Abstract

A simple all-fiber design for implementing an all-optical temporal Hilbert transformer is proposed and numerically demonstrated. We show that an all-optical Hilbert transformer can be implemented using a uniform-period fiber Bragg grating (FBG) with a properly designed amplitude-only grating apodization profile incorporating a single π phase shift in the middle of the grating length. All-optical Hilbert transformers capable of processing arbitrary optical waveforms with bandwidths up to a few hundreds of gigahertz can be implemented using feasible FBGs.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. L. Hahn, in The Transforms and Applications Handbook, 2nd ed., A.D.Poularikas, ed. (CRC Press, 2000), p. 551.
  2. K. Takano, N. Hanzawa, S. Tanji, and K. Nakagawa, in Optical Fiber Communication Conference, OSA Technical Digest Series (CD), (Optical Society of America, 2007), paper JThA48.
  3. H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, Opt. Lett. 33, 98 (2008).
    [CrossRef] [PubMed]
  4. H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, Opt. Express 16, 13707 (2008).
    [CrossRef] [PubMed]
  5. M. Hanawa, K. Nakamura, K. Takano, and K. Nakagawa, in Proceedings of the European Conference on Optical Communication (ECOC) (VDE-Verlag, 2007), paper 01.5.6.
  6. J. Azaña and L. R. Chen, J. Opt. Soc. Am. B 19, 2758 (2002).
    [CrossRef]
  7. T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
    [CrossRef]

2008 (2)

2007 (2)

K. Takano, N. Hanzawa, S. Tanji, and K. Nakagawa, in Optical Fiber Communication Conference, OSA Technical Digest Series (CD), (Optical Society of America, 2007), paper JThA48.

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

2002 (1)

2000 (1)

S. L. Hahn, in The Transforms and Applications Handbook, 2nd ed., A.D.Poularikas, ed. (CRC Press, 2000), p. 551.

1997 (1)

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

Azaña, J.

Bui, L. A.

Chen, L. R.

Emami, H.

Erdogan, T.

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

Hahn, S. L.

S. L. Hahn, in The Transforms and Applications Handbook, 2nd ed., A.D.Poularikas, ed. (CRC Press, 2000), p. 551.

Hanawa, M.

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

Hanzawa, N.

K. Takano, N. Hanzawa, S. Tanji, and K. Nakagawa, in Optical Fiber Communication Conference, OSA Technical Digest Series (CD), (Optical Society of America, 2007), paper JThA48.

Mitchell, A.

Nakagawa, K.

K. Takano, N. Hanzawa, S. Tanji, and K. Nakagawa, in Optical Fiber Communication Conference, OSA Technical Digest Series (CD), (Optical Society of America, 2007), paper JThA48.

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

Sarkhosh, N.

Takano, K.

K. Takano, N. Hanzawa, S. Tanji, and K. Nakagawa, in Optical Fiber Communication Conference, OSA Technical Digest Series (CD), (Optical Society of America, 2007), paper JThA48.

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

Tanji, S.

K. Takano, N. Hanzawa, S. Tanji, and K. Nakagawa, in Optical Fiber Communication Conference, OSA Technical Digest Series (CD), (Optical Society of America, 2007), paper JThA48.

J. Lightwave Technol. (1)

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (1)

Other (3)

S. L. Hahn, in The Transforms and Applications Handbook, 2nd ed., A.D.Poularikas, ed. (CRC Press, 2000), p. 551.

K. Takano, N. Hanzawa, S. Tanji, and K. Nakagawa, in Optical Fiber Communication Conference, OSA Technical Digest Series (CD), (Optical Society of America, 2007), paper JThA48.

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Schematic showing the (a) baseband spectral transfer function and (b) envelope of the temporal impulse response of an ideal PHT (dotted curves) and the physically realizable PHT proposed in this Letter (solid curves).

Fig. 2
Fig. 2

Spectral and temporal responses of a PHT based on a 2 - cm -long mid-strength uniform-period FBG with the apodization profile plotted in the inset of Fig. 2b. (a) Reflectivity as a function of optical frequency deviation (around 193 THz ); the insets show the phase change of the reflection FBG spectral response and corresponding amplitude in decibels around the central frequency. (b) Envelope amplitude of the reflection temporal impulse response (solid curve) shown in normalized units [n.u.]. The impulse response amplitude of an ideal bandwidth-limited PHT is also shown (circles).

Fig. 3
Fig. 3

Results from numerical simulations for the designed PHT assuming an input signal (complex envelope); (a) 50 GHZ sinusoid; (b) first-order derivative of a Gaussian pulse with FWHM = 15 ps . Each plot shows the input temporal envelope (dashed curve), the envelope of the reflected optical signal from the FBG-based PHT (solid curve), and the numerically calculated ideal Hilbert transform of the input temporal envelope (circles).

Equations (3)

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

y ( t ) P.V. [ τ = x ( τ ) t τ d τ ] ,
h ( t ) ( I 1 { H r ( f ) } × Π ( t Δ T ) ) δ ( t T c ) ( [ I 1 { Π ( f + Δ f 4 Δ f 2 ) } + I 1 { Π ( f Δ f 4 Δ f 2 ) } ] × Π ( t Δ T ) ) δ ( t T c ) sin 2 ( π ( t T c ) Δ f 2 ) ( t T c ) Π ( t T c Δ T ) ,
Δ n ( z ) sin 2 ( π n av Δ f ( z z c ) c ) ( z z c ) ,

Metrics