Abstract

The intensity of two-photon-excited fluorescence measured relative to the intensity of hyper-Rayleigh scattering in the same apparatus was used to determine the two-photon-excited fluorescence cross sections of the xanthene dyes Rhodamine B, Rhodamine 6G, and Fluorescein. The measured cross sections at λ0=1064 nm are σ2PF(2)=1.5±0.3×10-50 cm4 s, 2.0±0.4×10-50 cm4 s, and 1.4±0.3×10-52 cm4 s, for the three dyes, respectively. The two-photon-excited fluorescence cross section of Rhodamine B was also calibrated with one-photon-excited fluorescence in this apparatus. The result, σ2PF(2)=2.3±0.7×10-50 cm4 s, is in reasonable agreement with the result calibrated by hyper-Rayleigh scattering. The results for Rhodamine B are 1.5–6 times smaller than previous results calibrated by one-photon-excited fluorescence.

© 1999 Optical Society of America

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    [CrossRef]
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    [CrossRef]

1998 (2)

P. Kaatz, E. A. Donley, and D. P. Shelton, “A comparison of molecular hyperpolarizabilities from gas and liquid phase measurements,” J. Chem. Phys. 108, 849–856 (1998).
[CrossRef]

D. A. Haner, B. T. McGuckin, R. T. Menzies, C. T. Bruegge, and V. Duval, “Directional–hemispherical reflectance for spectralon by integration of its bidirectional reflectance,” Appl. Opt. 37, 3996–3999 (1998).
[CrossRef]

1997 (4)

P. Norman, Y. Luo, D. Jonsson, H. Ågren, K. O. Sylvester-Hvid, and K. V. Mikkelsen, “Hyperpolarizability depolarization ratios of nitroanilines,” J. Chem. Phys. 107, 9063–9066 (1997).
[CrossRef]

I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14, 2268–2294 (1997).
[CrossRef]

S. Marou, O. Nakamura, and S. Kawata, “Three-dimensional microfabrication with two-photon-absorbed photopolymerization,” Opt. Lett. 22, 132–134 (1997).
[CrossRef]

C. Xu, J. B. Shear, and W. W. Webb, “Hyper-Rayleigh and hyper-Raman scattering background of liquid water in two-photon excited fluorescence detection,” Anal. Chem. 69, 1285–1287 (1997).
[CrossRef] [PubMed]

1996 (4)

P. Kaatz and D. P. Shelton, “Polarized hyper-Rayleigh light scattering measurements of nonlinear optical chromophores,” J. Chem. Phys. 105, 3918–3929 (1996).
[CrossRef]

P. Kaatz and D. P. Shelton, “Spectral measurements of hyper-Rayleigh light scattering,” Rev. Sci. Instrum. 67, 1438–1444 (1996).
[CrossRef]

C. Xu and W. W. Webb, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm,” J. Opt. Soc. Am. B 13, 481–491 (1996).
[CrossRef]

R. J. Bartlett and H. Sekino, “Can quantum chemistry provide reliable molecular hyperpolarizabilities?” in Nonlinear Optical Materials: Theory and Modeling, S. P. Kama and A. T. Yeates, eds., ACS Symp. Ser. 628, 23–57 (1996).
[CrossRef]

1995 (3)

1994 (2)

D. P. Shelton and J. E. Rice, “Measurements and calculations of the hyperpolarizabilities of atoms and small molecules in the gas phase,” Chem. Rev. 94, 3–29 (1994).
[CrossRef]

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

1992 (1)

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

1991 (1)

D. M. Bishop and J. Pipin, “Calculated Raman overtone intensities for H2 and D2,” J. Chem. Phys. 94, 6073–6080 (1991).
[CrossRef]

1990 (3)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

D. P. Shelton, “Raman overtone intensities measured for H2,” J. Chem. Phys. 93, 1491–1495 (1990).
[CrossRef]

D. P. Shelton, “Nonlinear-optical susceptibilities of gases measured at 1064 and 1319 nm,” Phys. Rev. A 42, 2578–2592 (1990).
[CrossRef] [PubMed]

1989 (1)

D. M. Bishop and J. Pipin, “Improved dynamic hyperpolarizabilities and field-gradient polarizabilities for helium,” J. Chem. Phys. 91, 3549–3551 (1989).
[CrossRef]

1986 (1)

