Abstract

An all-fiber temporal photonic fractional Hilbert transform (FHT) based on a fiber Bragg grating (FBG) is proposed and investigated, for the first time to our knowledge. The photonic FHT is designed based on the discrete layer peeling method, which enables the FBG to have a strong strength. Numerical results show that the FBG can be used to efficiently and accurately implement broadband all-optical FHT for an arbitrary optical waveform with a bandwidth up to hundreds of gigahertz.

© 2010 Optical Society of America

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References

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2009 (1)

2008 (2)

2003 (1)

L. Venema, Nature Insight 424, 809 (2003).
[CrossRef]

2002 (2)

K. Tanaka, K. Takano, K. Kondo, and K. Nakagawa, Electron. Lett. 38, 133 (2002).
[CrossRef]

J. Azaña and L. R. Chen, J. Opt. Soc. Am. B 19, 2758 (2002).
[CrossRef]

2001 (1)

J. Skaar, L. Wang, and T. Erdogen, IEEE J. Quantum Electron. 37, 165 (2001).
[CrossRef]

2000 (1)

C. C. Tseng and S. C. Pei, IEEE Trans. Circuits Syst., II: Analog Digital Signal Process. 47, 1529 (2000).
[CrossRef]

1999 (1)

R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

1996 (1)

1995 (1)

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, Electron. Lett. 31, 1488 (1995).
[CrossRef]

Asghari, M. H.

Azaña, J.

Barcelos, S.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, Electron. Lett. 31, 1488 (1995).
[CrossRef]

Bui, L. A.

Chen, L. R.

Cole, M. J.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, Electron. Lett. 31, 1488 (1995).
[CrossRef]

Emami, H.

Erdogen, T.

J. Skaar, L. Wang, and T. Erdogen, IEEE J. Quantum Electron. 37, 165 (2001).
[CrossRef]

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R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

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S. L. Hahn, in The Transforms and Applications Handbook, 2nd ed., A.D.Poularikas, ed. (CRC Press, 2000).

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M. Hanawa, K. Nakamura, K. Takano, and K. Nakagawa, in Proceedings of the European Conference on Optical Communication (VDE-Verlag, 2007), paper 01.5.6.

Kondo, K.

K. Tanaka, K. Takano, K. Kondo, and K. Nakagawa, Electron. Lett. 38, 133 (2002).
[CrossRef]

K. Tanaka, K. Takano, K. Kondo, and K. Nakagawa, in Conference on Lasers and Electro-Optics (Optical Society of America, 2001), Vol. 11, pp. 554-555.

Laming, R. I.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, Electron. Lett. 31, 1488 (1995).
[CrossRef]

Loh, W. H.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, Electron. Lett. 31, 1488 (1995).
[CrossRef]

Lohmann, A. W.

Mendlovic, D.

Mitchell, A.

Muriel, M. A.

R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

Nakagawa, K.

K. Tanaka, K. Takano, K. Kondo, and K. Nakagawa, Electron. Lett. 38, 133 (2002).
[CrossRef]

K. Tanaka, K. Takano, K. Kondo, and K. Nakagawa, in Conference on Lasers and Electro-Optics (Optical Society of America, 2001), Vol. 11, pp. 554-555.

M. Hanawa, K. Nakamura, K. Takano, and K. Nakagawa, in Proceedings of the European Conference on Optical Communication (VDE-Verlag, 2007), paper 01.5.6.

Nakamura, K.

M. Hanawa, K. Nakamura, K. Takano, and K. Nakagawa, in Proceedings of the European Conference on Optical Communication (VDE-Verlag, 2007), paper 01.5.6.

Pei, S. C.

C. C. Tseng and S. C. Pei, IEEE Trans. Circuits Syst., II: Analog Digital Signal Process. 47, 1529 (2000).
[CrossRef]

Sarkhosh, N.

Skaar, J.

J. Skaar, L. Wang, and T. Erdogen, IEEE J. Quantum Electron. 37, 165 (2001).
[CrossRef]

Takano, K.

