Abstract

We have developed a Brillouin spectrometer based on frequency modulation (FM) spectroscopy in order to enhance the detection sensitivity and to detect separately the real and imaginary parts of the Brillouin spectrum. With this spectrometer, we have measured Brillouin spectra at room temperature in a variety of single crystals including SiO2, CaF2, LiNbO3, deuterated L-arginine phosphate, PbMoO4, TeO2, langatate (La3Ta0.5Ga5.3Al0.2O14), and KRS-5. To determine the Brillouin linewidth and shift from the observed FM spectrum, we have derived a spectral formula for the FM-stimulated Brillouin spectrum by taking into account several contributions from both electrostrictive and absorptive Brillouin scattering and polarization ellipticity of pump or probe waves. This formula reproduces the observed FM Brillouin spectra quite well.

© 2007 Optical Society of America

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  1. S. Ohno, T. Sonehara, E. Tatsu, A. Koreeda, and S. Saikan, 'kHz stimulated Brillouin spectroscopy,' Rev. Sci. Instrum. 77, 123104 (2006).
    [CrossRef]
  2. W. T. Grubbs and R. A. MacPhail, 'High resolution stimulated Brillouin gain spectrometer,' Rev. Sci. Instrum. 65, 34-41 (1994).
    [CrossRef]
  3. G. W. Faris, L. E. Jusinski, and A. P. Hickman, 'High-resolution stimulated Brillouin gain spectroscopy in glasses and crystals,' J. Opt. Soc. Am. B 10, 587-599 (1993).
    [CrossRef]
  4. G. W. Faris, M. Gerken, C. Jirauschek, D. Hogan, and Y. Chen, 'High-spectral-resolution stimulated Rayleigh-Brillouin scattering at 1 μm,' Opt. Lett. 26, 1894-1896 (2001).
    [CrossRef]
  5. G. C. Bjorklund, 'Frequency-modulation spectroscopy--new method for measuring weak absorptions and dispersions,' Opt. Lett. 5, 15-17 (1980).
    [CrossRef] [PubMed]
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    [CrossRef]
  7. M. Yoshimura, Y. Mori, T. Sasaki, H. Yoshida, and M. Nakatsuka, 'Efficient stimulated Brillouin scattering in the organic crystal deuterated L-arginine phosphate monohydrate,' J. Opt. Soc. Am. B 15, 446-450 (1998).
    [CrossRef]
  8. M. A. Dubinskii and L. D. Merkle, 'Ultrahigh-gain bulk solid-state stimulated Brillouin scattering phase-conjugation material,' Opt. Lett. 29, 992-994 (2004).
    [CrossRef] [PubMed]
  9. R. W. Boyd, Nonlinear Optics (Academic, 1992).
  10. T. Haga, M. Higuchi, K. Abe, and T. Shigenari, 'Optical heterodyned coherent Brillouin spectroscopy (OHD-BIKES) using continuous-wave (cw) dye lasers,' Jpn. J. Appl. Phys., Part 1 28, 1199-1205 (1989).
    [CrossRef]
  11. This Brillouin scattering is always observed in the FM spectroscopy, because the phase modulator for the FM spectroscopy consists of LiNbO3 crystal with the crystal orientation of [100].
  12. N. Uchida and N. Niizeki, 'Acousto-optic deflection materials and techniques,' Proc. IEEE 61, 1073-1092 (1973).
    [CrossRef]
  13. K. Ogusu, H. Li, and M. Kitao, 'Brillouin-gain coefficients of chalcogenide glasses,' J. Opt. Soc. Am. B 21, 1302-1304 (2004).
    [CrossRef]
  14. D. W. Oliver and G. A. Slack, 'Ultrasonic attenuation in insulator at room temperature,' J. Appl. Phys. 37, 1542-1548 (1966).
    [CrossRef]

2006 (1)

S. Ohno, T. Sonehara, E. Tatsu, A. Koreeda, and S. Saikan, 'kHz stimulated Brillouin spectroscopy,' Rev. Sci. Instrum. 77, 123104 (2006).
[CrossRef]

