Abstract

A mathematical formalism based on the classical theory of Brillouin scattering with non-monochromatic incident radiation is developed and used to account for the effect of radiation linewidths on the spectral resolution of the pump-probe technique (PPT) in application to the Brillouin spectroscopy. Theoretical findings are verified by comparison with corresponding experimental PPT data from an earlier study on CS2, a paradigm of SBS, which is well documented for its acousto-optical properties.

© 2019 Optical Society of America

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References

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2018 (3)

P.-J. Wu, I. V. Kabakova, J. W. Ruberti, J. M. Sherwood, I. E. Dunlop, C. Paterson, P. Torok, and D. R. Overby, “Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials,” Nat. Methods 15, 561–562 (2018).
[Crossref]

T. Hao, J. Tang, W. Li, N. Zhu, and M. Li, “Fourier domain mode locked optoelectronic oscillator based on the deamplification of stimulated Brillouin scattering,” OSA Contin. 1, 408–415 (2018).
[Crossref]

E. A. Kittlaus, N. T. Otterstrom, P. Kharel, S. Gertler, and P. T. Rakich, “Non-reciprocal interband Brillouin modulation,” Nat. Photonics 12, 613–619 (2018).
[Crossref]

2016 (2)

Z. Meng, A. J. Traverso, C. W. Ballmann, M. Troyanova-Wood, and V. V. Yakovlev, “Seeing cells in a new light: a renaissance of Brillouin spectroscopy,” Adv. Opt. Photon. 8, 300–327 (2016).
[Crossref]

C. Wolff, R. Van Laer, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Brillouin resonance broadening due to structural variations in nanoscale waveguides,” New J. Phys. 18, 025006 (2016).
[Crossref]

2014 (2)

2013 (1)

K. Hotate, “Fiber distributed Brillouin sensing with optical correlation domain techniques,” Opt. Fiber Technol. 19, 700–719 (2013).
[Crossref]

2011 (3)

2009 (1)

2008 (1)

V. I. Kovalev, R. G. Harrison, and J. D. Simonotto, “On the emergence and collapse of coherent periodic emission in stochastic stimulated Brilloiun scattering in optical fiber,” Phys. Rev. A 78, 043820(2008).
[Crossref]

2007 (1)

2006 (1)

2004 (1)

2000 (1)

V. I. Kovalev and R. G. Harrison, “Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber,” Phys. Rev. Lett. 85, 1879–1882 (2000).
[Crossref]

1988 (1)

1987 (1)

1986 (1)

A. I. Erokhin, V. I. Kovalev, and F. S. Faizullov, “Determination of the parameters of a nonlinear response in liquids in an acoustic resonance region by the method of nondegenerate four-wave interaction,” Sov. J. Quantum Electron. 16, 872–877 (1986).
[Crossref]

1972 (1)

J. R. Sandercock, “Structure in the Brillouin spectra of thin films,” Phys. Rev. Lett. 29, 1735–1738 (1972).
[Crossref]

1970 (1)

D. Pohl and W. Kaiser, “Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonon lifetime,” Phys. Rev. B 1, 31–43 (1970).
[Crossref]

1966 (1)

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945–2955 (1966).
[Crossref]

1964 (2)

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12, 592–595 (1964).
[Crossref]

R. G. Brewer and K. E. Rieckhoff, “Stimulated Brillouin scattering in liquids,” Phys. Rev. Lett. 13, 334–336 (1964).
[Crossref]

1930 (3)

E. Gross, “Change of wave-length of light due to elastic heat waves at scattering in liquids,” Nature 126, 201–202 (1930).
[Crossref]

E. Gross, “The splitting of spectral lines at scattering of light by liquids,” Nature 126, 400 (1930).
[Crossref]

E. Gross, “Splitting of the frequency of light scattered by liquids and optical anisotropy of molecules,” Nature 126, 603–604 (1930).
[Crossref]

Azuma, Y.

Ballmann, C. W.

Ben-Ezra, Y.

Benito, D.

Bernini, R.

Braun, R. P.

Brewer, R. G.

R. G. Brewer and K. E. Rieckhoff, “Stimulated Brillouin scattering in liquids,” Phys. Rev. Lett. 13, 334–336 (1964).
[Crossref]

Chiao, R. Y.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12, 592–595 (1964).
[Crossref]

Choi, D.-Y.

