Abstract

In this paper a microwave photonic filter using superstructured fiber Bragg grating and dispersive fiber is investigated. A theoretical model to describe the transfer function of the filter taking into consideration the spectral width of light source is established. Experiments are carried out to verify the theoretical analysis. Both theoretical and experimental results indicate that due to chromatic dispersion the source spectral width introduces an additional power penalty to the microwave photonic response of the filter.

©2005 Optical Society of America

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References

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  • Publication
  1. B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, “Fibre-optic lattice signal processing,” Proc. IEE 72, 909–930 (1984)
    [Crossref]
  2. R. A. Minasian, “Photonic Signal Processing of High-Speed Signals Using Fibre Gratings,” Opt. Fiber Technol. 6, 91–108 (2000)
    [Crossref]
  3. B. A. L. Gwandu, W. Zhang, J. A. R. Williams, L. Zhang, and I. Bennion, “Microwave photonic filtering using Gaussian-profiled superstructured fibre Bragg grating and dispersive fibre,” Electron. Lett. 38, 1328–1330, (2002)
    [Crossref]
  4. J. S. Leng, W. Zhang, and J. A. R. Williams, “Optimisation of superstructured fibre Bragg gratings for microwave photonic filters response,” IEEE Photonics Technol. Lett. 16, 1736–1738 (2004)
    [Crossref]
  5. H. Schmuck, “Comparison of optical millimetre wave system concepts with regard to chromatic dispersion,” Electron. Lett. 31, 1848–1849 (1995)
    [Crossref]
  6. G. J. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employinh direct detection,” IEEE J. Quantum Electron. 20, 1208–1216 (1984)
    [Crossref]
  7. W. Zhang, J. A. R. Williams, and I. Bennion, “Analysis of Frequency Response of a Microwave Photonic Filter using Superstructured Fiber Bragg Grating,” in Proceedings of 17th Annual Meeting of the IEEE-Lasers-and-Electro-Optics-Society, (Porto Rico, 2004), pp. 276–277.
  8. D. Marcuse, “Pulse distortion in single-mode fibers,” Appl. Opt.,  19, 1653–1660 (1980)
    [Crossref] [PubMed]

2004 (1)

J. S. Leng, W. Zhang, and J. A. R. Williams, “Optimisation of superstructured fibre Bragg gratings for microwave photonic filters response,” IEEE Photonics Technol. Lett. 16, 1736–1738 (2004)
[Crossref]

2002 (1)

B. A. L. Gwandu, W. Zhang, J. A. R. Williams, L. Zhang, and I. Bennion, “Microwave photonic filtering using Gaussian-profiled superstructured fibre Bragg grating and dispersive fibre,” Electron. Lett. 38, 1328–1330, (2002)
[Crossref]

2000 (1)

R. A. Minasian, “Photonic Signal Processing of High-Speed Signals Using Fibre Gratings,” Opt. Fiber Technol. 6, 91–108 (2000)
[Crossref]

1995 (1)

H. Schmuck, “Comparison of optical millimetre wave system concepts with regard to chromatic dispersion,” Electron. Lett. 31, 1848–1849 (1995)
[Crossref]

1984 (2)

G. J. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employinh direct detection,” IEEE J. Quantum Electron. 20, 1208–1216 (1984)
[Crossref]

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, “Fibre-optic lattice signal processing,” Proc. IEE 72, 909–930 (1984)
[Crossref]

1980 (1)

Bennion, I.

B. A. L. Gwandu, W. Zhang, J. A. R. Williams, L. Zhang, and I. Bennion, “Microwave photonic filtering using Gaussian-profiled superstructured fibre Bragg grating and dispersive fibre,” Electron. Lett. 38, 1328–1330, (2002)
[Crossref]

W. Zhang, J. A. R. Williams, and I. Bennion, “Analysis of Frequency Response of a Microwave Photonic Filter using Superstructured Fiber Bragg Grating,” in Proceedings of 17th Annual Meeting of the IEEE-Lasers-and-Electro-Optics-Society, (Porto Rico, 2004), pp. 276–277.

Goodman, J. W.

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, “Fibre-optic lattice signal processing,” Proc. IEE 72, 909–930 (1984)
[Crossref]

Gwandu, B. A. L.

B. A. L. Gwandu, W. Zhang, J. A. R. Williams, L. Zhang, and I. Bennion, “Microwave photonic filtering using Gaussian-profiled superstructured fibre Bragg grating and dispersive fibre,” Electron. Lett. 38, 1328–1330, (2002)
[Crossref]

Leng, J. S.

J. S. Leng, W. Zhang, and J. A. R. Williams, “Optimisation of superstructured fibre Bragg gratings for microwave photonic filters response,” IEEE Photonics Technol. Lett. 16, 1736–1738 (2004)
[Crossref]

Marcuse, D.

Meslener, G. J.