K. Tanaka, K. Takano, K. Kondo, and K. Nakagawa, Electron. Lett. 38, 133 (2002).
[CrossRef]

K. Tanaka, K. Takano, K. Kondo, and K. Nakagawa, in Conference on Lasers and Electro-Optics (Optical Society of America, 2001), Vol. 11, pp. 554-555.

M. Hanawa, K. Nakamura, K. Takano, and K. Nakagawa, in Proceedings of the European Conference on Optical Communication (VDE-Verlag, 2007), paper 01.5.6.

Tanaka, K.

K. Tanaka, K. Takano, K. Kondo, and K. Nakagawa, Electron. Lett. 38, 133 (2002).
[CrossRef]

K. Tanaka, K. Takano, K. Kondo, and K. Nakagawa, in Conference on Lasers and Electro-Optics (Optical Society of America, 2001), Vol. 11, pp. 554-555.

Tseng, C. C.

C. C. Tseng and S. C. Pei, IEEE Trans. Circuits Syst., II: Analog Digital Signal Process. 47, 1529 (2000).
[CrossRef]

Venema, L.

L. Venema, Nature Insight 424, 809 (2003).
[CrossRef]

Wang, L.

J. Skaar, L. Wang, and T. Erdogen, IEEE J. Quantum Electron. 37, 165 (2001).
[CrossRef]

Zalevsky, Z.

Zervas, M. N.

R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, Electron. Lett. 31, 1488 (1995).
[CrossRef]

Electron. Lett. (2)

K. Tanaka, K. Takano, K. Kondo, and K. Nakagawa, Electron. Lett. 38, 133 (2002).
[CrossRef]

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, Electron. Lett. 31, 1488 (1995).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogen, IEEE J. Quantum Electron. 37, 165 (2001).
[CrossRef]

IEEE Trans. Circuits Syst., II: Analog Digital Signal Process. (1)

C. C. Tseng and S. C. Pei, IEEE Trans. Circuits Syst., II: Analog Digital Signal Process. 47, 1529 (2000).
[CrossRef]

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

Nature Insight (1)

L. Venema, Nature Insight 424, 809 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Other (3)

S. L. Hahn, in The Transforms and Applications Handbook, 2nd ed., A.D.Poularikas, ed. (CRC Press, 2000).

K. Tanaka, K. Takano, K. Kondo, and K. Nakagawa, in Conference on Lasers and Electro-Optics (Optical Society of America, 2001), Vol. 11, pp. 554-555.

M. Hanawa, K. Nakamura, K. Takano, and K. Nakagawa, in Proceedings of the European Conference on Optical Communication (VDE-Verlag, 2007), paper 01.5.6.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram showing the (a) magnitude response and (b) phase response of an ideal (solid lines) and a practically realizable (dotted lines) photonic FHT.

Fig. 2
Fig. 2

(a) Magnitude and phase responses of the designed photonic FHT based on a 3 cm multiple-phase-shifted FBG; (b) the index modulation and phase profile of the designed photonic FHT.

Fig. 3
Fig. 3

(a) Numerical results for the photonic FHTs designed based on the DLP and SFTM methods and based on an ideal FHT when the input is a first-order Hermite–Gaussian pulse. (b) NRMSEs of the PHTs based on the DLP and SFTM methods for different reflectivities.

Fig. 4
Fig. 4

(a) Simulated temporal response of a photonic FHT for a fractional order of four different values. The envelope of the input optical signal and the envelope of the output signal for (b) P = 0.5 , (c) P = 1.0 , (d) P = 1.5 , and (e) P = 2.0 .

Equations (2)

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H FHT ( ω ) = cos φ + sin ( φ ) × [ j sgn ( ω ) ] = { e j φ , ω > 0 0 , ω = 0 e j φ , ω < 0 } ,
r ( ω ) = R exp { ln 2 [ ω 0.5 ω FWHM ] m } exp [ j ϕ ( ω ) ] ,

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