Dunlop, I. E.

P.-J. Wu, I. V. Kabakova, J. W. Ruberti, J. M. Sherwood, I. E. Dunlop, C. Paterson, P. Torok, and D. R. Overby, “Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials,” Nat. Methods 15, 561–562 (2018).
[Crossref]

Eggleton, B. J.

C. Wolff, R. Van Laer, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Brillouin resonance broadening due to structural variations in nanoscale waveguides,” New J. Phys. 18, 025006 (2016).
[Crossref]

R. Pant, C. G. Poulton, D.-Y. Choi, H. McFarlane, S. Hile, E. Li, L. Thevenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “On-chip stimulated Brillouin scattering,” Opt. Express 19, 8285–8290 (2011).
[Crossref]

Erokhin, A. I.

A. I. Erokhin, V. I. Kovalev, and F. S. Faizullov, “Determination of the parameters of a nonlinear response in liquids in an acoustic resonance region by the method of nondegenerate four-wave interaction,” Sov. J. Quantum Electron. 16, 872–877 (1986).
[Crossref]

Fabelinskii, I. L.

I. L. Fabelinskii, Molecular Scattering of Light (1968).

Faizullov, F. S.

A. I. Erokhin, V. I. Kovalev, and F. S. Faizullov, “Determination of the parameters of a nonlinear response in liquids in an acoustic resonance region by the method of nondegenerate four-wave interaction,” Sov. J. Quantum Electron. 16, 872–877 (1986).
[Crossref]

Galech, S.

Gertler, S.

E. A. Kittlaus, N. T. Otterstrom, P. Kharel, S. Gertler, and P. T. Rakich, “Non-reciprocal interband Brillouin modulation,” Nat. Photonics 12, 613–619 (2018).
[Crossref]

Gross, E.

E. Gross, “Change of wave-length of light due to elastic heat waves at scattering in liquids,” Nature 126, 201–202 (1930).
[Crossref]

E. Gross, “The splitting of spectral lines at scattering of light by liquids,” Nature 126, 400 (1930).
[Crossref]

E. Gross, “Splitting of the frequency of light scattered by liquids and optical anisotropy of molecules,” Nature 126, 603–604 (1930).
[Crossref]

Hao, T.

T. Hao, J. Tang, W. Li, N. Zhu, and M. Li, “Fourier domain mode locked optoelectronic oscillator based on the deamplification of stimulated Brillouin scattering,” OSA Contin. 1, 408–415 (2018).
[Crossref]

Harrison, R. G.

V. I. Kovalev and R. G. Harrison, “On the material response in stimulated Brillouin scattering,” Phys. Lett. A 375, 2581–2584 (2011).
[Crossref]

V. I. Kovalev, N. E. Kotova, and R. G. Harrison, “Slow Light” in stimulated Brillouin scattering: on the influence of the spectral width of pump radiation on the group index,” Opt. Express 17, 17317–17323(2009).
[Crossref]

V. I. Kovalev, R. G. Harrison, and J. D. Simonotto, “On the emergence and collapse of coherent periodic emission in stochastic stimulated Brilloiun scattering in optical fiber,” Phys. Rev. A 78, 043820(2008).
[Crossref]

V. I. Kovalev and R. G. Harrison, “Threshold for stimulated Brillouin scattering in optical fiber,” Opt. Express 15, 17625–17630 (2007).
[Crossref]

V. I. Kovalev and R. G. Harrison, “Suppression of stimulated Brillouin scattering in high-power single frequency fiber amplifiers,” Opt. Lett. 31, 161–163 (2006).
[Crossref]

V. I. Kovalev and R. G. Harrison, “Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber,” Phys. Rev. Lett. 85, 1879–1882 (2000).
[Crossref]

Hernandez, R.

Hile, S.

Horiguchi, T.

Hotate, K.

Ishigure, T.

Kabakova, I. V.

P.-J. Wu, I. V. Kabakova, J. W. Ruberti, J. M. Sherwood, I. E. Dunlop, C. Paterson, P. Torok, and D. R. Overby, “Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials,” Nat. Methods 15, 561–562 (2018).
[Crossref]

Kaiser, W.

