Abstract

Fourier mode coupling theory was first employed in the spectral analysis of several nonuniform fiber Bragg grating (FBG)-based acousto-optic modulators (NU-FBG-AOMs) with the effects of Gaussian-apodization (GA), phase shift (PS), and linear chirp (LC). Because of the accuracy and simplicity of the algorithm applied in this model, the modulation performances of these modulators can be acquired effectively and efficiently. Based on the model, the reflected spectra of these modulators were simulated under various acoustic frequencies and acoustically induced strains. The simulation results of the GA-FBG-AOM and PS-FBG-AOM showed that the wavelength spacing between the primary reflection peak and the secondary reflection peak is proportional to the acoustic frequency, and the reflectivity of reflection peaks depends on the acoustically induced strains. But for the LC-FBG-AOM, the wavelength spacing between the neighboring reflection peaks increased linearly and inversely with the acoustic frequency, and the extinction ratio of each peak relates to the acoustically induced strain. These numerical analysis results, which were effectively used in the designs and fabrications of these NU-FBG-AOMs, can broaden the AOM-based application scope and shed light on the performance optimization of optical wavelength-division multiplex system.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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2012 (2)

2011 (3)

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]

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]

X. Zeng, “Application of Fourier mode coupling theory to real-time analyses of nonuniform Bragg gratings,” IEEE Photon. Technol. Lett. 23, 854–856 (2011).

2008 (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, 4899–4905 (2008).
[CrossRef]

H. M. Chan, R. Huang, F. Alhassen, O. Finch, I. V. Tomov, C. Park, and H. P. Lee, “A compact all-fiber LPG-AOTF frequency shifter on single-mode fiber and its application to vibration measurement,” IEEE Photon. Technol. Lett. 20, 1572–1574 (2008).
[CrossRef]

2000 (2)

1997 (1)

1996 (1)

T. A. Birks, P. St. J. Russell, and D. O. Culverhouse, “The acousto-optic effect in single-mode fiber tapers and couplers,” J. Lightwave Technol. 14, 2519–2529 (1996).
[CrossRef]

1987 (1)

H. Taylor, “Acoustooptic modulators for single-mode fibers,” J. Lightwave Technol. 5, 990–992 (1987).
[CrossRef]

Alhassen, F.

H. M. Chan, R. Huang, F. Alhassen, O. Finch, I. V. Tomov, C. Park, and H. P. Lee, “A compact all-fiber LPG-AOTF frequency shifter on single-mode fiber and its application to vibration measurement,” IEEE Photon. Technol. Lett. 20, 1572–1574 (2008).
[CrossRef]

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]

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]

Birks, T. A.

T. A. Birks, P. St. J. Russell, and D. O. Culverhouse, “The acousto-optic effect in single-mode fiber tapers and couplers,” J. Lightwave Technol. 14, 2519–2529 (1996).
[CrossRef]

Bo, F.

Canning, J.

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]

Chan, H. M.

H. M. Chan, R. Huang, F. Alhassen, O. Finch, I. V. Tomov, C. Park, and H. P. Lee, “A compact all-fiber LPG-AOTF frequency shifter on single-mode fiber and its application to vibration measurement,” IEEE Photon. Technol. Lett. 20, 1572–1574 (2008).
[CrossRef]

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]

Cuadrado-Laborde, C.

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]

Culverhouse, D. O.

T. A. Birks, P. St. J. Russell, and D. O. Culverhouse, “The acousto-optic effect in single-mode fiber tapers and couplers,” J. Lightwave Technol. 14, 2519–2529 (1996).
[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]

Dong, L.

Finch, O.

H. M. Chan, R. Huang, F. Alhassen, O. Finch, I. V. Tomov, C. Park, and H. P. Lee, “A compact all-fiber LPG-AOTF frequency shifter on single-mode fiber and its application to vibration measurement,” IEEE Photon. Technol. Lett. 20, 1572–1574 (2008).
[CrossRef]

Gao, F.

Huang, L. G.

Huang, R.

H. M. Chan, R. Huang, F. Alhassen, O. Finch, I. V. Tomov, C. Park, and H. P. Lee, “A compact all-fiber LPG-AOTF frequency shifter on single-mode fiber and its application to vibration measurement,” IEEE Photon. Technol. Lett. 20, 1572–1574 (2008).
[CrossRef]

Lee, H. P.

H. M. Chan, R. Huang, F. Alhassen, O. Finch, I. V. Tomov, C. Park, and H. P. Lee, “A compact all-fiber LPG-AOTF frequency shifter on single-mode fiber and its application to vibration measurement,” IEEE Photon. Technol. Lett. 20, 1572–1574 (2008).
[CrossRef]

Li, Z. X.

Liu, C.

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]

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]

Ning, T. G.

Nogueira, R. N.

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]

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]

Park, C.

