Abstract

The interaction frequencies between longitudinal acoustic waves and fiber Bragg grating are numerically and experimentally assessed. Since the grating modulation depends on the acoustic drive, the combined analysis provides a more efficient operation. In this paper, 3-D finite element and transfer matrix methods allow investigating the electrical, mechanical and optical resonances of an acousto-optical device. The frequency response allows locating the resonances and characterizing their mechanical displacements. Measurements of the grating response under resonant excitation are compared to simulated results. A smaller than <1.5% average difference between simulated-measured resonances indicates that the method is useful for the design and characterization of optical modulators.

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References

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  1. W. F. Liu, P. S. Russell, and L. Dong, “Acousto-optic superlattice modulator using a fiber Bragg grating,” Opt. Lett. 22(19), 1515–1517 (1997).
    [CrossRef] [PubMed]
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    [CrossRef]
  3. R. A. Oliveira, K. Cook, J. Canning, and A. A. P. Pohl, “Bragg grating writing in acoustically excited optical fiber,” Appl. Phys. Lett. 97(4), 5–6 (2010).
    [CrossRef]
  4. M. Delgado-Pinar, D. Zalvidea, A. Diez, P. Perez-Millan, and M. Andres, “Q-switching of an all-fiber laser by acousto-optic modulation of a fiber Bragg grating,” Opt. Express 14(3), 1106–1112 (2006).
    [CrossRef] [PubMed]
  5. P. de Tarso Neves and A. de Almeida Prado Pohl, “Time analysis of the wavelength shift in fiber Bragg gratings,” J. Lightwave Technol. 25(11), 3580–3588 (2007).
    [CrossRef]
  6. R. A. Oliveira, P. T. Neves, J. T. Pereira, and A. A. P. Pohl, “Numerical approach for designing a Bragg grating acousto-optic modulator using the finite element and the transfer matrix methods,” Opt. Commun. 281(19), 4899–4905 (2008).
    [CrossRef]
  7. R. A. Oliveira, P. T. Neves, J. T. Pereira, J. Canning, and A. A. P. Pohl, “Vibration mode analysis of a silica horn–fiber Bragg grating device,” Opt. Commun. 283(7), 1296–1302 (2010).
    [CrossRef]
  8. H. A. Kunkel, S. Locke, and B. Pikeroen, “Finite-element analysis of vibrational modes in piezoelectric ceramic disks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37(4), 316–328 (1990).
    [CrossRef] [PubMed]
  9. G. Chesini, V. A. Serrão, M. A. R. Franco, and C. M. B. Cordeiro, “Analysis and optimization of an all-fiber device based on photonic crystal fiber with integrated electrodes,” Opt. Express 18(3), 2842–2848 (2010).
    [CrossRef] [PubMed]
  10. C. M. B. Cordeiro, M. A. R. Franco, G. Chesini, E. C. S. Barretto, R. Lwin, C. H. Brito Cruz, and M. C. J. Large, “Microstructured-core optical fibre for evanescent sensing applications,” Opt. Express 14(26), 13056–13066 (2006).
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    [CrossRef] [PubMed]
  12. Ferroperm piezoceramics, “Full data matrix,” http://app04.swwwing.net/swwwing/app/cm/Browse.jsp?PAGE=1417 .

2012 (1)

R. E. Silva and A. A. P. Pohl, “Characterization of flexural acoustic waves in optical fibers using an extrinsic Fabry–Perot interferometer,” Meas. Sci. Technol. 23(5), 055206 (2012).
[CrossRef]

2010 (3)

R. A. Oliveira, K. Cook, J. Canning, and A. A. P. Pohl, “Bragg grating writing in acoustically excited optical fiber,” Appl. Phys. Lett. 97(4), 5–6 (2010).
[CrossRef]

