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230

4.3.3 Individual scattering processes

[Ref. p. 232

 

 

 

Table 4.3.4. Stimulated Rayleigh scattering: gain factors and linewidth values.

Medium

Gain factor

 

gRLe

 

[cm/MW]

Gain coe cient

Linewidth

Reference

gRLa (max.)/α

δν

 

[cm2/MW]

[MHz]

 

Acetone

2

0.47

21

[70Rot]

Benzene

2.2

0.57

24

[70Rot]

Carbondisulfide

6

0.62

36

[70Rot]

Ethanol

 

0.38

18

[70Rot]

Methanol

8.4

0.32

20

[70Rot]

Tetrachloromethane

2.6 × 10−4

0.82

17

[70Rot]

Water

0.02

0.019

27.5

[70Rot]

Here ΓRL = π δν is the halfwidth (HWHM) of the spontaneous Rayleigh line in circular frequency units that originates from the damping of entropy changes via thermal conductivity Λ :

ΓRL =

4 kL2

Λ sin2 (θ/2)

(4.3.20)

 

 

.

 

 

 

 

ρo Cp

 

Via ΓRL the gain constant gRLa strongly depends on scattering angle. The frequency dependencies of SRLS and STRS have opposite sign, leading to the total gain factor:

g(ωS) =

(gBe − gBa ) 2 ΓRL(ωL − ωS)

.

(4.3.21)

 

(ωL − ωS)2 + ΓRL2

 

For dominant coupling via electrostriction positive gain occurs on the Stokes side, ωS < ωL . Small absorption values, α > 10−3 cm−1 , can be su cient for dominant STRS that produces gain on the anti-Stokes side. For zero frequency shift, ωS = ωL, the gain factor vanishes in the steady state, (4.3.21), but not in the transient case. Stimulated scattering in forward scattering is particularly delicate since ΓRL → 0, (4.3.20), and Stokes–anti-Stokes coupling has to be included. Values for g and δν are listed in Table 4.3.4.

3. Stimulated Rayleigh wing scattering is connected with the overdamped rotational motion of liquid molecules in combination with an anisotropic polarizability tensor. The latter is also involved in the optical Kerr e ect enhancing the nonlinear refractive index of the medium (optical selffocusing, self-phase modulation). The maximum steady-state gain factor for SRWS is given by:

gRW =

16 π2 N ωS (α − α )2

.

(4.3.22)

 

45 kB To c2 nS2

 

The di erence of the molecular polarizability parallel and perpendicular to the (assumed) molecular axis of rotational symmetry is denoted by α − α . kB is the Boltzmann constant, To the sample temperature. The frequency dependence of the gain factor is analogous to the previous cases:

g(ωS) =

gRW 2 ΓRW (ωL − ωS)

.

(4.3.23)

 

(ωL − ωS)2 + ΓRW2

 

Maximum gain of SRWS occurs for ωS = ωL − ΓRW . The halfwidth ΓRW of the Rayleigh wing line may be taken from spontaneous scattering observations or from the reorientational time τor . The latter can be derived from spontaneous Raman spectroscopy, NMR, or time-resolved spectroscopy, e.g. transient optical Kerr e ect observations: τor = T2,RW = 1/ΓRW . An estimate of the halfwidth may be computed from shear viscosity and the size of the molecules using the Debye theory:

ΓRW =

3 kB To

.

(4.3.24)

 

 

8 π R η S

 

Landolt-B¨ornstein

New Series VIII/1A1

Ref. p. 232]

4.3 Stimulated scattering

231

 

 

 

Here R denotes an e ective mean radius of the molecule. The proportionality ΓRW η S was demonstrated experimentally for numerous examples.

Equations (4.3.6), (4.3.22), and (4.3.23) hold for large scattering angles where Stokes–anti- Stokes coupling can be neglected. Close to forward direction simultaneous anti-Stokes scattering enhances the stimulated Stokes scattering, in contrast to SRS. Including the Stokes–anti-Stokes coupling maximum gain is predicted for an optimum scattering angle

1

θopt =

2 gRW IL c

2

 

nL ωL

.

(4.3.25)

The corresponding gain factor for stimulated amplification in the scattering direction θopt without frequency shift, ωS = ωA = ωL , amounts to:

gopt = 2 gRW ,

(4.3.26)

where gRW is given by (4.3.22). For more general cases the reader is referred to the literature, e.g. [72Mai]. Frequency shift and gain factor numbers are compiled in Table 4.3.5.

Table 4.3.5. Frequency shift and gain factor of stimulated Rayleigh wing scattering.

