Abstract

Fourier mode coupling model was first applied to achieve the spectra property of a fiber Bragg grating (FBG)-based longitudinal-acousto-optic modulator. Compared with traditional analysis algorithms, such as the transfer matrix method, the Fourier mode coupling model could improve the computing efficiency up to 100 times with a guarantee of accuracy. In this paper, based on the theoretical analysis of this model, the spectra characteristics of the modulator in different frequencies and acoustically induced strains were numerically simulated. In the experiment, a uniform FBG was modulated by acoustic wave (AW) at 12 different frequencies. In particular, the modulator responses at 563 and 885.5 KHz with three different lead zirconate titanate (PZT) loads applied were plotted for illustration, and the linear fitting of experimental data demonstrated a good match with the simulation result. The acoustic excitation of the longitudinal wave is obtained using a conic silica horn attached to the surface of a shear-mode PZT plate paralleled to the fiber axis. This way of generating longitudinal AW with a transversal PZT may shed light on the optimal structural design for the FBG-based longitudinal-acousto-optic modulator.

© 2012 Optical Society of America

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References

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  1. H. Tsuda, “A Bragg wavelength-insensitive fiber Bragg grating ultrasound sensing system that uses a broadband light and no optical filter,” Sensors 11, 6954–6966 (2011).
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  2. C. Cuadrado-Laborde, A. Díez, M. V. Andrés, J. L. Cruz, and M. Bello-Jiménez, “In-fiber acousto-optic devices for laser applications,” Opt. Photon. News 22, 36–41 (2011).
    [CrossRef]
  3. C. A. F. Marques, R. A. Oliveira, A. A. P. Pohl, J. Canning, and R. N. Nogueira, “Dynamic control of a phase-shifted FBG through acousto-optic modulation,” Opt. Commun. 284, 1228–1231 (2011).
    [CrossRef]
  4. R. A. Oliveira, C. A. F. Marques, K. Cook, J. Canning, R. N. Nogueira, and A. A. P. Pohl, “Complex Bragg grating writing using direct modulation of the optical fiber with flexural waves,” Appl. Phys. Lett. 99, 161111 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. X. Zeng and K. Liang, “Analytic solutions for spectral properties of superstructure, Gaussian-apodized and phase shift gratings with short- or long-period,” Opt. Express 19, 22797–22808 (2011).
    [CrossRef]
  11. C. Cuadrado-Laborde, A. Díez, J. L. Cruz, and M. V. Andrés, “Q-switched and mode locked all-fiber lasers based on advanced acousto-optic devices,” Laser Photon. Rev. 3, 404–421 (2011).
    [CrossRef]

2011

H. Tsuda, “A Bragg wavelength-insensitive fiber Bragg grating ultrasound sensing system that uses a broadband light and no optical filter,” Sensors 11, 6954–6966 (2011).
[CrossRef]

C. Cuadrado-Laborde, A. Díez, M. V. Andrés, J. L. Cruz, and M. Bello-Jiménez, “In-fiber acousto-optic devices for laser applications,” Opt. Photon. News 22, 36–41 (2011).
[CrossRef]

C. A. F. Marques, R. A. Oliveira, A. A. P. Pohl, J. Canning, and R. N. Nogueira, “Dynamic control of a phase-shifted FBG through acousto-optic modulation,” Opt. Commun. 284, 1228–1231 (2011).
[CrossRef]

R. A. Oliveira, C. A. F. Marques, K. Cook, J. Canning, R. N. Nogueira, and A. A. P. Pohl, “Complex Bragg grating writing using direct modulation of the optical fiber with flexural waves,” Appl. Phys. Lett. 99, 161111 (2011).
[CrossRef]

C. Cuadrado-Laborde, A. Díez, J. L. Cruz, and M. V. Andrés, “Q-switched and mode locked all-fiber lasers based on advanced acousto-optic devices,” Laser Photon. Rev. 3, 404–421 (2011).
[CrossRef]

X. Zeng and K. Liang, “Analytic solutions for spectral properties of superstructure, Gaussian-apodized and phase shift gratings with short- or long-period,” Opt. Express 19, 22797–22808 (2011).
[CrossRef]

2008

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, 4899–4905 (2008).
[CrossRef]

2005

S. S. Fatemeh Abrishamian and M. Imai, “A new method of solving multimode coupled equations for analysis of uniform and non-uniform fiber Bragg grating and its application to acoustically induced superstructure modulation,” Opt. Rev. 12, 467–471 (2005).
[CrossRef]

2002

2000

Andrés, M. V.

C. Cuadrado-Laborde, A. Díez, M. V. Andrés, J. L. Cruz, and M. Bello-Jiménez, “In-fiber acousto-optic devices for laser applications,” Opt. Photon. News 22, 36–41 (2011).
[CrossRef]

C. Cuadrado-Laborde, A. Díez, J. L. Cruz, and M. V. Andrés, “Q-switched and mode locked all-fiber lasers based on advanced acousto-optic devices,” Laser Photon. Rev. 3, 404–421 (2011).
[CrossRef]

Bello-Jiménez, M.