R. A. Oliveira, P. T. Neves, J. T. Pereira, J. Canning, and A. A. P. Pohl, “Vibration mode analysis of a silica horn–fiber Bragg grating device,” Opt. Commun. 283(7), 1296–1302 (2010).
[CrossRef]

G. Chesini, V. A. Serrão, M. A. R. Franco, and C. M. B. Cordeiro, “Analysis and optimization of an all-fiber device based on photonic crystal fiber with integrated electrodes,” Opt. Express 18(3), 2842–2848 (2010).
[CrossRef] [PubMed]

2008 (1)

R. A. Oliveira, P. T. Neves, J. T. Pereira, and A. A. P. Pohl, “Numerical approach for designing a Bragg grating acousto-optic modulator using the finite element and the transfer matrix methods,” Opt. Commun. 281(19), 4899–4905 (2008).
[CrossRef]

2007 (1)

2006 (2)

2001 (1)

A. Ballato, “Modeling piezoelectric and piezomagnetic devices and structures via equivalent networks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48(5), 1189–1240 (2001).
[CrossRef] [PubMed]

1997 (1)

1990 (1)

H. A. Kunkel, S. Locke, and B. Pikeroen, “Finite-element analysis of vibrational modes in piezoelectric ceramic disks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37(4), 316–328 (1990).
[CrossRef] [PubMed]

Andres, M.

Ballato, A.

A. Ballato, “Modeling piezoelectric and piezomagnetic devices and structures via equivalent networks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48(5), 1189–1240 (2001).
[CrossRef] [PubMed]

Barretto, E. C. S.

Brito Cruz, C. H.

Canning, J.

R. A. Oliveira, P. T. Neves, J. T. Pereira, J. Canning, and A. A. P. Pohl, “Vibration mode analysis of a silica horn–fiber Bragg grating device,” Opt. Commun. 283(7), 1296–1302 (2010).
[CrossRef]

R. A. Oliveira, K. Cook, J. Canning, and A. A. P. Pohl, “Bragg grating writing in acoustically excited optical fiber,” Appl. Phys. Lett. 97(4), 5–6 (2010).
[CrossRef]

Chesini, G.

Cook, K.

R. A. Oliveira, K. Cook, J. Canning, and A. A. P. Pohl, “Bragg grating writing in acoustically excited optical fiber,” Appl. Phys. Lett. 97(4), 5–6 (2010).
[CrossRef]

Cordeiro, C. M. B.

de Almeida Prado Pohl, A.

de Tarso Neves, P.

Delgado-Pinar, M.

Diez, A.

Dong, L.

Franco, M. A. R.

Kunkel, H. A.

H. A. Kunkel, S. Locke, and B. Pikeroen, “Finite-element analysis of vibrational modes in piezoelectric ceramic disks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37(4), 316–328 (1990).
[CrossRef] [PubMed]

Large, M. C. J.

Liu, W. F.

Locke, S.

H. A. Kunkel, S. Locke, and B. Pikeroen, “Finite-element analysis of vibrational modes in piezoelectric ceramic disks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37(4), 316–328 (1990).
[CrossRef] [PubMed]

Lwin, R.

Neves, P. T.

R. A. Oliveira, P. T. Neves, J. T. Pereira, J. Canning, and A. A. P. Pohl, “Vibration mode analysis of a silica horn–fiber Bragg grating device,” Opt. Commun. 283(7), 1296–1302 (2010).
[CrossRef]

R. A. Oliveira, P. T. Neves, J. T. Pereira, and A. A. P. Pohl, “Numerical approach for designing a Bragg grating acousto-optic modulator using the finite element and the transfer matrix methods,” Opt. Commun. 281(19), 4899–4905 (2008).
[CrossRef]

Oliveira, R. A.