Medium

Frequency shift × c−1

Gain factor GRW

Reference

 

[cm−1]

[1012 m/W]

 

Azoxybenzene

0.036

 

[68Fol]

Benzene

 

6

[72Mai]

Benzonitrol

0.198

 

[68Fol]

Benzoylchloride

0.184

 

[68Fol]

Benzylidenaniline

0.065

 

[68Fol]

Bromobenzene

 

14

[72Mai]

1-Bromonaphthalene

0.076

 

[68Fol]

Carbondisulfide

 

30

[72Mai]

Chlorobenzene

 

10

[72Mai]

Chloronaphthalene

0.100

 

[68Fol]

1,4-Dimethylnitrobenzene

0.090

 

[68Fol]

m-Dinitrobenzene

0.116

 

[68Fol]

2,4-Dinitrotoluene

0.098

 

[68Fol]

Naphthalene

0.5

 

[68Fol]

Nitroacetophenone

0.105

 

[68Fol]

o-Nitroaniline

0.107

 

[68Fol]

p-Nitroanisol

0.075

 

[68Fol]

Nitrobenzaldehyde

0.101

 

[68Fol]

Nitrobenzene

0.111

76

[72Mai]

o-Nitrophenol

0.078

 

[68Fol]

m-Nitrotoluene

0.097

 

[68Fol]

o-Nitrotoluene

0.133

 

[68Fol]

p-Nitrotoluene

0.145

 

[68Fol]

Styrene

0.4

 

[68Fol]

Toluene

 

20

[72Mai]

 

 

 

 

Landolt-B¨ornstein

New Series VIII/1A1

232

References for 4.3

 

 

References for 4.3

31Goe

G¨oppert-Mayer, M.: Ann. Phys. (Leipzig) 9 (1931) 273.

62Eck

Eckhardt, G., Hellwarth, R.W., McClung, F.J., Schwarz, S.E., Weiner, D., Woodbury,

 

E.J.: Phys. Rev. Lett. 9 (1962) 455.

62Woo

Woodbury, E.J., Ng, W.K.: Proc. IRE 50 (1962) 2367.

66Bar

Barret, J.J., Tobin, M.C.: J. Opt. Soc. Am. 56 (1966) 129.

66Eck

Eckhardt, G.: IEEE J. Quantum Electron. 2 (1966) 1.

67Blo

Bloembergen, N.: Am. J. Phys. 35 (1967) 989.

67Sha

Shapiro, S.L., Giordmaine, J.A., Wecht, K.W.: Phys. Rev. Lett. 19 (1967) 1093.

67Wig

Wiggins, T.A., Wick, R.V., Foltz, N.D., Cho, C.W., Rank, D.H.: J. Opt. Soc. Am. 57

 

(1967) 661.

68Bre

Bret, C.G., Weber, H.P.: IEEE J. Quantum Electron. 4 (1968) 807.

68Den

Denariez, M., Bret, G.: C. R. Acad Sci. (Paris) 265 (1968) 144.

68Fol

Foltz, N.D., Cho, C.W., Rank, D.H., Wiggins, T.A.: Phys. Rev. 165 (1968) 396.

69Col

Colles, M.J.: Opt. Commun. 1 (1969) 169.

69Rah

Rahn, O., Maier, M., Kaiser, W.: Opt. Commun. 1 (1969) 109.

70Alf

Alfano, R.R., Shapiro, S.L.: Phys. Rev. A 2 (1970) 2376.

70Mac

Mack, M.E., Carman, R.L., Reintjes, J., Bloombergen, N.: Appl. Phys. Lett. 16 (1970)

 

209.

70Poh

Pohl, D., Kaiser, W.: Phys. Rev. B 4 (1970) 31.

70Rot

Rother, W.: Z. Naturforsch. A 25 (1970) 1120.

71Lau

Laubereau, A., von der Linde, D., Kaiser, W.: Phys. Rev. Lett 27 (1971) 802.

71Lin

von der Linde, D., Laubereau, A., Kaiser, W.: Phys. Rev. Lett. 26 (1971) 954.

72Car

Carman, R.L., Mack, M.E.: Phys. Rev. A 5 (1972) 341.

72Lau

Laubereau, A., von der Linde, D., Kaiser, W.: Phys. Rev. Lett. 28 (1972) 1162.

72Mai

Maier, M. Kaiser, W., in: Laser Handbook, Arecchi, F.T., Schulz-Dubois, E.O. (eds.),

 

Vol. 2, Amsterdam: North Holland, 1972, p. 1077.

73Lau

Laubereau, A., von der Linde, D., Kaiser, W.: Opt. Commun. 1 (1973) 173.