H. M. Chan, R. Huang, F. Alhassen, O. Finch, I. V. Tomov, C. Park, and H. P. Lee, “A compact all-fiber LPG-AOTF frequency shifter on single-mode fiber and its application to vibration measurement,” IEEE Photon. Technol. Lett. 20, 1572–1574 (2008).
[CrossRef]

Pei, L.

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.

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.

Taylor, H.

H. Taylor, “Acoustooptic modulators for single-mode fibers,” J. Lightwave Technol. 5, 990–992 (1987).
[CrossRef]

Tomov, I. V.

H. M. Chan, R. Huang, F. Alhassen, O. Finch, I. V. Tomov, C. Park, and H. P. Lee, “A compact all-fiber LPG-AOTF frequency shifter on single-mode fiber and its application to vibration measurement,” IEEE Photon. Technol. Lett. 20, 1572–1574 (2008).
[CrossRef]

Xu, J. J.

Xuan, L.

Yu, S. W.

Zeng, X.

X. Zeng, “Application of Fourier mode coupling theory to real-time analyses of nonuniform Bragg gratings,” IEEE Photon. Technol. Lett. 23, 854–856 (2011).

Zhang, G. Q.

Zhang, W. D.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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]

IEEE Photon. Technol. Lett. (2)

X. Zeng, “Application of Fourier mode coupling theory to real-time analyses of nonuniform Bragg gratings,” IEEE Photon. Technol. Lett. 23, 854–856 (2011).

H. M. Chan, R. Huang, F. Alhassen, O. Finch, I. V. Tomov, C. Park, and H. P. Lee, “A compact all-fiber LPG-AOTF frequency shifter on single-mode fiber and its application to vibration measurement,” IEEE Photon. Technol. Lett. 20, 1572–1574 (2008).
[CrossRef]

J. Lightwave Technol. (2)

T. A. Birks, P. St. J. Russell, and D. O. Culverhouse, “The acousto-optic effect in single-mode fiber tapers and couplers,” J. Lightwave Technol. 14, 2519–2529 (1996).
[CrossRef]

H. Taylor, “Acoustooptic modulators for single-mode fibers,” J. Lightwave Technol. 5, 990–992 (1987).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (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, 4899–4905 (2008).
[CrossRef]

Opt. Lett. (3)

Opt. Photon. News (1)

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]

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Figures (10)

Fig. 1.
Fig. 1.

Structure of the NU-FBG-AOM.

Fig. 2.
Fig. 2.

GA-FBG reflected spectra with AW applied at frequency of (a) 1.5 MHz and (b) 3.0 MHz.

Fig. 3.
Fig. 3.

Acoustic frequency versus wavelength spacing Δλ. The crosses are the calculated data, and the solid line is the fit for the data.

Fig. 4.
Fig. 4.

GA-FBG reflected spectra with AW applied under different amplitude of acoustically induced strain.

Fig. 5.
Fig. 5.

PS-FBG reflected spectra with AW applied at frequency of (a) 8.0 MHz and (b) 16.0 MHz.

Fig. 6.
Fig. 6.

Acoustic frequency versus wavelength spacing Δλ. The crosses are the calculated data, and the solid line is the fit for the data.

Fig. 7.
Fig. 7.

PS-FBG reflected spectra with AW applied with different amplitude of acoustically induced strain.

Fig. 8.
Fig. 8.

LC-FBG reflected spectra with AW applied at frequency of (a) 1.4 MHz and (b) 2.8 MHz.

Fig. 9.
Fig. 9.

Acoustic frequency versus wavelength spacing Δλ. The crosses are the calculated data, and the solid line is the fit for the data.

Fig. 10.
Fig. 10.

LC-FBG reflected spectra with AW applied with different amplitude of acoustically induced strain of (a) 80 με, (b) 120 με, (c) 160 με, and (d) 200 με.

Equations (10)

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s(z)=s0sin(kaz),ka=2π/λa,
Δn(z)=δn[1+exp(αz2L2)sin(2πΛz+s0λaΛsin(kaz))],L2zL2,
Δn(z)={δn[1+cos(2πΛz+s0λaΛsin(kaz))],0z<lδn[1+cos(2πΛz+ϕ+s0λaΛsin(kaz))],lzL,
Δn(z)=δn[1+cos(Kz+s0Kkasin(kaz))],K=2πΛπF2nmLΛ2z,0zL,
dAs(z)dz=jmksAm(z)Δn(z)ej(βm+βs)z,
ks=ε0ωn02SEm(r,ϕ)Es*(r,ϕ)dS,
As(z0)As(zL)dAs(z)Am(z)=jksz0zLΔn(z)ej(βm+βs)zdz.
Am2(z)=Am2(zL)+As2(z).
z0zLΔn(z)ej2πvszdz=γ(vs)+jη(vs)=Hejφ,
R=cos2(ksγ)sinh2(ksη)+sin2(ksγ)cosh2(ksη)1+cos2(ksγ)sinh2(ksη)+sin2(ksγ)cosh2(ksη)=tanh2(ksH).

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