2004 (2)

2001 (1)

1998 (1)

1997 (1)

1994 (1)

W. T. Grubbs and R. A. MacPhail, 'High resolution stimulated Brillouin gain spectrometer,' Rev. Sci. Instrum. 65, 34-41 (1994).
[CrossRef]

1993 (1)

1989 (1)

T. Haga, M. Higuchi, K. Abe, and T. Shigenari, 'Optical heterodyned coherent Brillouin spectroscopy (OHD-BIKES) using continuous-wave (cw) dye lasers,' Jpn. J. Appl. Phys., Part 1 28, 1199-1205 (1989).
[CrossRef]

1980 (1)

1973 (1)

N. Uchida and N. Niizeki, 'Acousto-optic deflection materials and techniques,' Proc. IEEE 61, 1073-1092 (1973).
[CrossRef]

1966 (1)

D. W. Oliver and G. A. Slack, 'Ultrasonic attenuation in insulator at room temperature,' J. Appl. Phys. 37, 1542-1548 (1966).
[CrossRef]

Abe, K.

T. Haga, M. Higuchi, K. Abe, and T. Shigenari, 'Optical heterodyned coherent Brillouin spectroscopy (OHD-BIKES) using continuous-wave (cw) dye lasers,' Jpn. J. Appl. Phys., Part 1 28, 1199-1205 (1989).
[CrossRef]

Bjorklund, G. C.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Chen, Y.

Dubinskii, M. A.

Faris, G. W.

Fujita, H.

Gerken, M.

Grubbs, W. T.

W. T. Grubbs and R. A. MacPhail, 'High resolution stimulated Brillouin gain spectrometer,' Rev. Sci. Instrum. 65, 34-41 (1994).
[CrossRef]

Haga, T.

T. Haga, M. Higuchi, K. Abe, and T. Shigenari, 'Optical heterodyned coherent Brillouin spectroscopy (OHD-BIKES) using continuous-wave (cw) dye lasers,' Jpn. J. Appl. Phys., Part 1 28, 1199-1205 (1989).
[CrossRef]

Hickman, A. P.

Higuchi, M.

T. Haga, M. Higuchi, K. Abe, and T. Shigenari, 'Optical heterodyned coherent Brillouin spectroscopy (OHD-BIKES) using continuous-wave (cw) dye lasers,' Jpn. J. Appl. Phys., Part 1 28, 1199-1205 (1989).
[CrossRef]

Hogan, D.

Jirauschek, C.

Jusinski, L. E.

Kitao, M.

Koreeda, A.

S. Ohno, T. Sonehara, E. Tatsu, A. Koreeda, and S. Saikan, 'kHz stimulated Brillouin spectroscopy,' Rev. Sci. Instrum. 77, 123104 (2006).
[CrossRef]

Li, H.

MacPhail, R. A.

W. T. Grubbs and R. A. MacPhail, 'High resolution stimulated Brillouin gain spectrometer,' Rev. Sci. Instrum. 65, 34-41 (1994).
[CrossRef]

Merkle, L. D.

Mori, Y.

Nakatsuka, M.

Niizeki, N.

N. Uchida and N. Niizeki, 'Acousto-optic deflection materials and techniques,' Proc. IEEE 61, 1073-1092 (1973).
[CrossRef]

Ogusu, K.

Ohno, S.

S. Ohno, T. Sonehara, E. Tatsu, A. Koreeda, and S. Saikan, 'kHz stimulated Brillouin spectroscopy,' Rev. Sci. Instrum. 77, 123104 (2006).
[CrossRef]

Oliver, D. W.

D. W. Oliver and G. A. Slack, 'Ultrasonic attenuation in insulator at room temperature,' J. Appl. Phys. 37, 1542-1548 (1966).
[CrossRef]

Saikan, S.

S. Ohno, T. Sonehara, E. Tatsu, A. Koreeda, and S. Saikan, 'kHz stimulated Brillouin spectroscopy,' Rev. Sci. Instrum. 77, 123104 (2006).
[CrossRef]

Sasaki, T.