D. Pohl and W. Kaiser, “Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonon lifetime,” Phys. Rev. B 1, 31–43 (1970).
[Crossref]

Kharel, P.

E. A. Kittlaus, N. T. Otterstrom, P. Kharel, S. Gertler, and P. T. Rakich, “Non-reciprocal interband Brillouin modulation,” Nat. Photonics 12, 613–619 (2018).
[Crossref]

Kishi, M.

Kittlaus, E. A.

E. A. Kittlaus, N. T. Otterstrom, P. Kharel, S. Gertler, and P. T. Rakich, “Non-reciprocal interband Brillouin modulation,” Nat. Photonics 12, 613–619 (2018).
[Crossref]

Kotova, N. E.

Kovalev, V. I.

V. I. Kovalev and R. G. Harrison, “On the material response in stimulated Brillouin scattering,” Phys. Lett. A 375, 2581–2584 (2011).
[Crossref]

V. I. Kovalev, N. E. Kotova, and R. G. Harrison, “Slow Light” in stimulated Brillouin scattering: on the influence of the spectral width of pump radiation on the group index,” Opt. Express 17, 17317–17323(2009).
[Crossref]

V. I. Kovalev, R. G. Harrison, and J. D. Simonotto, “On the emergence and collapse of coherent periodic emission in stochastic stimulated Brilloiun scattering in optical fiber,” Phys. Rev. A 78, 043820(2008).
[Crossref]

V. I. Kovalev and R. G. Harrison, “Threshold for stimulated Brillouin scattering in optical fiber,” Opt. Express 15, 17625–17630 (2007).
[Crossref]

V. I. Kovalev and R. G. Harrison, “Suppression of stimulated Brillouin scattering in high-power single frequency fiber amplifiers,” Opt. Lett. 31, 161–163 (2006).
[Crossref]

V. I. Kovalev and R. G. Harrison, “Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber,” Phys. Rev. Lett. 85, 1879–1882 (2000).
[Crossref]

A. I. Erokhin, V. I. Kovalev, and F. S. Faizullov, “Determination of the parameters of a nonlinear response in liquids in an acoustic resonance region by the method of nondegenerate four-wave interaction,” Sov. J. Quantum Electron. 16, 872–877 (1986).
[Crossref]

Li, E.

Li, M.

T. Hao, J. Tang, W. Li, N. Zhu, and M. Li, “Fourier domain mode locked optoelectronic oscillator based on the deamplification of stimulated Brillouin scattering,” OSA Contin. 1, 408–415 (2018).
[Crossref]

Li, W.

T. Hao, J. Tang, W. Li, N. Zhu, and M. Li, “Fourier domain mode locked optoelectronic oscillator based on the deamplification of stimulated Brillouin scattering,” OSA Contin. 1, 408–415 (2018).
[Crossref]

Loayssa, A.

Luther-Davies, B.

Madden, S. J.

McFarlane, H.

Meng, Z.

Minardo, A.

Mizuno, Y.

Nakamura, K.

Otterstrom, N. T.

E. A. Kittlaus, N. T. Otterstrom, P. Kharel, S. Gertler, and P. T. Rakich, “Non-reciprocal interband Brillouin modulation,” Nat. Photonics 12, 613–619 (2018).
[Crossref]

Overby, D. R.

P.-J. Wu, I. V. Kabakova, J. W. Ruberti, J. M. Sherwood, I. E. Dunlop, C. Paterson, P. Torok, and D. R. Overby, “Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials,” Nat. Methods 15, 561–562 (2018).
[Crossref]

Pant, R.

Paterson, C.

P.-J. Wu, I. V. Kabakova, J. W. Ruberti, J. M. Sherwood, I. E. Dunlop, C. Paterson, P. Torok, and D. R. Overby, “Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials,” Nat. Methods 15, 561–562 (2018).
[Crossref]

Pohl, D.

D. Pohl and W. Kaiser, “Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonon lifetime,” Phys. Rev. B 1, 31–43 (1970).
[Crossref]

Poulton, C. G.

C. Wolff, R. Van Laer, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Brillouin resonance broadening due to structural variations in nanoscale waveguides,” New J. Phys. 18, 025006 (2016).
[Crossref]

R. Pant, C. G. Poulton, D.-Y. Choi, H. McFarlane, S. Hile, E. Li, L. Thevenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “On-chip stimulated Brillouin scattering,” Opt. Express 19, 8285–8290 (2011).
[Crossref]

Rakich, P. T.