R. A. Oliveira, P. T. Neves, J. T. Pereira, J. Canning, and A. A. P. Pohl, “Vibration mode analysis of a silica horn–fiber Bragg grating device,” Opt. Commun. 283(7), 1296–1302 (2010).
[CrossRef]

R. A. Oliveira, K. Cook, J. Canning, and A. A. P. Pohl, “Bragg grating writing in acoustically excited optical fiber,” Appl. Phys. Lett. 97(4), 5–6 (2010).
[CrossRef]

R. A. Oliveira, P. T. Neves, J. T. Pereira, and A. A. P. Pohl, “Numerical approach for designing a Bragg grating acousto-optic modulator using the finite element and the transfer matrix methods,” Opt. Commun. 281(19), 4899–4905 (2008).
[CrossRef]

Pereira, J. T.

R. A. Oliveira, P. T. Neves, J. T. Pereira, J. Canning, and A. A. P. Pohl, “Vibration mode analysis of a silica horn–fiber Bragg grating device,” Opt. Commun. 283(7), 1296–1302 (2010).
[CrossRef]

R. A. Oliveira, P. T. Neves, J. T. Pereira, and A. A. P. Pohl, “Numerical approach for designing a Bragg grating acousto-optic modulator using the finite element and the transfer matrix methods,” Opt. Commun. 281(19), 4899–4905 (2008).
[CrossRef]

Perez-Millan, P.

Pikeroen, B.

H. A. Kunkel, S. Locke, and B. Pikeroen, “Finite-element analysis of vibrational modes in piezoelectric ceramic disks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37(4), 316–328 (1990).
[CrossRef] [PubMed]

Pohl, A. A. P.

R. E. Silva and A. A. P. Pohl, “Characterization of flexural acoustic waves in optical fibers using an extrinsic Fabry–Perot interferometer,” Meas. Sci. Technol. 23(5), 055206 (2012).
[CrossRef]

R. A. Oliveira, K. Cook, J. Canning, and A. A. P. Pohl, “Bragg grating writing in acoustically excited optical fiber,” Appl. Phys. Lett. 97(4), 5–6 (2010).
[CrossRef]

R. A. Oliveira, P. T. Neves, J. T. Pereira, J. Canning, and A. A. P. Pohl, “Vibration mode analysis of a silica horn–fiber Bragg grating device,” Opt. Commun. 283(7), 1296–1302 (2010).
[CrossRef]

R. A. Oliveira, P. T. Neves, J. T. Pereira, and A. A. P. Pohl, “Numerical approach for designing a Bragg grating acousto-optic modulator using the finite element and the transfer matrix methods,” Opt. Commun. 281(19), 4899–4905 (2008).
[CrossRef]

Russell, P. S.

Serrão, V. A.

Silva, R. E.

R. E. Silva and A. A. P. Pohl, “Characterization of flexural acoustic waves in optical fibers using an extrinsic Fabry–Perot interferometer,” Meas. Sci. Technol. 23(5), 055206 (2012).
[CrossRef]

Zalvidea, D.

Appl. Phys. Lett. (1)

R. A. Oliveira, K. Cook, J. Canning, and A. A. P. Pohl, “Bragg grating writing in acoustically excited optical fiber,” Appl. Phys. Lett. 97(4), 5–6 (2010).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (2)

H. A. Kunkel, S. Locke, and B. Pikeroen, “Finite-element analysis of vibrational modes in piezoelectric ceramic disks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37(4), 316–328 (1990).
[CrossRef] [PubMed]

A. Ballato, “Modeling piezoelectric and piezomagnetic devices and structures via equivalent networks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48(5), 1189–1240 (2001).
[CrossRef] [PubMed]

J. Lightwave Technol. (1)

Meas. Sci. Technol. (1)

R. E. Silva and A. A. P. Pohl, “Characterization of flexural acoustic waves in optical fibers using an extrinsic Fabry–Perot interferometer,” Meas. Sci. Technol. 23(5), 055206 (2012).
[CrossRef]

Opt. Commun. (2)