74Lau

Laubereau, A.: Chem. Phys. Lett. 27 (1974) 600.

75Cha

Chatelet, M., Ogsengorn, B.: Chem. Phys. Lett. 36 (1975) 73.

75Lau

Laubereau, A.: Unpublished data, 1975.

76Ber

Berne, B.J., Pecora, R.: Dynamic light scattering, New York: Wiley, 1976, Chap. 10.5.

76Mai

Maier, M.: Appl. Phys. 11 (1976) 209.

77Rys

Rysakov, V.M., Korotkov, V.I.: Sov. J. Quantum Electron. (English Transl.) 7 (1977)

 

83.

Landolt-B¨ornstein

New Series VIII/1A1

 

References for 4.3

233

 

 

 

78Lau

Laubereau, A., Kaiser, W.: Rev. Mod. Phys. 50 (1978) 3607.

 

78Map

Maple, J.R., Knudtson, J.T.: Chem. Phys. Lett. 56 (1978) 241.

 

79Pen

Penzkofer, A., Laubereau, A., Kaiser, W.: Prog. Quantum Electron. 6 (1979) 55.

 

83Sap

Sapondzhyan, S.O., Sarkisyan, D.G.: Sov. J. Quantum Electron. (English Transl.) 13

 

(1983) 1062.

 

83Tel

Telle, H.R., Laubereau, A.: Chem. Phys. Lett. 94 (1983) 467.

 

84Har

Harris, A.L., Berg, M., Brown, J.K., Harris, C.B., in: Ultrafast phenomena IV, Auston,

 

D.H., Eisenthal, K.B. (eds.), Springer Ser. Chem. Phys., Vol. 38, Berlin, Heidelberg,

 

New York, Tokyo: Springer-Verlag, 1984.

 

84Kru

Kruminsh, A.V., Nikogosyan, D.N., Oraevsky, A.A.: Sov. J. Quantum Electron. (English

 

Transl.) 11 (1984) 1479.

 

86Han

Hanna, D.C., Pointer, D.J., Pratt, D.J.: IEEE J. Quantum Electron. 22 (1986) 332.

87Glo

Glownia, J.H., Misewich, J., Sorokin, P.P.: Opt. Lett. 12 (1987) 19.

 

89Agr

Agrawal, G.P.: Nonlinear fiber optics, Boston: Academic, 1989.

 

90Lai

Lai, K.K., Sch¨usslbauer, W., Amler, H., Bogner, U., Maier, M., Jordan, M., Jodl, H.J.:

 

Phys. Rev. B 42 (1990) 5834.

 

93Fil

Filippo, A.A., Perrone, M.R.: Appl. Phys. B 57 (1993) 103.

 

94Yos

Yoshizawa, M., Hattori, Y., Kobayashi, T.: Phys. Rev. B 49 (1994) 13259.

 

95Go

Go, C.S., Lee, J.H., Chang, J.S.: Appl. Opt. 34 (1995) 2671.

 

95Lim

Limaye, R., Sen, P.K.: Phys. Rev. B 51 (1995) 1546.

 

97Bai

Bairamov, B.H., Aydinli, A., Bodnar, I.V., Rud, Yu.V., Nogoduyko, V.K., Toporov,

 

V.V.: Inst. Phys. Conf. Ser. No. 155, Bristol: IOP, 1997, p. 993.

 

97Jo

Jo, M.S., Nam, C.H.: Appl. Opt. 36 (1997) 1149.

 

97Kam1

Kaminskii, A.A., Butashin, A.V., Eichler, H.-J., Grebe, D., MacDonald, R., Ueda, K.,

 

Nishioka, H., Odajima, W., Tateno, M., Song, J., Musha, M., Bagaev, S.N., Pavlyuk,

 

A.A.: Opt. Mater. 7 (1997) 59.

 

97Kam2

Kaminskii, A.A., Eichler, H.-J., Grebe, D., MacDonald, R., Butashin, A.V.: Phys. Status

 

Solidi (b) 199 (1997) R3.

 

97Kam3

Kaminskii, A.A., Hulliger, J., Eichler, H.-J., Findeisen, J., Butashin, A.V., MacDonald,

 

R., Bagaev, S.N.: Phys. Status Solidi (b) 203 (1997) R9.

 

97Yos

Yoshida, H., Kmetik, V., Fujita, H., Nakatsuka, M., Yamanaka, T., Yoshida, K.: Appl.

 

Opt. 36 (1997) 3739.

 

Landolt-B¨ornstein

New Series VIII/1A1

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