G. J. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employinh direct detection,” IEEE J. Quantum Electron. 20, 1208–1216 (1984)
[Crossref]

Minasian, R. A.

R. A. Minasian, “Photonic Signal Processing of High-Speed Signals Using Fibre Gratings,” Opt. Fiber Technol. 6, 91–108 (2000)
[Crossref]

Moslehi, B.

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, “Fibre-optic lattice signal processing,” Proc. IEE 72, 909–930 (1984)
[Crossref]

Schmuck, H.

H. Schmuck, “Comparison of optical millimetre wave system concepts with regard to chromatic dispersion,” Electron. Lett. 31, 1848–1849 (1995)
[Crossref]

Shaw, H. J.

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, “Fibre-optic lattice signal processing,” Proc. IEE 72, 909–930 (1984)
[Crossref]

Tur, M.

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, “Fibre-optic lattice signal processing,” Proc. IEE 72, 909–930 (1984)
[Crossref]

Williams, J. A. R.

J. S. Leng, W. Zhang, and J. A. R. Williams, “Optimisation of superstructured fibre Bragg gratings for microwave photonic filters response,” IEEE Photonics Technol. Lett. 16, 1736–1738 (2004)
[Crossref]

B. A. L. Gwandu, W. Zhang, J. A. R. Williams, L. Zhang, and I. Bennion, “Microwave photonic filtering using Gaussian-profiled superstructured fibre Bragg grating and dispersive fibre,” Electron. Lett. 38, 1328–1330, (2002)
[Crossref]

W. Zhang, J. A. R. Williams, and I. Bennion, “Analysis of Frequency Response of a Microwave Photonic Filter using Superstructured Fiber Bragg Grating,” in Proceedings of 17th Annual Meeting of the IEEE-Lasers-and-Electro-Optics-Society, (Porto Rico, 2004), pp. 276–277.

Zhang, L.

B. A. L. Gwandu, W. Zhang, J. A. R. Williams, L. Zhang, and I. Bennion, “Microwave photonic filtering using Gaussian-profiled superstructured fibre Bragg grating and dispersive fibre,” Electron. Lett. 38, 1328–1330, (2002)
[Crossref]

Zhang, W.

J. S. Leng, W. Zhang, and J. A. R. Williams, “Optimisation of superstructured fibre Bragg gratings for microwave photonic filters response,” IEEE Photonics Technol. Lett. 16, 1736–1738 (2004)
[Crossref]

B. A. L. Gwandu, W. Zhang, J. A. R. Williams, L. Zhang, and I. Bennion, “Microwave photonic filtering using Gaussian-profiled superstructured fibre Bragg grating and dispersive fibre,” Electron. Lett. 38, 1328–1330, (2002)
[Crossref]

W. Zhang, J. A. R. Williams, and I. Bennion, “Analysis of Frequency Response of a Microwave Photonic Filter using Superstructured Fiber Bragg Grating,” in Proceedings of 17th Annual Meeting of the IEEE-Lasers-and-Electro-Optics-Society, (Porto Rico, 2004), pp. 276–277.

Appl. Opt. (1)

Electron. Lett. (2)

H. Schmuck, “Comparison of optical millimetre wave system concepts with regard to chromatic dispersion,” Electron. Lett. 31, 1848–1849 (1995)
[Crossref]

B. A. L. Gwandu, W. Zhang, J. A. R. Williams, L. Zhang, and I. Bennion, “Microwave photonic filtering using Gaussian-profiled superstructured fibre Bragg grating and dispersive fibre,” Electron. Lett. 38, 1328–1330, (2002)
[Crossref]

IEEE J. Quantum Electron. (1)

G. J. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employinh direct detection,” IEEE J. Quantum Electron. 20, 1208–1216 (1984)
[Crossref]

IEEE Photonics Technol. Lett. (1)

J. S. Leng, W. Zhang, and J. A. R. Williams, “Optimisation of superstructured fibre Bragg gratings for microwave photonic filters response,” IEEE Photonics Technol. Lett. 16, 1736–1738 (2004)
[Crossref]

Opt. Fiber Technol. (1)

R. A. Minasian, “Photonic Signal Processing of High-Speed Signals Using Fibre Gratings,” Opt. Fiber Technol. 6, 91–108 (2000)
[Crossref]

Proc. IEE (1)

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, “Fibre-optic lattice signal processing,” Proc. IEE 72, 909–930 (1984)
[Crossref]

Other (1)

W. Zhang, J. A. R. Williams, and I. Bennion, “Analysis of Frequency Response of a Microwave Photonic Filter using Superstructured Fiber Bragg Grating,” in Proceedings of 17th Annual Meeting of the IEEE-Lasers-and-Electro-Optics-Society, (Porto Rico, 2004), pp. 276–277.

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Figures (9)
Fig. 1.
Fig. 1. Measured optical reflection spectrum of a superstructured Bragg grating.

