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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 16 — Aug. 6, 2007
  • pp: 10189–10195
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Storage capacity of slow-light tunable optical buffers based on fiber Brillouin amplifiers for real signal bit streams

Liang Xing, Li Zhan, Lilin Yi, and Yuxing Xia  »View Author Affiliations


Optics Express, Vol. 15, Issue 16, pp. 10189-10195 (2007)
http://dx.doi.org/10.1364/OE.15.010189


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Abstract

We present a theoretical analysis of the slow-light tunable optical buffers based on fiber Brillouin amplifiers (FBA). Its storage capacity was discussed for return-to-zero (RZ) and non-return-to-zero (NRZ) bit streams. Gain saturation and pulse broadening are two key factors which limit the buffer capacity. Gain saturation is an inherent characteristic of the FBA. Broadening of the amplified pulse always accumulates with increasing gain owing to the dispersion during stimulated Brillouin scattering (SBS) process. It is shown that the maximum buffer capacity varies with data bit rate and for continuous wave (CW) or quasi-CW pump it is 0.53 and 1.04 bit for RZ and NRZ respectively. Also, the optimum data bit rate to achieve the best storage capacity is obtained.

© 2007 Optical Society of America

1. Introduction

Tunable optical buffers (TOB) are key components in future all-optical routers (AOR). The lack of feasible AOR is a well-known bottleneck of all-optical communication network. To realize the TOB, one needs to control the group velocity of light. In the last two years, slowlight using the dispersion associated with a laser-induced amplifying resonance, such as SBS in optical fiber, has been widely studied both experimentally and theoretically. Compared with former schemes, SBS seems to be the most promising one for its large fractional delay, roomtemperature operation, low threshold, possibility of inducing delays at any wavelength, and compatibility with existing optical communication systems.

In early SBS slow-light experiments [1

1. K. Y. Song, M. G. Herraez, and L. Thevenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82–88 (2005). [CrossRef] [PubMed]

, 2

2. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005). [CrossRef] [PubMed]

], the delay is relatively small and the applicable bandwidth is limited by tens of MHz due to the narrow gain bandwidth. Further experiments extend the delay to several pulse widths by employing cascaded scheme [3

3. K. Y. Song, M. G. Herraez, and L. Thevenaz, “Long optically controlled delays in optical fibers,” Opt. Lett. 30, 1782–1784 (2005). [CrossRef] [PubMed]

] and increase the bandwidth to hundreds of MHz [4

4. M. G. Herraez, K. Y. Song, and L. Thevenaz, “Arbitrary-bandwidth Brillouin slow light in optical fibers,” Opt. Express 14, 1395–1400 (2006). [CrossRef]

], and 12GHz [5

5. Z. M. Zhu, M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “12-GHz-Bandwidth SBS slow light in optical fibers,” in proceedings of OFC 2006, paper PDP1.

] by using a modulated pump, even exceed 25GHz by employing a double pump method [6

6. K. Y. Song and K. Hotate, “25 GHz bandwidth Brillouin slow light in optical fibers,” Opt. Lett. 32, 217–219 (2007). [CrossRef] [PubMed]

]. However, pulse distortion is an inevitable phenomenon in all SBS slow-light experiments, although it can be reduced, at the cost of more pump consuming, by using a broadband pump which can be achieved by using a variety of modulating schemes [4

4. M. G. Herraez, K. Y. Song, and L. Thevenaz, “Arbitrary-bandwidth Brillouin slow light in optical fibers,” Opt. Express 14, 1395–1400 (2006). [CrossRef]

, 5

5. Z. M. Zhu, M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “12-GHz-Bandwidth SBS slow light in optical fibers,” in proceedings of OFC 2006, paper PDP1.