P. Sperber and A. Penzkofer, “S0-Sn two-photon absorption dynamics of rhodamine dyes,” Opt. Quantum Electron. 18, 381–401 (1986).
[CrossRef]

1982 (1)

S. Li and C. Y. She, “Two-photon absorption cross-section measurements in common laser dyes at 1064 μm,” Opt. Acta 29, 281–287 (1982).
[CrossRef]

1981 (1)

I. M. Catalano and A. Cingolani, “Absolute two-photon fluorescence with low-power lasers,” Appl. Phys. Lett. 38, 745–747 (1981).
[CrossRef]

1973 (1)

N. N. Vsevolodov, L. P. Kostikov, L. P. Kayushin, and V. I. Gorbatenkov, “Two-photon absorption of laser radiation by chlorophyll-a and certain organic dyes,” Biophysics (GB) 18, 807 (1973).

1972 (3)

D. J. Bradley, M. H. R. Hutchinson, and H. Koetser, “Interactions of picosecond laser pulses with organic molecules. II. Two-photon absorption cross sections,” Proc. R. Soc. London, Ser. A 329, 105–119 (1972).
[CrossRef]

J. P. Hermann and J. Ducuing, “Dispersion of the two-photon cross section in rhodamine dyes,” Opt. Commun. 6, 101–105 (1972).
[CrossRef]

J. P. Hermann and J. Ducuing, “Absolute measurement of two-photon cross sections,” Phys. Rev. A 5, 2557–2568 (1972).
[CrossRef]

1966 (1)

R. Bersohn, Y. H. Pao, and H. L. Frisch, “Double-quantum light scattering by molecules,” J. Chem. Phys. 45, 3184–3198 (1966).
[CrossRef]

Ågren, H.

P. Norman, Y. Luo, D. Jonsson, H. Ågren, K. O. Sylvester-Hvid, and K. V. Mikkelsen, “Hyperpolarizability depolarization ratios of nitroanilines,” J. Chem. Phys. 107, 9063–9066 (1997).
[CrossRef]

Bartlett, R. J.

R. J. Bartlett and H. Sekino, “Can quantum chemistry provide reliable molecular hyperpolarizabilities?” in Nonlinear Optical Materials: Theory and Modeling, S. P. Kama and A. T. Yeates, eds., ACS Symp. Ser. 628, 23–57 (1996).
[CrossRef]

Bersohn, R.

R. Bersohn, Y. H. Pao, and H. L. Frisch, “Double-quantum light scattering by molecules,” J. Chem. Phys. 45, 3184–3198 (1966).
[CrossRef]

Bhatt, J. C.

Bishop, D. M.

D. M. Bishop and J. Pipin, “Calculated Raman overtone intensities for H2 and D2,” J. Chem. Phys. 94, 6073–6080 (1991).
[CrossRef]

D. M. Bishop and J. Pipin, “Improved dynamic hyperpolarizabilities and field-gradient polarizabilities for helium,” J. Chem. Phys. 91, 3549–3551 (1989).
[CrossRef]

Bradley, D. J.

D. J. Bradley, M. H. R. Hutchinson, and H. Koetser, “Interactions of picosecond laser pulses with organic molecules. II. Two-photon absorption cross sections,” Proc. R. Soc. London, Ser. A 329, 105–119 (1972).
[CrossRef]

Bruegge, C. T.

Catalano, I. M.

I. M. Catalano and A. Cingolani, “Absolute two-photon fluorescence with low-power lasers,” Appl. Phys. Lett. 38, 745–747 (1981).
[CrossRef]

Cha, M.

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

Cingolani, A.

I. M. Catalano and A. Cingolani, “Absolute two-photon fluorescence with low-power lasers,” Appl. Phys. Lett. 38, 745–747 (1981).
[CrossRef]

Cremer, C.

Denk, W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Dillard, A. G.

Donley, E. A.

P. Kaatz, E. A. Donley, and D. P. Shelton, “A comparison of molecular hyperpolarizabilities from gas and liquid phase measurements,” J. Chem. Phys. 108, 849–856 (1998).
[CrossRef]

Ducuing, J.

J. P. Hermann and J. Ducuing, “Absolute measurement of two-photon cross sections,” Phys. Rev. A 5, 2557–2568 (1972).
[CrossRef]

J. P. Hermann and J. Ducuing, “Dispersion of the two-photon cross section in rhodamine dyes,” Opt. Commun. 6, 101–105 (1972).
[CrossRef]

Duval, V.