C. Cuadrado-Laborde, A. Díez, M. V. Andrés, J. L. Cruz, and M. Bello-Jiménez, “In-fiber acousto-optic devices for laser applications,” Opt. Photon. News 22, 36–41 (2011).
[CrossRef]

Canning, J.

C. A. F. Marques, R. A. Oliveira, A. A. P. Pohl, J. Canning, and R. N. Nogueira, “Dynamic control of a phase-shifted FBG through acousto-optic modulation,” Opt. Commun. 284, 1228–1231 (2011).
[CrossRef]

R. A. Oliveira, C. A. F. Marques, K. Cook, J. Canning, R. N. Nogueira, and A. A. P. Pohl, “Complex Bragg grating writing using direct modulation of the optical fiber with flexural waves,” Appl. Phys. Lett. 99, 161111 (2011).
[CrossRef]

Chang, M. J.

Chou, C. C.

Chung, L. W.

Cook, K.

R. A. Oliveira, C. A. F. Marques, K. Cook, J. Canning, R. N. Nogueira, and A. A. P. Pohl, “Complex Bragg grating writing using direct modulation of the optical fiber with flexural waves,” Appl. Phys. Lett. 99, 161111 (2011).
[CrossRef]

Cruz, J. L.

C. Cuadrado-Laborde, A. Díez, M. V. Andrés, J. L. Cruz, and M. Bello-Jiménez, “In-fiber acousto-optic devices for laser applications,” Opt. Photon. News 22, 36–41 (2011).
[CrossRef]

C. Cuadrado-Laborde, A. Díez, J. L. Cruz, and M. V. Andrés, “Q-switched and mode locked all-fiber lasers based on advanced acousto-optic devices,” Laser Photon. Rev. 3, 404–421 (2011).
[CrossRef]

Cuadrado-Laborde, C.

C. Cuadrado-Laborde, A. Díez, J. L. Cruz, and M. V. Andrés, “Q-switched and mode locked all-fiber lasers based on advanced acousto-optic devices,” Laser Photon. Rev. 3, 404–421 (2011).
[CrossRef]

C. Cuadrado-Laborde, A. Díez, M. V. Andrés, J. L. Cruz, and M. Bello-Jiménez, “In-fiber acousto-optic devices for laser applications,” Opt. Photon. News 22, 36–41 (2011).
[CrossRef]

Díez, A.

C. Cuadrado-Laborde, A. Díez, M. V. Andrés, J. L. Cruz, and M. Bello-Jiménez, “In-fiber acousto-optic devices for laser applications,” Opt. Photon. News 22, 36–41 (2011).
[CrossRef]

C. Cuadrado-Laborde, A. Díez, J. L. Cruz, and M. V. Andrés, “Q-switched and mode locked all-fiber lasers based on advanced acousto-optic devices,” Laser Photon. Rev. 3, 404–421 (2011).
[CrossRef]

Fatemeh Abrishamian, S. S.

S. S. Fatemeh Abrishamian and M. Imai, “A new method of solving multimode coupled equations for analysis of uniform and non-uniform fiber Bragg grating and its application to acoustically induced superstructure modulation,” Opt. Rev. 12, 467–471 (2005).
[CrossRef]

Huang, D. W.

Imai, M.

S. S. Fatemeh Abrishamian and M. Imai, “A new method of solving multimode coupled equations for analysis of uniform and non-uniform fiber Bragg grating and its application to acoustically induced superstructure modulation,” Opt. Rev. 12, 467–471 (2005).
[CrossRef]

Kiang, Y. W.

Liang, K.

Lin, C. N.

Liu, I. M.

Liu, W. F.

Marques, C. A. F.

R. A. Oliveira, C. A. F. Marques, K. Cook, J. Canning, R. N. Nogueira, and A. A. P. Pohl, “Complex Bragg grating writing using direct modulation of the optical fiber with flexural waves,” Appl. Phys. Lett. 99, 161111 (2011).
[CrossRef]

C. A. F. Marques, R. A. Oliveira, A. A. P. Pohl, J. Canning, and R. N. Nogueira, “Dynamic control of a phase-shifted FBG through acousto-optic modulation,” Opt. Commun. 284, 1228–1231 (2011).
[CrossRef]

Neves, P. T.

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, 4899–4905 (2008).
[CrossRef]

Nogueira, R. N.

C. A. F. Marques, R. A. Oliveira, A. A. P. Pohl, J. Canning, and R. N. Nogueira, “Dynamic control of a phase-shifted FBG through acousto-optic modulation,” Opt. Commun. 284, 1228–1231 (2011).
[CrossRef]

R. A. Oliveira, C. A. F. Marques, K. Cook, J. Canning, R. N. Nogueira, and A. A. P. Pohl, “Complex Bragg grating writing using direct modulation of the optical fiber with flexural waves,” Appl. Phys. Lett. 99, 161111 (2011).
[CrossRef]

Oliveira, R. A.