, 7

7. A. Minardo, R. Bernini, and L. Zeni, “Low distortion Brillouin slow light in optical fibers using AM modulation,” Opt. Express 14, 5866–5876 (2006). [CrossRef] [PubMed]

9

9. L. L. Yi, L. Zhan, W. S. Hu, and Y. X. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering With phase-modulated pump,” IEEE Photon. Technol. Lett. 19, 619–621 (2007). [CrossRef]

] or various gain profiles, such as gain doublet [10

10. M. D. Stenner and M. A. Neifeld, “Distortion management in slow-light pulse delay,” Opt. Express 13, 9995–10002 (2005). [CrossRef] [PubMed]

], or multi-line Brillouin gain spectrum [7

7. A. Minardo, R. Bernini, and L. Zeni, “Low distortion Brillouin slow light in optical fibers using AM modulation,” Opt. Express 14, 5866–5876 (2006). [CrossRef] [PubMed]

, 11

11. T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, “Distortion reduction in cascaded slow light delays,” Electron. Lett. 42, 1110–1112 (2006). [CrossRef]

, 12

12. Z. W. Lu, Y. K. Dong, and Q. Li, “Slow light in multi-line Brillouin gain spectrum,” Opt. Express 15, 1871–1877 (2007). [CrossRef] [PubMed]

], instead of a single Lorentzian gain line.

E. Shumakher et al. [16

16. E. Shumakher, N. Orbach, A. Nevet, D. Dahan, and G. Eisenstein, “On the balance between delay, bandwidth and signal distortion in slow light systems based on stimulated Brillouin scattering in optical fibers,” Opt. Express 14, 5877–5884 (2006). [CrossRef] [PubMed]

] investigated the relationship between delay, bandwidth and signal distortion in SBS slow-light systems where the signal bandwidth is of the order of the entire gain spectrum, which are prone to distortions. However, a detailed theoretical model of SBS slow-light for bit streams has not been proposed yet and the problem of the real storage capacity of the TOB based on FBA remains unsolved. In this paper, we highlight SBS slowlight systems where the signal bandwidth is smaller than the Brillouin gain bandwidth and propose a detailed analysis on the optimum buffer ability of SBS slow-light, in which the pulse broadening has been considered. Our analysis shows that the maximum of storage bits is dominated by the available net gain, which is limited by both the gain saturation and pulse broadening. Detailed analysis shows the storage capacity of SBS slow-light buffer varies with data bit rate and best storage capacity is around one bit.

2. SBS-based slow-light buffer

SBS can be viewed as a nonlinear interaction, in which the pump wave interacts with Stokes fields through an acoustic wave and produces narrowband gain or loss [17

17. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2005), Chap. 9.

].

Fig. 1. Characteristics of the SBS resonances (a) Gain and effective refractive index (b) Delay time

Figure 1 shows the characteristics of the SBS resonance. The probe pulse is being amplified (attenuated) due to the spectral resonance, which has a complex response function. Thus, according to the Kramers-Kronig (KK) relations, the amplification (attenuation) will result in a sharp transition in the refractive index of the material. Consequently, the group index will experience a strong transition, which is responsible for the pulse delay or advancement. The delay time is tunable via simply changing the pump power. For a CW or quasi-CW pump, the Brillouin gain has a Lorentzian spectrum of the form [17

17. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2005), Chap. 9.

],

g(ω)=gpIp(ΓB2)2(ωω0)2+(ΓB2)2
(1)

where, g p is the peak value of the Brillouin-gain coefficient, I p is the pump intensity, Γ B is the Brillouin gain linewidth, and ω0 is the frequency in the gain line center. KK relations can be written as

nr1=c2πωPg(s)sωds
(2)

where, P before the integral means to take the Cauchy principal value, nr is the real part of the phase refractive index. Substituting (1) into (2), by solving the integral we obtain

nr=cgpIpω(ωω0)ΓB(1+[2(ωω0)ΓB]2)+1
(3)

Consequently, with the group velocity vg=c(nr+ωdnr/dω)-1 and the group delay Td=L(c/vg-nr)/c, pulse delay can be approximated as

TdgpIpLΓB1[2(ωω0)ΓB]2(1+[2(ωω0)ΓB]2)2
(4)

