Abstract

The dispersion experienced by a signal in a slow light system leads to a significant pulse broadening and sets a limit to the maximum delay actually achievable by the system. To overcome this limitation, a substantial research effort is currently being carried out, and successful strategies to reduce distortion in linear slow light systems have already been demonstrated. Recent theoretical and experimental works have even claimed the achievement of zero-broadening of pulses in these systems. In this work we obtain some physical limits to broadening compensation in linear slow light systems based on simple Fourier analysis. We show that gain and dispersion broadening can never compensate in such a system. Additionally, it is simply proven that all the linear slow light systems that introduce a low-pass filtering of the signal (a reduction in the signal root-mean-square spectral width), will always cause pulse broadening. These demonstrations are done using a rigorous shape-independent definition of pulse width (the root-mean-square temporal width) and arguments borrowed from time-frequency analysis.

© 2009 Optical Society of America

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References

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  1. M. Gonzalez Herráez, K. Y. Song, and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87, 081113 (2005).
    [CrossRef]
  2. M. González Herráez, K. Y. Song, and L. Thévenaz, "Arbitrary-bandwidth Brillouin slow light in optical fibers," Opt. Express 14, 1395-1400 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-4-1395
    [CrossRef]
  3. M. D. Stenner, M. A. Neifeld, Z. Zhu, A. M. C. Dawes, and D. J. Gauthier, "Distortion management in slow-light pulse delay," Opt. Express 13, 9995-10002 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-25-9995
    [CrossRef] [PubMed]
  4. R. Pant, M. D. Stenner, M. A. Neifeld, and D. J. Gauthier, "Optimal pump profile designs for broadband SBS slow-light systems," Opt. Express 16, 2764-2777 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-4-2764
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. S. Wang, L. Ren, Y. Liu, and Y. Tomita, "Zero-broadening SBS slow light propagation in an optical fiber using two broadband pump beams," Opt. Express 16, 8067-8076 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-11-8067
    [CrossRef] [PubMed]
  8. T. Schneider, A. Wiatrek, and R. Henker, "Zero-broadening and pulse compression slow light in an optical fiber at high pulse delays," Opt. Express 16, 15617-15622 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15617
    [CrossRef] [PubMed]
  9. R. Trebino "Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses" Springer, (2002).
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    [CrossRef]
  11. R. M. Camacho, M. V. Pack, and J. C. Howell, "Low-distortion slow light using two absorption resonances", Phys. Rev. A,  73, 063812 (2006).
    [CrossRef]
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    [CrossRef]
  14. G. Folland and A. Sitaram, "The Uncertainty Principle: A Mathematical Survey," J. Fourier Anal. Appl. 3, 207-238 (1997).
    [CrossRef]
  15. L. Ren and Y. Tomita, "Reducing group-velocity-dispersion-dependent broadening of stimulated Brillouin scattering slow light in an optical fiber by use of a single pump laser," J. Opt. Soc. Am. B 25, 741-746 (2008), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-25-5-741
    [CrossRef]
  16. A. Wiatrek, R. Henker, S. Preußler, M. J. Ammann, A. T. Schwarzbacher, and T. Schneider, "Zero-broadening measurement in Brillouin based slow-light delays," Opt. Express 17, 797-802 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-2-797
    [CrossRef] [PubMed]

2009

2008

2007

2006

2005

M. Gonzalez Herráez, K. Y. Song, and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

M. D. Stenner, M. A. Neifeld, Z. Zhu, A. M. C. Dawes, and D. J. Gauthier, "Distortion management in slow-light pulse delay," Opt. Express 13, 9995-10002 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-25-9995
[CrossRef] [PubMed]

1997

G. Folland and A. Sitaram, "The Uncertainty Principle: A Mathematical Survey," J. Fourier Anal. Appl. 3, 207-238 (1997).
[CrossRef]

Ammann, M. J.

Boyd, R. W.

R. W. Boyd and P. Narum, "Slow- and fast-light: fundamental limitations," J. Mod. Opt. 54, 2403-2411 (2007).
[CrossRef]

Camacho, R. M.

R. M. Camacho, M. V. Pack, and J. C. Howell, "Low-distortion slow light using two absorption resonances", Phys. Rev. A,  73, 063812 (2006).
[CrossRef]

Dawes, A. M. C.

Eyal, A.

Folland, G.

G. Folland and A. Sitaram, "The Uncertainty Principle: A Mathematical Survey," J. Fourier Anal. Appl. 3, 207-238 (1997).
[CrossRef]

Gauthier, D. J.

Gonzalez Herráez, M.

M. Gonzalez Herráez, K. Y. Song, and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

González Herráez, M.

Henker, R.

Howell, J. C.

R. M. Camacho, M. V. Pack, and J. C. Howell, "Low-distortion slow light using two absorption resonances", Phys. Rev. A,  73, 063812 (2006).
[CrossRef]

Khurgin, J. B.

Liu, Y.

Narum, P.

R. W. Boyd and P. Narum, "Slow- and fast-light: fundamental limitations," J. Mod. Opt. 54, 2403-2411 (2007).
[CrossRef]

Neifeld, M. A.

Pack, M. V.