E. A. Kittlaus, N. T. Otterstrom, P. Kharel, S. Gertler, and P. T. Rakich, “Non-reciprocal interband Brillouin modulation,” Nat. Photonics 12, 613–619 (2018).
[Crossref]

Rieckhoff, K. E.

R. G. Brewer and K. E. Rieckhoff, “Stimulated Brillouin scattering in liquids,” Phys. Rev. Lett. 13, 334–336 (1964).
[Crossref]

Ruberti, J. W.

P.-J. Wu, I. V. Kabakova, J. W. Ruberti, J. M. Sherwood, I. E. Dunlop, C. Paterson, P. Torok, and D. R. Overby, “Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials,” Nat. Methods 15, 561–562 (2018).
[Crossref]

Sandercock, J. R.

J. R. Sandercock, “Structure in the Brillouin spectra of thin films,” Phys. Rev. Lett. 29, 1735–1738 (1972).
[Crossref]

Schneider, T.

Sherwood, J. M.

P.-J. Wu, I. V. Kabakova, J. W. Ruberti, J. M. Sherwood, I. E. Dunlop, C. Paterson, P. Torok, and D. R. Overby, “Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials,” Nat. Methods 15, 561–562 (2018).
[Crossref]

Shibata, N.

Simonotto, J. D.

V. I. Kovalev, R. G. Harrison, and J. D. Simonotto, “On the emergence and collapse of coherent periodic emission in stochastic stimulated Brilloiun scattering in optical fiber,” Phys. Rev. A 78, 043820(2008).
[Crossref]

Steel, M. J.

C. Wolff, R. Van Laer, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Brillouin resonance broadening due to structural variations in nanoscale waveguides,” New J. Phys. 18, 025006 (2016).
[Crossref]

Stern, Y.

Stoicheff, B. P.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12, 592–595 (1964).
[Crossref]

Tang, C. L.

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945–2955 (1966).
[Crossref]

Tang, J.

T. Hao, J. Tang, W. Li, N. Zhu, and M. Li, “Fourier domain mode locked optoelectronic oscillator based on the deamplification of stimulated Brillouin scattering,” OSA Contin. 1, 408–415 (2018).
[Crossref]

Tateda, M.

Thevenaz, L.

Torok, P.

P.-J. Wu, I. V. Kabakova, J. W. Ruberti, J. M. Sherwood, I. E. Dunlop, C. Paterson, P. Torok, and D. R. Overby, “Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials,” Nat. Methods 15, 561–562 (2018).
[Crossref]

Townes, C. H.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12, 592–595 (1964).
[Crossref]

Traverso, A. J.

Troyanova-Wood, M.

Tur, M.

Van Laer, R.

C. Wolff, R. Van Laer, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Brillouin resonance broadening due to structural variations in nanoscale waveguides,” New J. Phys. 18, 025006 (2016).
[Crossref]

Waarts, R. G.

Wolff, C.

C. Wolff, R. Van Laer, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Brillouin resonance broadening due to structural variations in nanoscale waveguides,” New J. Phys. 18, 025006 (2016).
[Crossref]

Wu, P.-J.

P.-J. Wu, I. V. Kabakova, J. W. Ruberti, J. M. Sherwood, I. E. Dunlop, C. Paterson, P. Torok, and D. R. Overby, “Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials,” Nat. Methods 15, 561–562 (2018).
[Crossref]

Yakovlev, V. V.

Zadok, A.

Zeni, L.

Zhang, R.

Zhong, K.

Zhu, N.