Shigenari, T.

T. Haga, M. Higuchi, K. Abe, and T. Shigenari, 'Optical heterodyned coherent Brillouin spectroscopy (OHD-BIKES) using continuous-wave (cw) dye lasers,' Jpn. J. Appl. Phys., Part 1 28, 1199-1205 (1989).
[CrossRef]

Slack, G. A.

D. W. Oliver and G. A. Slack, 'Ultrasonic attenuation in insulator at room temperature,' J. Appl. Phys. 37, 1542-1548 (1966).
[CrossRef]

Sonehara, T.

S. Ohno, T. Sonehara, E. Tatsu, A. Koreeda, and S. Saikan, 'kHz stimulated Brillouin spectroscopy,' Rev. Sci. Instrum. 77, 123104 (2006).
[CrossRef]

Tatsu, E.

S. Ohno, T. Sonehara, E. Tatsu, A. Koreeda, and S. Saikan, 'kHz stimulated Brillouin spectroscopy,' Rev. Sci. Instrum. 77, 123104 (2006).
[CrossRef]

Uchida, N.

N. Uchida and N. Niizeki, 'Acousto-optic deflection materials and techniques,' Proc. IEEE 61, 1073-1092 (1973).
[CrossRef]

Yoshida, H.

Yoshida, K.

Yoshimura, M.

Appl. Opt. (1)

J. Appl. Phys. (1)

D. W. Oliver and G. A. Slack, 'Ultrasonic attenuation in insulator at room temperature,' J. Appl. Phys. 37, 1542-1548 (1966).
[CrossRef]

J. Opt. Soc. Am. B (3)

Jpn. J. Appl. Phys., Part 1 (1)

T. Haga, M. Higuchi, K. Abe, and T. Shigenari, 'Optical heterodyned coherent Brillouin spectroscopy (OHD-BIKES) using continuous-wave (cw) dye lasers,' Jpn. J. Appl. Phys., Part 1 28, 1199-1205 (1989).
[CrossRef]

Opt. Lett. (3)

Proc. IEEE (1)

N. Uchida and N. Niizeki, 'Acousto-optic deflection materials and techniques,' Proc. IEEE 61, 1073-1092 (1973).
[CrossRef]

Rev. Sci. Instrum. (2)

S. Ohno, T. Sonehara, E. Tatsu, A. Koreeda, and S. Saikan, 'kHz stimulated Brillouin spectroscopy,' Rev. Sci. Instrum. 77, 123104 (2006).
[CrossRef]

W. T. Grubbs and R. A. MacPhail, 'High resolution stimulated Brillouin gain spectrometer,' Rev. Sci. Instrum. 65, 34-41 (1994).
[CrossRef]

Other (2)

R. W. Boyd, Nonlinear Optics (Academic, 1992).

This Brillouin scattering is always observed in the FM spectroscopy, because the phase modulator for the FM spectroscopy consists of LiNbO3 crystal with the crystal orientation of [100].

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Figures (8)

Fig. 1
Fig. 1

Experimental setup for FM-stimulated Brillouin spectroscopy. F.P. denotes confocal Fabry–Perot. The electro-optical modulator (E.O.M) is driven at 80 MHz . Mirrors M 1 and M 2 have a reflectivity of 98% and 50%, respectively, at the wavelength of 1.06 μ m . Other mirrors have a reflectivity of 100%.

Fig. 2
Fig. 2

ϕ 1 dependence of FM spectrum for electrostrictive Brillouin scattering with ϕ 2 = 0 in Eq. (8). The abscissa 1 and the frequency interval 0.15 correspond to the Brillouin frequency shift ω B and the modulation frequency ω m , respectively. Γ is set to 0.01. (a) ϕ 1 = π 2 , (b) ϕ 1 = π 3 , (c) ϕ 1 = π 6 , (d) ϕ 1 = 0 .