R. M. Camacho, M. V. Pack, and J. C. Howell, "Low-distortion slow light using two absorption resonances", Phys. Rev. A,  73, 063812 (2006).
[CrossRef]

Pant, R.

Preußler, S.

Ren, L.

Schneider, T.

Schwarzbacher, A. T.

Sitaram, A.

G. Folland and A. Sitaram, "The Uncertainty Principle: A Mathematical Survey," J. Fourier Anal. Appl. 3, 207-238 (1997).
[CrossRef]

Song, K. Y.

M. González Herráez, K. Y. Song, and L. Thévenaz, "Arbitrary-bandwidth Brillouin slow light in optical fibers," Opt. Express 14, 1395-1400 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-4-1395
[CrossRef]

M. Gonzalez Herráez, K. Y. Song, and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

Stenner, M. D.

Thévenaz, L.

M. González Herráez, K. Y. Song, and L. Thévenaz, "Arbitrary-bandwidth Brillouin slow light in optical fibers," Opt. Express 14, 1395-1400 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-4-1395
[CrossRef]

M. Gonzalez Herráez, K. Y. Song, and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

Tomita, Y.

Tur, M.

Wang, S.

Wiatrek, A.

Zadok, A.

Zhu, Z.

Appl. Phys. Lett.

M. Gonzalez Herráez, K. Y. Song, and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

J. Fourier Anal. Appl.

G. Folland and A. Sitaram, "The Uncertainty Principle: A Mathematical Survey," J. Fourier Anal. Appl. 3, 207-238 (1997).
[CrossRef]

J. Mod. Opt.

R. W. Boyd and P. Narum, "Slow- and fast-light: fundamental limitations," J. Mod. Opt. 54, 2403-2411 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

S. Wang, L. Ren, Y. Liu, and Y. Tomita, "Zero-broadening SBS slow light propagation in an optical fiber using two broadband pump beams," Opt. Express 16, 8067-8076 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-11-8067
[CrossRef] [PubMed]

T. Schneider, A. Wiatrek, and R. Henker, "Zero-broadening and pulse compression slow light in an optical fiber at high pulse delays," Opt. Express 16, 15617-15622 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15617
[CrossRef] [PubMed]

A. Wiatrek, R. Henker, S. Preußler, M. J. Ammann, A. T. Schwarzbacher, and T. Schneider, "Zero-broadening measurement in Brillouin based slow-light delays," Opt. Express 17, 797-802 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-2-797
[CrossRef] [PubMed]

A. Zadok, A. Eyal, and M. Tur, "Extended delay of broadband signals in stimulated Brillouin scattering slow light using synthesized pump chirp," Opt. Express 14, 8498-8505 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-19-8498
[CrossRef] [PubMed]

R. Pant, M. D. Stenner, M. A. Neifeld, and D. J. Gauthier, "Optimal pump profile designs for broadband SBS slow-light systems," Opt. Express 16, 2764-2777 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-4-2764
[CrossRef] [PubMed]

M. D. Stenner, M. A. Neifeld, Z. Zhu, A. M. C. Dawes, and D. J. Gauthier, "Distortion management in slow-light pulse delay," Opt. Express 13, 9995-10002 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-25-9995
[CrossRef] [PubMed]

M. González Herráez, K. Y. Song, and L. Thévenaz, "Arbitrary-bandwidth Brillouin slow light in optical fibers," Opt. Express 14, 1395-1400 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-4-1395
[CrossRef]

Opt. Lett.

Phys. Rev. A

R. M. Camacho, M. V. Pack, and J. C. Howell, "Low-distortion slow light using two absorption resonances", Phys. Rev. A,  73, 063812 (2006).
[CrossRef]

Other

L. Cohen, "Time-Frequency Analysis" Prentice-Hall (1995).

R. Trebino "Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses" Springer, (2002).

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Figures (3)

Fig. 1.
Fig. 1.

Input (blue) and output (grey and red) waveforms for the gain medium combining a broadband gain and 2 lateral narrowband losses (sample spectrum shown in the inset). The frequency separation between the loss resonances is varied from 100 to 400 MHz. Red curve corresponds to a separation of 130 MHz between the loss resonances, grey curves to larger separations.

Fig. 2.
Fig. 2.

Pulse broadening as a function of the frequency separation between the two loss resonances. The measurement of pulse broadening based on the RMS or the FWHM values results in very different estimations when the system operates in the “pulse splitting” regime (frequency separations below180 MHz).

Fig. 3.
Fig. 3.

Transmission of a “101” sequence in the slow light medium described above for the cases of loss resonances separation of 400 MHz (grey curve) and 130 MHz (red curve). The input sequence is shown in blue. In the “pulse splitting” regime in red (“FWHM zero-broadening”), the distortion experienced is so strong that the extraction of the information turns out to be impossible and leads to a severe intersymbol interference.

Equations (5)

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

σ t 2 = 1 E + t 2 A ( t ) 2 dt
E = + A ( t ) 2 dt
σ t 2 = 1 E [ + dA ( ω ) 2 + + A ( ω ) 2 ( ( ω ) ) 2 ]
σ ω 2 = 1 2 π E + ω 2 A ( ω ) 2
σ t σ ω 1 2

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