4/8 No. 2

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1 4/8 No. 1

2 4/8 No. 2

3 Laser-related Nobel laureates Townes, Basov, Prokhorov (1964-Physics): レーザーの開発 Gabor(1971-Physics) : ホログラフィーの発明と開発 Bloembergen, Schawlow (1981-Physics): レーザー分光 Kroto, Curl, Smalley (1996-Chemistry): フラーレンの合成 Chu, Cohen-Tannoudji, Phillips (1997-Physics): レーザー光を用いた原子の冷却とトラップ Zewail(1999-Chemistry): フェムト秒化学 Wieman, Ketterle, Cornell (2001-Physics): アルカリ元素のボーズアインシュタイン凝縮 Tanaka( 田中耕一 ), Fenn (2002-Chemistry): 生体分子の質量分析のためのイオン化法 Glauber (2005-Physics): 量子光学 Hall, Hänsch (2005 年 -Physics): レーザーによる精密分光学 ( 光周波数コム技術 ) Kao (2009-Physics): optical fiber Haroche, Wineland (2012 Physics) cavity QED Laser is omnipresent from basic science to our daily life. 4/8 No. 3

4 4/8 No. 4

5 4/8 No. 5

6 Advanced Plasma and Laser Science (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo) Monochromaticity 単色性 Laser light has a single frequency or wavelength (pure color). 各種のレーザー光はそれぞれある特定の波長のみを含みその波長は時間的に一定である 4/8 No. 6

7 4/8 No. 7

8 Atom Energy level Bohr s condition hν light absorption spontaneous emission stimulated emission E 2 E 1 ν hν = E 2 E 1 frequency h = J s Planck constant Emission of light (photon) upon transition to a lower level Spontaneous emission happens without an incident light Stimulated emission emits a photon induced by the incident light 4/8 No. 8

9 Before After spontaneous" emission photon stimulated" emission photon 2 photons (stimulated)" absorption photon 4/8 No. 9

10 Light Amplification by Stimulated Emission of Radiation highly directional, high-intensity, very pure wavelength by spontaneous emission diverse direction and wavelength, low-intensity 4/8 No. 10

11 Unique properties of a laser Directionality & monochromacity Polarization E = E e ik x iωt+iφ 0 Frequency (wavelength) Phase Direction Laser is an ideal classical electromagnetic wave! 4/8 No. 11

12 Laser wavelength region 4/8 No. 12

13 Argon ion/ 488/514 nm CW/ Krypton ion/ 531/568/647 nm CW/ He-Ne/ 633 nm CW/ CO µm CW or pulse/ Dye/ 450 nm 900 nm CW or pulse/ Diode/ 650 nm 900 nm CW or pulse/ Ruby/ 694 nm µs Nd:YLF 1053 nm 100 ns 250 µs Nd:YAG 1064 nm 100 ns 250 µs Ho:YAG 2120 nm 100 ns 250 µs Ho:YSGG 2780 nm 100 ns 250 µs Er:YAG 2940 nm 100 ns 250 µs Alexandrite/ 720 nm µs XeCl 308 nm ns XeF エキシマ 351 nm ns KrF レーザー 248 nm ns ArF 193 nm ns Nd:YLF 1053 nm ps Nd:YAG 1064 nm ps Ti:Sapphire/ 700 nm 1000 nm 5 fs 100 ps Short pulse laser Continuous wave laser (CW) Pulse laser Ultrashort pulse laser 4/8 No. 13

14 参考書 (Reference):W. T. Silfvast, Laser Fundamentals 4/8 No. 14

15 Advanced Plasma and Laser Science (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo) Einstein A and B coeﬃcients (1916) アインシュタインのA, B係数の理論(1916年) Temporal evolution of population density N1 and N2 占位数密度N1, N2の時間変化 spontaneous" absorption emission Thermal equilibrium (T) 熱平衡状態温度 T stimulated" emission incident light" ω A 入射光 BW 12 Boltzmann distribution ボルツマン分布 E2,N2 自然放出吸収 W BW 21 誘導放出 E1,N1 Planck s law for cavity radiation" プランクの黒体放射の法則 4/8 No. 15

16 Advanced Plasma and Laser Science (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo) Cavity (black body) radiation 4/8 No. 16

17 4/8 No. 17

18 dz I(z) I(z+dz) di dz = B(N 2 N 1 ) c I S Gain coefficient g = B(N 2 N 1 ) c Extended Lambert-Beer law I(z) =I 0 e gz = I 0 e (N 2 N 1 )z = B c 4/8 No. 18

19 Stimulated emission cross section for a variety of lasers Laser λ(nm) σ(m -2 ) He-Ne Argon He-Cd Copper (CVL) CO 2 10, Excimer Dye (Rh6G) Semiconductor Nd:YAG Nd:Glass Ti:Sapphire Cr:LiSrAlF /8 No. 19

20 I(z) >I 0 for z>0 N 2 >N 1 a necessary condition Stimulated emission > absorption At thermal equilibrium N 2 = N 1 exp ω /k B T [ ] << N 1 Energy E 2 E 1 N 2 thermal" equilibrium N 1 Energy E 2 population" inversion e E kt e E kt E 1 N 1 N 2 Population density Population density 4/8 No. 20

21 Solid, liquid, gas Plasma Free electron Pumping energy source is necessary. Flash lump LED Gas discharge Electric current Chemical reaction Another laser, R 1 R 2 Oscillator (resonator) Gain medium Pump Laser light 4/8 No. 21

22 pump Γ spontaneous" emission N 2 A = N 2 stimulated" emission N 2 N 2 B I c steady state N 1 dn 2 dt = N BI c =0 N 2 = 1 + BI c 4/8 No. 22

23 I sat = c B = = B c sufficient condition saturation length gl sat = (N 2 N 1 )L sat = 12 ± 5 e gl sat /8 No. 23

24 gl sat = (N 2 N 1 )L sat = 12 ± 5 g =0.15 m 1 L sat 80 m! one path L =0.2m e gl = 1.03 amplification by one path is small in general L sat L 400 paths is necessary 4/8 No. 24

25 R 1 R 2 The gain medium is put in a cavity (resonator) with two flat mirrors for lasing. Oscillator (resonator) Gain medium Pumping Laser light Amplifier Feedback amplifier βi o I i I o I i I o ( 1 β)i o I o = AI i I o = A 1 Aβ I i Aβ <1 4/8 No. 25

26 I i Advanced Plasma and Laser Science (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo) Feedback amplifier R 1 R 2 Oscillator (resonator) Gain medium I o Pumping βi o ( 1 β)i o Laser light I o = Aβ =1 A 1 Aβ I i Infinite amplication Lasing condition exp[2(g a)l]r 1 R 2 =1 A β g =(N 2 N 1 ) Necessary population inversion N 2 N 1 = a ln R 1R 2 2L 4/8 No. 26

27 Laser g (m -1 ) L (m) m He-Ne Argon He-Cd Copper (CVL) CO Excimer Dye (Rh6G) GaAs 100, Nd:YAG Nd:glass /8 No. 27

28 R 1 R 2 Gain medium Laser light Oscillator (resonator) Pumping energy source 4/8 No. 28

Advanced Laser and Photon Science (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo) Laser : the greatest invention of the 20th century レーザー 20

4/5 No. 1 Advanced Laser and Photon Science (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo) Laser : the greatest invention of the 20th century レーザー 20世紀最大の発明 Industrial and medical application