Note that Eqs. (3) and (4) can also be obtained by employing the method in ref. [14

14. Z. M. Zhu and D. J. Gauthier, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378–2384 (2005). [CrossRef]

]. Nevertheless it is more convenient to derive them from KK relations. When [2(ω-ω0)/ΓB]2≪1, Eq. (4) can be approximated by Td≈GBB, where GB=gpIp L is described as the Brillouin gain parameter. We first consider the RZ data with 50% dutycycle, pulse period τ, bit interval bit T and corresponding bit rate Bbit. The temporal duration (FWHM) of Gaussian pulses can be expressed as τFWHM ≈τ/2≈Tbit/4=1/4Bbit. For the case of NRZ

data, τFWHM≈τ/2≈Tbit/2=1/2Bbit. The storage bits of the data in the buffer Nbit (namely delay-bandwidth product), which represents the storage capacity [18

18. R. S. Tucker, P. C. Ku, and C. J. Chang-Hasnain, “Slow-light optical buffers: Capabilities and fundamental limitations,” J. Lightw. Technol. 23, 4046–4066 (2005). [CrossRef]

], can be approximated as

Nbit=TdBbitGBBbitΓB={GB(4ΓBτFWHM)RZGB(2ΓBτFWHM)NRZ
(5)

We can see from Eq. (5), Nbit is proportional to GB for a given τFWHM, and inversely proportional to τFWHM for a given GB, as has been experimentally verified [1

1. K. Y. Song, M. G. Herraez, and L. Thevenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82–88 (2005). [CrossRef] [PubMed]

, 2

2. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005). [CrossRef] [PubMed]

]. However, deviations occur, for instance, due to pulse distortion when the bandwidth of input pulses is larger than SBS gain bandwidth and due to gain saturation when the input intensity of the probe pulses is too high.

3. Numerical investigation and discussions

In fact, delay is always accompanied by pulse distortion during the SBS process. In our case (signal pulses longer than tens of nanoseconds and CW or quasi-CW pump), the dispersion caused pulse broadening dominates the changing of the pulse shape. For an input Gaussian pulse with width τin (FWHM), we can obtain a longer output pulse width τout (FWHM). The output pulse remains Gaussian shape and the pulse broadening factor B is given by [2

2. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005). [CrossRef] [PubMed]

]

B=τoutτin=[1+GB16ln2/(τin2τB2)]12
(6)

For a given tolerable B, the gain parameter is limited by

GBΓB2τin2(B21)(16ln2)
(7)

Figure 2(a) shows the maximum of broadening-constrained gain parameter GB,max as a function of input pulse width. For practical TOB, high data fidelity is desired. For any datacoding format the broadening factor B should be bounded to the condition B≤τ/τFWHM, where τ is a full pulse period, otherwise the pulses cannot be identified in the receiver. For Gaussian pulses, the limit condition is B≤2 for real signal bit streams.

Fig. 2. (a). The maximum of broadening-constrained gain parameter versus input pulse width (b) Relations between saturation gain and the peak power of the probe pulse (c) Comparison of Gsat and GB,max as a function of input pulse width for different peak powers for NRZ data when B=1.5. There is an available gain zone in red dot frame.

On the basis of the analyses above, the gain parameter GB in Eq. (5) is dominated by two key factors. One is gain saturation induced by the high intensity of the probe pulses. The other is the pulse broadening that simultaneously occurs with the delay due to the dispersion in SBS process. In fact, GB is also limited by the process of SBS seeded by spontaneous Brillouin scattering [2

2. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005). [CrossRef] [PubMed]

]. When GB reaches the Brillouin threshold, around 21 [17

17. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2005), Chap. 9.

