld1) + ν(ecdl1) = (128 ± 3)kHz (3.35) ν(ecdl1) + ν(ecdl2) = (142 ± 4)kHz (3.36) ν(ecdl2) + ν(ifld1) = (15.6 ± 0.6)kHz (3.37)
64 64 3 IFLD IFLD 1 ECDL2
65 IFLD1 ECDL1 ECDL2 3 3 ECDL1 ECDL2 ECDL2 IFLD ECDL1 IFLD IFLD1 ECDL1 ECDL2 IFLD1 ECDL1 (796 ± 5)kHz 128 ± 3kHz
66 66 3 IFLD IFLD1 ECDL1 ECDL2
67 IFLD IFLD IFLD < e i(ϕ ϕ) > < e i( ϕ) > (4.1) t t + τ ϕ g( ϕ) = 1 2π < ( ϕ)2 > e ( ϕ) 2 2<( ϕ) 2 > (4.2)
68 68 4 < e i( ϕ) > = + = e 1 2 <( ϕ)2 > g( ϕ) e i ϕ d( ϕ) (4.3) [32] 3 2 < ( ϕ) 2 > 0 0 [31] ν ν = πhν( ν c) 2 P (4.4) Schawlow-Townes Limit h ν ν c 4.5 P 4.4 ν c ν c = c 2πL ( ln T 2 R 1 R 2 ) (4.5) [32] c R 1 R 2 T 4.4 (1 + α 2 ) [30] ν = πhν( ν c) 2 (1 + α 2 ) (4.6) P (1 + α 2 ) α 2 α
69 [33] n = n r + in i n r n i n r n i α = n r n i (4.7) n i [33] g g = ( 2ω/c) n i n i n r IFLD ν = (2.6 ± 0.4)kHz P = 28mW IFLD ν = 385THz L = 64mm T = 0.83 R 1 = 1 R 2 = 0.3 LD 1 α = (16 ± 3) [30] α 8 IFLD [35] IFLD IFLD Cateye 4.1 IFLD L 2 IFLD 2 IFLD 4.6 ν 4.6 ν P 2 IFLD
70 I-P 130mm LD IFLD IFLD Cateye LD 2 Cateye D Cateye LD Thorlabs LT230P-B Cateye Cateye LD LD LD LD ϕ9.0mm 0.7mm ϕ9.65mm LD LD LD
71 4.2 I-P 71 LD mm LD 1.0mm LD 64mm z r z, r z = 59.5mm r = 1.0mm z = 196.5mm r = 3.5mm LD f = 4.5mm z, r θ θ tanθ = 3.5mm 1.0mm 196.5mm 59.5mm = 2.5 [rad] 1 [ ] (4.8) 137 r r = 2.5 (z[mm] 59.5mm) + 1.0mm (4.9) z = 0 LD r 0.1mm 130mm Cateye z = 107.1mm
72 mm LD 3.5mm LD 201mm r 1.9mm Cateye 5.5mm LD 3mm LD Cateye Cateye Thorlabs C280TMD-B ϕ5.5mm f18.4mm Thorlabs AL2520M-B ϕ20.4mm f20.0mm 154mm Cateye ϕ20.4mm f20.0mm
73 4.2 I-P z LD 4.5mm 4.5 LD r = 0 r = 0, z = 0 LD LD
74 mW IFLD L = 154mm 4.9 L = 154mm L = 154mm Q Q 4.5 ν c Q ν c 4.6 L = 154mm ν c
75 4.2 I-P IFLD y = AL x L = 154mm x = ( 2.1 ± 0.4) L = 154mm LD LD LD LD L = 154mm Cateye L = 180mm IFLD L = 137mm 900Hz
76 y = AL x L = 154mm x = ( 2.1 ± 0.3) 4.9 L = 154mm
77 IFLD 64mm 4.10 LD 4.10
78
79 79 5 IFLD IFLD ECDL 3 IFLD ECDL 8 IFLD ECDL IFLD IFLD IFLD 900Hz IFLD IFLD
80
81 81 A LD A.1 LD
82
83 83 B PD B.1
84
85 85 C C.1 (LM399H) -6.95V
86
87 87 D IFLD IFLD IFLD D.1 IFLD Thorlabs
88 88 D IFLD D.2 IFLD Z-MAX ( RS ) Thorlabs 75mm
89 89 Cateye D.3 Cateye Thorlabs PSM30-15C /800 PZT 15mm 14mm 10mm Working distance 18.4mm Working distance 15.6mm 2.8mm 20.1mm 20.1mm 2.8mm = 17.3mm
90 90 D IFLD Cateye D.4 Cateye IFLD 6.3mm,2.9mm Cateye D.5 Cateye M9 M9 18.4mm Working distance 15.6mm ϕ5.5mm
91 91 S1TM09 D.6 S1TM09 PZT D.7 PZT TorrSeal
92 92 D IFLD PZT D.8 D.9 PZT Cateye
93 93 SM1C6 D.10 SM1C6
94 94 D IFLD D.11 A2017
95 95 D.12 ϕ20mm 8mm D.13 A2017
96 96 D IFLD A2017
97 97 D.14 Thorlabs Laseroptik 2.1 TorrSeal
98 98 D IFLD D.15 A2017 SM1C6
99 99 D.16 A2017 TorrSeal
100 100 D IFLD IFLD D.17 IFLD IFLD TAKACHI BDN mm 140mm 70mm
101 101 D.18
102 102 D IFLD D.19 WBMA-25C /1000 AR AR 780nm 0.5 LD
103 103 D.20 A2017
104 104 D IFLD D.21 A2017
105 105 D.22 D.23 IFLD
106 106 D IFLD LD D.24 LD LD LD LD interlock
107 D.25 IFLD 2.1 D.26
108
109 109 [1] A. Einstein, Quantentheorie des einatomigen idealen gases. zweite abhandlung, Sitzungsber. K. Preuss. Akad. Wiss., Phys. Math. kl. 3 (1925) [2] P. Kapitza, Viscosity of Liquid Helium below the λ-point, Nature, 141, 74 (1938) [3] F. London, The λ-phenomenon of Liquid Helium and the Bose- Einstein Degeneracy, Nature, 141, 643 (1938) [4] T. H. Maiman, Stimulated Optical Radiation in Ruby, Nature, 187, (1960) [5] T. W. Hänsch and A. L. Schawlow, Cooling of gases by laser radiation Opt. Commun. 13, (1975) [6] S. Chu, et al. Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure, Phys. Rev. Lett 55, 48, (1985) [7] E. L. Raab, et al. Trapping of Neutral Sodium Atoms with Radiation Pressure, Phys. Rev. Lett. 59, (1987) [8] M. H. Anderson, et al. Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor, Science, 269, (1995) [9] K. B. Davis, et al., Bose-Einstein Condensation in a Gas of Sodium Atoms, Phys. Rev. Lett. 75, (1995) [10] C. C. Bradley, et al., Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions, Phys. Rev. Lett. 75, 1687 (1995) [11] S. Stellmer, et al., Bose-Einstein Condensation of Strontium, Phys. Rev. Lett. 103, (2009) [12] Y. Takasu, et al., Spin-Singlet Bose-Einstein Condensation of Two- Electron Atoms, Phys. Rev. Lett. 91, (2003) [13] S. Inouye, et al., Observation of Feshbach resonances in a Bose-Einstein condensate, Nature, 392, , (1998) [14] C. A. Regal, et al., Observation of Resonance Condensation of Fermionic Atom Pairs, Phys. Rev. Lett. 92, (2004) [15] M. Greiner, et al., Quantum phase transition from a superfluid to a Mott
110 110 insulator in a gas of ultracold atoms, Nature, 415, (2002) [16] C. E. Wieman, Using diode lasers for atomic physics, Rev. Sci. Instrum. 62, 1 (1991) [17] M. G. Littman and H. J. Metcalf, Spectrally narrow pulsed dye laser without beam expander, Appl. Optics. 17, 2224 (1978) [18] X. Baillard, et al., Interfernce-filter-stabilized externalcavity diode lasers, Opt. Commun. 266, (2006) [19] Preparation of ultracold atomic sources towards ground state polar molecules, (2008) [20] All-optical selective formation of ultracold molecules in the rovibrational ground state, (2011) [21] E. D. Black, An introduction to Pound-Drever- Hall laser frequency stabilization, Am. J. Phys. 69, 79 (2001) [22] Qian Lin, et al., Long-external-cavity distributed Bragg reflector laser with subkilohertz intrinsic linewidth Opt. Lett. 37, (2012) [23] Yb, (2014) [24] D. S. Elliott, et al., Extracavity laser band-shape and bandwidth modification, Phys. Rev. A (1982) [25], < images/product/application/ceramics handbook.pdf> [26] M. Gilowski, et al. Narrow bandwidth interference filterstabilized diode laser system for the manipulation of neutral atoms, Opt. Commun. 280, (2007) [27] Shayne Bennetts, et al., External cavity diode lasers with 5kHz linewidth and 200nm tuning range at 1.55um and methods for linewidth measurement, Opt. Express 22, (2014) [28] T. Ida, et al., Extended pseudo-voigt function for approximating the Voigt profile, J. Appl. Cryst. 33, (2000) [29] J. B. HASTINGS, et al., Synchrotron X-ray Powder Diffraction, J. Appl. Cryst. 17, 85 (1984) [30] Sebastian D. Saliba and Robert E. Scholten, Linewidths below 100kHz with external cavity diode lasers, Appl. Opt. 48, (2009)
111 [31] A. L. Shawlow and C. H. Townes, Infrared and Optical Masers, Phys. Rev. 112, (1958) [32] A. Yariv, QUANTUM ELECTRONICS THIRD EDITION, John Willey & Sons (1989) [33] C. H. Henry, Theory of the Linewidth of Semiconductor Lasers, IEEE J. Quantum Electron. 18, (1982) [34] D. Welford, and, A. Mooradian, Output power and temperature dependence of the linewidth of single-frequency cw (GaAl)As diode lasers, Appl. Phys. Lett. 40, 865 (1982) [35] C. Harder, et al., Measurement of the linewidth enhancement factor α of semiconductor lasers, Appl. Phys. Lett. 42, 328 (1983) 111
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ETL NEWS 1999.9 ETL NEWS 1999.11 Establishment of an Evaluation Technique for Laser Pulse Timing Fluctuations Optoelectronics Division Hidemi Tsuchida e-mail:tsuchida@etl.go.jp A new technique has been
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2 Light Source Technologies 2-1 Fourier Synthesis of Optical Pulses HYODO Masaharu, Kazi Sarwar ABEDIN, ONODERA Noriaki, and WATANABE Masayoshi With the rapid progress made recently in the field of optical
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