Fischer, A.

Frisch, H. L.

R. Bersohn, Y. H. Pao, and H. L. Frisch, “Double-quantum light scattering by molecules,” J. Chem. Phys. 45, 3184–3198 (1966).
[CrossRef]

Gorbatenkov, V. I.

N. N. Vsevolodov, L. P. Kostikov, L. P. Kayushin, and V. I. Gorbatenkov, “Two-photon absorption of laser radiation by chlorophyll-a and certain organic dyes,” Biophysics (GB) 18, 807 (1973).

Hagimoto, K.

Haner, D. A.

He, G. S.

Hermann, J. P.

J. P. Hermann and J. Ducuing, “Absolute measurement of two-photon cross sections,” Phys. Rev. A 5, 2557–2568 (1972).
[CrossRef]

J. P. Hermann and J. Ducuing, “Dispersion of the two-photon cross section in rhodamine dyes,” Opt. Commun. 6, 101–105 (1972).
[CrossRef]

Horsthuis, W. H. G.

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

Hutchinson, M. H. R.

D. J. Bradley, M. H. R. Hutchinson, and H. Koetser, “Interactions of picosecond laser pulses with organic molecules. II. Two-photon absorption cross sections,” Proc. R. Soc. London, Ser. A 329, 105–119 (1972).
[CrossRef]

Ito, R.

Jonsson, D.

P. Norman, Y. Luo, D. Jonsson, H. Ågren, K. O. Sylvester-Hvid, and K. V. Mikkelsen, “Hyperpolarizability depolarization ratios of nitroanilines,” J. Chem. Phys. 107, 9063–9066 (1997).
[CrossRef]

Kaatz, P.

P. Kaatz, E. A. Donley, and D. P. Shelton, “A comparison of molecular hyperpolarizabilities from gas and liquid phase measurements,” J. Chem. Phys. 108, 849–856 (1998).
[CrossRef]

P. Kaatz and D. P. Shelton, “Spectral measurements of hyper-Rayleigh light scattering,” Rev. Sci. Instrum. 67, 1438–1444 (1996).
[CrossRef]

P. Kaatz and D. P. Shelton, “Polarized hyper-Rayleigh light scattering measurements of nonlinear optical chromophores,” J. Chem. Phys. 105, 3918–3929 (1996).
[CrossRef]

Kawata, S.

Kayushin, L. P.

N. N. Vsevolodov, L. P. Kostikov, L. P. Kayushin, and V. I. Gorbatenkov, “Two-photon absorption of laser radiation by chlorophyll-a and certain organic dyes,” Biophysics (GB) 18, 807 (1973).

Kitamoto, A.

Koetser, H.

D. J. Bradley, M. H. R. Hutchinson, and H. Koetser, “Interactions of picosecond laser pulses with organic molecules. II. Two-photon absorption cross sections,” Proc. R. Soc. London, Ser. A 329, 105–119 (1972).
[CrossRef]

Kondo, T.

Kostikov, L. P.

N. N. Vsevolodov, L. P. Kostikov, L. P. Kayushin, and V. I. Gorbatenkov, “Two-photon absorption of laser radiation by chlorophyll-a and certain organic dyes,” Biophysics (GB) 18, 807 (1973).

Li, S.

S. Li and C. Y. She, “Two-photon absorption cross-section measurements in common laser dyes at 1064 μm,” Opt. Acta 29, 281–287 (1982).
[CrossRef]

Luo, Y.

P. Norman, Y. Luo, D. Jonsson, H. Ågren, K. O. Sylvester-Hvid, and K. V. Mikkelsen, “Hyperpolarizability depolarization ratios of nitroanilines,” J. Chem. Phys. 107, 9063–9066 (1997).
[CrossRef]

Marou, S.

McGuckin, B. T.

Menzies, R. T.

Meth, J.

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

Mikkelsen, K. V.

P. Norman, Y. Luo, D. Jonsson, H. Ågren, K. O. Sylvester-Hvid, and K. V. Mikkelsen, “Hyperpolarizability depolarization ratios of nitroanilines,” J. Chem. Phys. 107, 9063–9066 (1997).
[CrossRef]

Mito, A.