Fig. 3
Fig. 3

ϕ 1 dependence of FM spectrum for absorptive Brillouin scattering with ϕ 2 = π 2 in Eq. (8). The abscissa 1 and the frequency interval 0.15 correspond to the Brillouin frequency shift ω B and the modulation frequency ω m , respectively. Γ is set to 0.01. (a) ϕ 1 = π 2 , (b) ϕ 1 = π 3 , (c) ϕ 1 = π 6 , (d) ϕ 1 = 0 .

Fig. 4
Fig. 4

FM transverse Brillouin spectrum for the [100] direction of Li Nb O 3 . In Figs. 4, 5, 6, 7, 8, the upper and lower halves correspond, respectively, to the imaginary (Im) and real (Re) parts of FM Brillouin spectrum.

Fig. 5
Fig. 5

FM longitudinal Brillouin spectrum along the [100] direction of d-LAP.

Fig. 6
Fig. 6

FM transverse Brillouin spectrum along the [100] direction of d-LAP.

Fig. 7
Fig. 7

FM longitudinal Brillouin spectrum along the [100] direction of Pb Mo O 4 .

Fig. 8
Fig. 8

FM longitudinal Brillouin spectrum along the [110] direction of Te O 2 .

Tables (1)

Tables Icon

Table 1 Data for Brillouin Linewidth (HWHM) and Shift Determined in the Present Experiment a

Equations (10)

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E 2 ( t ) = E exp [ i ω 2 t + i m sin ( ω m t ) ] = E exp ( i ω 2 t ) n = J n ( m ) exp ( i n ω m t ) ,
E 2 ( t ) = E exp ( i ω 2 t ) [ J 2 e 2 i ω m t + J 1 e i ω m t + J 0 + J 1 e i ω m t + J 2 e 2 i ω m t ] .
E 2 ( t ) = E [ ( 1 + i X 2 ) J 2 e i ( ω 2 2 ω m ) t + ( 1 + i X 1 ) J 1 e i ( ω 2 ω m ) t + ( 1 + i X 0 ) J 0 e i ω 2 t + ( 1 + i X 1 ) J 1 e i ( ω 2 + ω m ) t + ( 1 + i X 2 ) J 2 e i ( ω 2 + 2 ω m ) t ] ,
X n ( ω ) = γ e + i γ a ω B 2 ( ω n ω m ) 2 + i ( ω n ω m ) Γ = γ e 2 + γ a 2 e i ϕ 2 χ n ( ω ) ,
ϕ 2 = arctan ( γ a γ e ) ,
χ n ( ω ) = 1 ω B 2 ( ω n ω m ) 2 + i ( ω n ω m ) Γ = χ n i χ n ,
X n S ( ω ) = γ e + i γ a 2 ω B [ ω B ( ω n ω m ) + i Γ 2 ] .
I 1 ( ω ) 2 E 2 J 1 e i [ ϕ 1 ( π 2 ) ] [ J 0 ( X 1 + X 1 * X 0 X 0 * ) + J 2 ( X 2 + X 2 * X 1 X 1 * ) ] + c.c. ,
I 2 ( ω ) 2 E 2 J 1 e i ϕ 1 [ J 2 χ 2 i J 2 χ 2 + ( J 0 + J 2 ) χ 1 i ( J 0 J 2 ) χ 1 + i 2 J 0 χ 0 ( J 0 + J 2 ) χ 1 i ( J 0 J 2 ) χ 1 J 2 χ 2 i J 2 χ 2 ] + c.c.
I 3 ( ω ) = 2 E 2 γ e 2 + γ a 2 J 1 e i [ ϕ 1 ( π 2 ) ] × [ J 0 { cos ϕ 2 ( χ 1 + χ 1 * χ 0 χ 0 * ) + i sin ϕ 2 ( χ 1 χ 1 * χ 0 + χ 0 * ) } + J 2 { cos ϕ 2 ( χ 2 + χ 2 * χ 1 χ 1 * ) + i sin ϕ 2 ( χ 2 χ 2 * χ 1 + χ 1 * ) } ] + c.c.

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