T. Hao, J. Tang, W. Li, N. Zhu, and M. Li, “Fourier domain mode locked optoelectronic oscillator based on the deamplification of stimulated Brillouin scattering,” OSA Contin. 1, 408–415 (2018).
[Crossref]

Adv. Opt. Photon. (1)

J. Appl. Phys. (1)

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945–2955 (1966).
[Crossref]

Nat. Methods (1)

P.-J. Wu, I. V. Kabakova, J. W. Ruberti, J. M. Sherwood, I. E. Dunlop, C. Paterson, P. Torok, and D. R. Overby, “Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials,” Nat. Methods 15, 561–562 (2018).
[Crossref]

Nat. Photonics (1)

E. A. Kittlaus, N. T. Otterstrom, P. Kharel, S. Gertler, and P. T. Rakich, “Non-reciprocal interband Brillouin modulation,” Nat. Photonics 12, 613–619 (2018).
[Crossref]

Nature (3)

E. Gross, “Change of wave-length of light due to elastic heat waves at scattering in liquids,” Nature 126, 201–202 (1930).
[Crossref]

E. Gross, “The splitting of spectral lines at scattering of light by liquids,” Nature 126, 400 (1930).
[Crossref]

E. Gross, “Splitting of the frequency of light scattered by liquids and optical anisotropy of molecules,” Nature 126, 603–604 (1930).
[Crossref]

New J. Phys. (1)

C. Wolff, R. Van Laer, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Brillouin resonance broadening due to structural variations in nanoscale waveguides,” New J. Phys. 18, 025006 (2016).
[Crossref]

Opt. Express (4)

Opt. Fiber Technol. (1)

K. Hotate, “Fiber distributed Brillouin sensing with optical correlation domain techniques,” Opt. Fiber Technol. 19, 700–719 (2013).
[Crossref]

Opt. Lett. (5)

OSA Contin. (1)

T. Hao, J. Tang, W. Li, N. Zhu, and M. Li, “Fourier domain mode locked optoelectronic oscillator based on the deamplification of stimulated Brillouin scattering,” OSA Contin. 1, 408–415 (2018).
[Crossref]

Photon. Res. (1)

Phys. Lett. A (1)

V. I. Kovalev and R. G. Harrison, “On the material response in stimulated Brillouin scattering,” Phys. Lett. A 375, 2581–2584 (2011).
[Crossref]

Phys. Rev. A (1)

V. I. Kovalev, R. G. Harrison, and J. D. Simonotto, “On the emergence and collapse of coherent periodic emission in stochastic stimulated Brilloiun scattering in optical fiber,” Phys. Rev. A 78, 043820(2008).
[Crossref]

Phys. Rev. B (1)

D. Pohl and W. Kaiser, “Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonon lifetime,” Phys. Rev. B 1, 31–43 (1970).
[Crossref]

Phys. Rev. Lett. (4)

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[Crossref]

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[Crossref]

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[Crossref]

V. I. Kovalev and R. G. Harrison, “Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber,” Phys. Rev. Lett. 85, 1879–1882 (2000).
[Crossref]

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[Crossref]

Other (1)

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Figures (3)

Fig. 1.
Fig. 1. Calculated spectra of IS(ω,δΩ) at ΓB/2π=35MHz and δΩ/2π=0(1), 10(2), 20(3), 30(4), 40(5), 50(6), and 60(7) MHz.
Fig. 2.
Fig. 2. Log-linear plot of Lorentzians at δΩ0, with ΔωL/2π=35 and 55 MHz (solid and dashed curves) and the calculated R(δΩ/2π) at ΓB/2π=35MHz, Δωp/2π=Δωpr/2π=30MHz, and six magnitudes δΩ/2π (dots 2–7).
Fig. 3.
Fig. 3. Dependence of the calculated Δωexp/ΓB on Δωp/2π=Δωpr/2π for ΓB/2π=35MHz (1) and 50 MHz (2) (solid lines), and those following from [19] (dashed lines). The dotted line illustrates the 5% level of Δωexp deviation from ΓB.

Equations (7)

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(2t2Vs22A2t)δρ(r,t)=116π(ρ0ερ)2[Ep(r,t)Epr*(r,t)+c.c.],
A=(43η+η01+Ω2τ2)/ρ,
ΩB=ωpωBs=Vsqs2nVscωpsin(θ/2),
|ρa(z,δΩ)|q2Ep(z)Epr(z)2Vsq(δΩ)2+(Aq2)2/4,
|ρa(ω,δΩ)|q2Ep(ν)Epr*(ων)dν2ΩB(ωδΩ)2+ΓB2/4
IS(ω,δΩ)=|ES(ω,δΩ)|2|Ep(ν)δρ*(ων,δΩ)dν|2,
R(δΩ)=IS(ω,δΩ)dω.

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