Möhlmann, G. R.

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

Nakamura, O.

Norman, P.

P. Norman, Y. Luo, D. Jonsson, H. Ågren, K. O. Sylvester-Hvid, and K. V. Mikkelsen, “Hyperpolarizability depolarization ratios of nitroanilines,” J. Chem. Phys. 107, 9063–9066 (1997).
[CrossRef]

Pao, Y. H.

R. Bersohn, Y. H. Pao, and H. L. Frisch, “Double-quantum light scattering by molecules,” J. Chem. Phys. 45, 3184–3198 (1966).
[CrossRef]

Penzkofer, A.

P. Sperber and A. Penzkofer, “S0-Sn two-photon absorption dynamics of rhodamine dyes,” Opt. Quantum Electron. 18, 381–401 (1986).
[CrossRef]

Pipin, J.

D. M. Bishop and J. Pipin, “Calculated Raman overtone intensities for H2 and D2,” J. Chem. Phys. 94, 6073–6080 (1991).
[CrossRef]

D. M. Bishop and J. Pipin, “Improved dynamic hyperpolarizabilities and field-gradient polarizabilities for helium,” J. Chem. Phys. 91, 3549–3551 (1989).
[CrossRef]

Prasad, P. N.

Reinhardt, B.

Rice, J. E.

D. P. Shelton and J. E. Rice, “Measurements and calculations of the hyperpolarizabilities of atoms and small molecules in the gas phase,” Chem. Rev. 94, 3–29 (1994).
[CrossRef]

Roberts, D. A.

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

Sekino, H.

R. J. Bartlett and H. Sekino, “Can quantum chemistry provide reliable molecular hyperpolarizabilities?” in Nonlinear Optical Materials: Theory and Modeling, S. P. Kama and A. T. Yeates, eds., ACS Symp. Ser. 628, 23–57 (1996).
[CrossRef]

She, C. Y.

S. Li and C. Y. She, “Two-photon absorption cross-section measurements in common laser dyes at 1064 μm,” Opt. Acta 29, 281–287 (1982).
[CrossRef]

Shear, J. B.

C. Xu, J. B. Shear, and W. W. Webb, “Hyper-Rayleigh and hyper-Raman scattering background of liquid water in two-photon excited fluorescence detection,” Anal. Chem. 69, 1285–1287 (1997).
[CrossRef] [PubMed]

Shelton, D. P.

P. Kaatz, E. A. Donley, and D. P. Shelton, “A comparison of molecular hyperpolarizabilities from gas and liquid phase measurements,” J. Chem. Phys. 108, 849–856 (1998).
[CrossRef]

P. Kaatz and D. P. Shelton, “Spectral measurements of hyper-Rayleigh light scattering,” Rev. Sci. Instrum. 67, 1438–1444 (1996).
[CrossRef]

P. Kaatz and D. P. Shelton, “Polarized hyper-Rayleigh light scattering measurements of nonlinear optical chromophores,” J. Chem. Phys. 105, 3918–3929 (1996).
[CrossRef]

D. P. Shelton and J. E. Rice, “Measurements and calculations of the hyperpolarizabilities of atoms and small molecules in the gas phase,” Chem. Rev. 94, 3–29 (1994).
[CrossRef]

D. P. Shelton, “Nonlinear-optical susceptibilities of gases measured at 1064 and 1319 nm,” Phys. Rev. A 42, 2578–2592 (1990).
[CrossRef] [PubMed]

D. P. Shelton, “Raman overtone intensities measured for H2,” J. Chem. Phys. 93, 1491–1495 (1990).
[CrossRef]

Shirane, M.

Shoji, I.

Sperber, P.

P. Sperber and A. Penzkofer, “S0-Sn two-photon absorption dynamics of rhodamine dyes,” Opt. Quantum Electron. 18, 381–401 (1986).
[CrossRef]

Stegeman, G. I.

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

Stelzer, E. H. K.

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Sylvester-Hvid, K. O.

P. Norman, Y. Luo, D. Jonsson, H. Ågren, K. O. Sylvester-Hvid, and K. V. Mikkelsen, “Hyperpolarizability depolarization ratios of nitroanilines,” J. Chem. Phys. 107, 9063–9066 (1997).
[CrossRef]

Torruellas, W. E.