R. A. Oliveira, C. A. F. Marques, K. Cook, J. Canning, R. N. Nogueira, and A. A. P. Pohl, “Complex Bragg grating writing using direct modulation of the optical fiber with flexural waves,” Appl. Phys. Lett. 99, 161111 (2011).
[CrossRef]

C. A. F. Marques, R. A. Oliveira, A. A. P. Pohl, J. Canning, and R. N. Nogueira, “Dynamic control of a phase-shifted FBG through acousto-optic modulation,” Opt. Commun. 284, 1228–1231 (2011).
[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, 4899–4905 (2008).
[CrossRef]

Pereira, J. T.

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, 4899–4905 (2008).
[CrossRef]

Pohl, A. A. P.

C. A. F. Marques, R. A. Oliveira, A. A. P. Pohl, J. Canning, and R. N. Nogueira, “Dynamic control of a phase-shifted FBG through acousto-optic modulation,” Opt. Commun. 284, 1228–1231 (2011).
[CrossRef]

R. A. Oliveira, C. A. F. Marques, K. Cook, J. Canning, R. N. Nogueira, and A. A. P. Pohl, “Complex Bragg grating writing using direct modulation of the optical fiber with flexural waves,” Appl. Phys. Lett. 99, 161111 (2011).
[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, 4899–4905 (2008).
[CrossRef]

Russell, P. St. J.

Sun, N. H.

Tsuda, H.

H. Tsuda, “A Bragg wavelength-insensitive fiber Bragg grating ultrasound sensing system that uses a broadband light and no optical filter,” Sensors 11, 6954–6966 (2011).
[CrossRef]

Yang, C. C.

Zeng, X.

Appl. Phys. Lett.

R. A. Oliveira, C. A. F. Marques, K. Cook, J. Canning, R. N. Nogueira, and A. A. P. Pohl, “Complex Bragg grating writing using direct modulation of the optical fiber with flexural waves,” Appl. Phys. Lett. 99, 161111 (2011).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

Laser Photon. Rev.

C. Cuadrado-Laborde, A. Díez, J. L. Cruz, and M. V. Andrés, “Q-switched and mode locked all-fiber lasers based on advanced acousto-optic devices,” Laser Photon. Rev. 3, 404–421 (2011).
[CrossRef]

Opt. Commun.

C. A. F. Marques, R. A. Oliveira, A. A. P. Pohl, J. Canning, and R. N. Nogueira, “Dynamic control of a phase-shifted FBG through acousto-optic modulation,” Opt. Commun. 284, 1228–1231 (2011).
[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, 4899–4905 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Photon. News

C. Cuadrado-Laborde, A. Díez, M. V. Andrés, J. L. Cruz, and M. Bello-Jiménez, “In-fiber acousto-optic devices for laser applications,” Opt. Photon. News 22, 36–41 (2011).
[CrossRef]

Opt. Rev.

S. S. Fatemeh Abrishamian and M. Imai, “A new method of solving multimode coupled equations for analysis of uniform and non-uniform fiber Bragg grating and its application to acoustically induced superstructure modulation,” Opt. Rev. 12, 467–471 (2005).
[CrossRef]

Sensors

H. Tsuda, “A Bragg wavelength-insensitive fiber Bragg grating ultrasound sensing system that uses a broadband light and no optical filter,” Sensors 11, 6954–6966 (2011).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

FBG reflected spectra with AW applied (solid line) at frequency of (a) 0.9 MHz, (b) 1.3 MHz, (c) 1.8 MHz, (d) 2.2 MHz, and without AW (dashed line).

Fig. 2.
Fig. 2.

FBG reflected spectra with AW applied (solid line) with amplitude of acoustically induced strain of (a) 50με, (b) 100με, (c) 150με, (d) 200με, and without AW (dashed line).

Fig. 3.
Fig. 3.

Experimental setup of the FBG acousto-optic modulator.

Fig. 4.
Fig. 4.

Effects of the 563 [(a) and (b)] and 885.5 KHz [(c) and (d)] acoustic excitations of FBG based on the setup in Fig. 3, with 0, 30, and 70 V load applied to the PZT.

Fig. 5.
Fig. 5.

(a) Simulated reflected spectrum (blue curve) and experimental reflected spectrum (red curve) of acoustically induced FBG. (b) Measured wavelength space between the primary and secondary reflection peak at different acoustic frequencies (diamond markers), the linear fitting of experimental data (red curve) and the simulation result (blue curve).

Tables (1)

Tables Icon

Table 1. Measured Δλ Versus Acoustic Frequencies

Equations (5)

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

Δn(z)=dn[1+cos(2πΛz+acos(ksz))],
dBs(z)dz=jmKBm(z)Δn(z)exp[j(βm+βs)z],
Bs(0)0dBs(z)[Bs(z)]2+[Bm(L)]2=jK0LΔn(z)ej2πvzdz.
0LΔn(z)ej2πvzdz=γ(v)+jη(v),
R=cos2(Kγ)sinh2(Kη)+sin2(Kγ)cosh2(Kη)1+cos2(Kγ)sinh2(Kη)+sin2(Kγ)cosh2(Kη)T=11+cos2(Kγ)sinh2(Kη)+sin2(Kγ)cosh2(Kη).

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