R. A. Oliveira, P. T. Neves, J. T. Pereira, and A. A. P. Pohl, “Numerical approach for designing a Bragg grating acousto-optic modulator using the finite element and the transfer matrix methods,” Opt. Commun. 281(19), 4899–4905 (2008).
[CrossRef]

R. A. Oliveira, P. T. Neves, J. T. Pereira, J. Canning, and A. A. P. Pohl, “Vibration mode analysis of a silica horn–fiber Bragg grating device,” Opt. Commun. 283(7), 1296–1302 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Other (1)

Ferroperm piezoceramics, “Full data matrix,” http://app04.swwwing.net/swwwing/app/cm/Browse.jsp?PAGE=1417 .

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Figures (8)

Fig. 1
Fig. 1

(a) Electrical, (b) mechanical and (c) optical properties of a coaxial acousto-optical FBG modulator.

Fig. 2
Fig. 2

Acousto-optical modulator design, material and geometric properties: (a) lateral, (b) 3-D and (c) frontal profiles.

Fig. 3
Fig. 3

Experimental setup used to characterize the FBG acousto-optical interaction.

Fig. 4
Fig. 4

(a) Measured-simulated PZT electric frequency response and (b) simulated displacements in resonances.

Fig. 5
Fig. 5

PZT vibration modes and qualitative displacement behavior in resonances.

Fig. 6
Fig. 6

(a) Modulator frequency response in terms of the fiber transversal and axial displacements and (b) longitudinal acoustic resonances obtained by the ratio between axial (z direction) and transversal displacements (xy directions).

Fig. 7
Fig. 7

Longitudinal modes. (a)-(b) 3D model and xy section of horn representing the displacements at 688 kHz and 1013 kHz, respectively. (c)-(d) yz section of horn displacement and fiber strain (for one acoustic wavelength) at 688 kHz. (e)-(f) yz section of horn displacement and fiber strain (for one acoustic wavelength) at 1013 kHz.

Fig. 8
Fig. 8

(a) FBG measured-simulated spectra and (b) spectral response in resonances. (c) FBG spectra and (d) side lobe reflectivity response for f = 1072 kHz.

Tables (1)

Tables Icon

Table 1 Measured FBG and simulated PZT-fiber resonances.

Equations (9)

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σ p = ( σ p S q ) Ε S q ( σ p Ε i ) S Ε i ,
D i = ( D i S p ) Ε S p + ( D i Ε j ) S Ε j ,
[ σ 1 σ 2 σ 3 σ 4 σ 5 σ 6 ]=[ c 11 c 12 c 13 0 0 0 c 12 c 11 c 13 0 0 0 c 13 c 13 c 33 0 0 0 0 0 0 c 44 0 0 0 0 0 0 c 44 0 0 0 0 0 0 c 66 ][ S 1 S 2 S 3 S 4 S 5 S 6 ][ 0 0 e 31 0 0 e 31 0 0 e 33 0 e 15 0 e 15 0 0 0 0 0 ][ Ε 1 Ε 2 Ε 3 ],
[ D 1 D 2 D 3 ]=[ 0 0 0 0 e 15 0 0 0 0 e 15 0 0 e 31 e 31 e 33 0 0 0 ][ S 1 S 2 S 3 S 4 S 5 S 6 ]+[ ε 11 S 0 0 0 ε 11 S 0 0 0 ε 33 S ][ Ε 1 Ε 2 Ε 3 ].
A z =i σ ^ A( z )+iκB( z ),
B z =i σ ^ B( z )i κ * A( z ),
[ A j B j ]= F j B [ A j1 B j1 ],
F j B =[ cosh( γ B Δz )i σ ^ γ B sinh( γ B Δz ) i κ γ B sinh( γ B Δz ) i κ γ B sinh( γ B Δz ) cosh( γ B Δz )+i σ ^ γ B sinh( γ B Δz ) ],
λ D ( S( z ) )= λ D0 [ 1+( 1 p e )S( z ) ],

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