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

Vsevolodov, N. N.

N. N. Vsevolodov, L. P. Kostikov, L. P. Kayushin, and V. I. Gorbatenkov, “Two-photon absorption of laser radiation by chlorophyll-a and certain organic dyes,” Biophysics (GB) 18, 807 (1973).

Webb, W. W.

C. Xu, J. B. Shear, and W. W. Webb, “Hyper-Rayleigh and hyper-Raman scattering background of liquid water in two-photon excited fluorescence detection,” Anal. Chem. 69, 1285–1287 (1997).
[CrossRef] [PubMed]

C. Xu and W. W. Webb, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm,” J. Opt. Soc. Am. B 13, 481–491 (1996).
[CrossRef]

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Xu, C.

C. Xu, J. B. Shear, and W. W. Webb, “Hyper-Rayleigh and hyper-Raman scattering background of liquid water in two-photon excited fluorescence detection,” Anal. Chem. 69, 1285–1287 (1997).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of the geometry of the sample cell used for the 1PF, 2PF, and HRS experiments, showing the placement of the incident laser beam with respect to the sample cell. The scattered light is detected in a solid angle dΩ=0.18 sr subtended by the camera lens at 90° to the incident beam.

Fig. 2
Fig. 2

Nearly quadratic power dependence is observed over the range of incident photon fluxes used for the measurements of HRS from a 0.096 M solution of p-nitroaniline (pNA) in methanol-d, and for measurements of 2PF from a 2.92×10-6 M solution of Rhodamine B (RhB), also in methanol-d. The results for Rhodamine 6G and Fluorescein are similar.

Fig. 3
Fig. 3

2PF spectrum of a 2.92×10-6 M solution of Rhodamine B (RhB) in methanol-d compared with the HRS spectrum (inset) of a 0.096 M solution of p-nitroaniline (pNA) also in methanol-d used for calibration. Both spectra were obtained in the VV polarization geometry with an 18-cm-1 spectral slit width. The arrow marks the position of the RhB HRS peak, which is too narrow and too weak to be seen on this scale.

Fig. 4
Fig. 4

Measured values of the two-photon absorption coefficient δ of RhB plotted versus the year the work was reported. Solid symbols correspond to the original data as given in Table 3, whereas the open symbols indicate the values as reassessed by the present authors (also given in Table 3). The dashed line indicates the best present estimate for δ of RhB.

Tables (6)

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Table 1 Hyper-Rayleigh-Scattering Calibration Data for Para-Nitroaniline (pNA) in Methanol-d at λ0=1064 nm

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Table 2 Data Used to Obtain σ2PF(2) and δ for Each Dye—All Dyes Were Studied as Solutions in CH3ODNaOH Was Added to Give a pH10 for the Fluorescein Solution

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Table 3 Comparison of Measurements of the Two-Photon Absorption Cross Section δ of Rhodamine B—All These Experiments Actually Measure the 2PF Cross Section Divided by the Fluorescence Quantum Efficiency ηF to Obtain the 2PA Coefficient δ

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Table 4 Comparison of Measurements of the Two-Photon Absorption Cross Section δ of Rhodamine 6G

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Table 5 Comparison of Measurements of the Two-Photon Absorption Cross Section δ of Fluorescein

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Table 6 Absolute Intensity Measurements Compared with Predictions

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

S(ω)=ρd2σ(2)dΩdωnωπM2λ0G(2)Nω21.64τFWHMdΩnω2×(Tω2Tω10-2Aωl110-Aωl2ηD),
σ2PF(2)=RF2,
σ2PF(2)=2×4π×dσ2PF(2)dΩ,
σ2PF(2)=8πS2PF*SHRS*dσHRS(2)dΩ,
S*=1ρS(ω)dω10-A(ω)l2ηD(ω)
dσHRS(2)dΩ=2h(4π0)32πλ05Lω4L2ω2βZZZ2,
S1PF(ω)=N2ω(1-10-A2ωl3)ηFg(ω)2×4πdΩnω2×(T2ωTω10-A2ωl410-Aωl2ηD),
δ=2σ2PF(2)ηF,
SRS(ω)=Nωρl3dσRSdΩdΩTωTωηD,
dσRSdΩ=ρ(J)ωω3c444532(J+1)(2J+1)(J+2)(2J+3)|Δα|2(4π0)2,

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