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Fig. 2.
Fig. 2. Diagram of the microwave photonic filter using SFBG and dispersive fiber.

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Fig. 3.
Fig. 3. Simulated responses without considering the source spectral width. i: ideal 8-tap response, ii: 8-tap response of 25km fiber, iii: 1-tap response of 25km fiber.

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Fig. 4.
Fig. 4. Measured and simulated responses of 25km fiber. i: measured 8-tap response, ii: simulated 8-tap response with zero source spectral width, iii 1-tap response with zero source spectral width.

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Fig. 5.
Fig. 5. Optical spectra of the central reflection channel of an SFBG

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Fig. 6.
Fig. 6. Measured and simulated responses of 25km fiber in consideration of a spectral width of 0.12 nm. i: simulated 1-tap response, ii: measured 8-tap response, iii: simulated 8-tap response.

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Fig. 7.
Fig. 7. Measured and simulated responses of 50 km fiber in consideration of a spectral width of 0.09 nm. i: simulated 1-tap response, ii: measured 8-tap response, iii: simulated 8-tap response.

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Fig. 8.
Fig. 8. Measured and simulated 1-tap responses of 25 km fiber.

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Fig. 9.
Fig. 9. (a) Filter output at fixed frequency vs. source spectral width. (b) Operational bandwidth vs. source spectral width.

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Equations (19)

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ψ ( t ) = f ( t ) ψ 0 ( t )
≈ [ I 0 + I 1 cos ( Ω t ) ] ψ 0 ( t )
ψ ( t ) ≈ [ J 0 ( m ) − 2 J 1 ( m ) cos ( Ω t ) ] ψ 0 ( t )
ϕ ( ω ) = 1 2 π ∫ − ∞ ∞ ψ ( t ) exp ( − iωt ) dt
= 1 2 π ∫ − ∞ ∞ ψ 0 ( t ) f ( t ) exp ( − iωt ) dt
= ∫ − ∞ ∞ ϕ 0 ( ω ′ ) F ( ω − ω ′ ) dω ′
ψ z t = ∫ − ∞ ∞ ϕ ( ω ) exp [ i ( ωt − βz ) ] dω
〈 P z t 〉 = ∫ − ∞ ∞ ∣ ϕ ̂ 0 ( ω 0 − ω ′ ) ∣ 2 · ∣ ∫ − ∞ ∞ F ( ω − ω ′ ) exp { i [ ( ω − ω ′ ) t − ( β − β ′ ) z ] } dω ∣ 2 dω ′
β = β 0 + β ˙ 0 ( ω − ω 0 ) + 1 2 β ̈ 0 ( ω − ω 0 ) 2 + ⋯
η ( ω ′ ) = ∫ − ∞ ∞ F ( ω − ω ′ ) exp { i [ ( ω − ω ′ ) t − ( β − β ′ ) z ] } dω
= ∫ − ∞ ∞ { J 0 ( m ) δ ( ω − ω ′ ) − J 1 ( m ) [ δ ( ω − ω ′ − Ω ) + δ ( ω − ω ′ + Ω ) ] } exp { i [ ( ω − ω ′ ) t − ( β − β ′ ) z ] } dω
= J 0 − J 1 cos { Ω t − Ω z [ β ˙ 0 + β ̈ 0 ( ω ′ − ω 0 ) ] } exp ( − i 1 2 β ̈ 0 Ω 2 z )
∣ η ( ω ′ ) ∣ 2 = J 0 2 − 2 J 0 J 1 cos { Ω t − Ω z [ β ˙ 0 + β ̈ 0 ( ω ′ − ω 0 ) ] } cos ( 1 2 β ̈ 0 Ω 2 z )
+ J 1 2 cos 2 { Ω t − Ω z [ β ˙ 0 + β ̈ 0 ( ω ′ − ω 0 ) ] }
∣ ϕ ̂ 0 ( ω − ω 0 ) ∣ 2 = P 0 π 1 2 W exp [ − ( ω − ω 0 ) 2 W 2 ]
〈 ∣ P z t ∣ 2 〉 = ∫ − ∞ ∞ P 0 π 1 2 W exp [ − ( ω ′ − ω 0 ) 2 W 2 ] ∣ η ( ω ′ ) ∣ 2 dω ′
= P 0 { J 0 2 + 1 2 J 1 2 + 2 J 0 J 1 exp [ − ( W β ̈ 0 Ω z 2 ) 2 ] cos ( β ̈ 0 Ω 2 z 2 ) cos [ Ω ( t − β ˙ 0 z ) ]
+ 1 2 J 1 2 exp [ − ( W β ̈ 0 Ω z ) 2 ] cos [ 2 Ω ( t − β ˙ 0 z ) ] }
I ∣ Ω ∝ 2 P 0 J 0 J 1 exp [ − ( W β ̈ 0 Ω z 2 ) 2 ] cos ( β ̈ 0 Ω 2 z 2 )

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