] (It depends on the fiber parameters), spontaneous Brillouin amplification will deplete the pump power in the absence of any input probe field. Z.M. Zhu et al. [14

14. Z. M. Zhu and D. J. Gauthier, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378–2384 (2005). [CrossRef]

] has shown that the delay increases with increasing gain in small signal regime and decreases with increasing gain in the gain saturation regime [14

14. Z. M. Zhu and D. J. Gauthier, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378–2384 (2005). [CrossRef]

]. Therefore, to achieve the maximum storage bits, GBGsat needs to be satisfied, where Gsat is the saturation gain parameter which is associated with the intensity of input pulse Is(in) for a given pump power. Is(in) can be written as Is(in)PpeakτinBbit/Aeff, where, Ppeak, Aeff and Bbit are the peak power of the input signal pulse, the mode area of the fiber and the signal bit rate respectively. We consider here no pump depletion and ignore the fiber loss. Then we can use the method in Ref. [17

17. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2005), Chap. 9.

] to calculate the saturation gain

Gsat=ln(exp[(1ξ)GA]ξ1ξ)
(8)

Where ξ=Is(out)/Ip(in), and Ip(in), Is(out) are the input intensity of the pump and output intensity of the signal pulses respectively, GA=gBIp(in)L is the non-saturation gain parameter. In our numerical simulations, we use the following values for standard single mode fiber at 1550nm, Aeff=50µm2, ΓB/2π=35 MHz, g0=5×10-11 m/w, effective fiber length Leff=1km, Ppump=21mw, corresponding GA=21. We first investigated the relations between Gsat and Ppeak for RZ and NRZ bit streams by numerically solving Eq. (8). It can be seen from Fig. 2(b) that the saturation gain goes up sharply as signal peak power decreases. We then compared Gsat and GB,max as a function of input NRZ pulse width for different input pulse peak powers (see Fig. 2(c)). The maximum available gain parameter can be obtained from Fig. 2(c). Further, according to Eq. (5), we can plot Fig. 3, which denotes the maximum of storage bits Nmax varying with different bit rates for variable peak powers or tolerable broadening factors.

Figures 3(a) and 3(c) show that the maximum of storage bits Nmax first goes up linearly as bit rate increases for a given peak power. However, as the bit rate increases, the data pulse become shorter, so the broadening limit is reached quickly as the gain increases and consequently the available net gain gets smaller [see Fig. 2(c)]. As a result, Nmax then goes down as bit rate continuously increases. Thus Nmax is limited owing to the limited net gain and we can obtain an optimal bit rate to achieve the maximum Nmax. For instance, under the condition of 1 peak P=nw, B=2, the maximum Nmax is 0.53 for RZ data (bit rate 7MHz) and 1.04 for NRZ data (bit rate 14.2MHz). The difference between RZ data and NRZ data is result from the nature of the two coding methods, as can be seen from Eq. (5).

To apply the FBA-based buffer for high bit rate data streams, a broad gain bandwidth is necessary, which can be achieved by utilizing a broadband-modulated pump. However, the pump modulation modifies the shape of SBS gain spectrum beyond broadening [16

16. E. Shumakher, N. Orbach, A. Nevet, D. Dahan, and G. Eisenstein, “On the balance between delay, bandwidth and signal distortion in slow light systems based on stimulated Brillouin scattering in optical fibers,” Opt. Express 14, 5877–5884 (2006). [CrossRef] [PubMed]

]. As a result, the signal pulse may experience unexpected distortion after being amplified by a modulated pump. More severely, for the same amount of signal gain an increase of the gain

bandwidth comes at the expense of a reduction of the delay of the same order of magnitude [4

4. M. G. Herraez, K. Y. Song, and L. Thevenaz, “Arbitrary-bandwidth Brillouin slow light in optical fibers,” Opt. Express 14, 1395–1400 (2006). [CrossRef]

]. Since the achievable net gain is limited, for modulated pump, the buffer ability will decrease in comparison with CW or quasi-CW pump. In fact, several other factors also play important roles in the SBS slow-light buffer. The pulse distortion can be impressively large under conditions of high bit rate (under this condition serious deviation from Eq. 6 will occur due to the signal bandwidth exceeds gain bandwidth. E.g. in Ref. [2

2. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005). [CrossRef] [PubMed]

], when τin=15ns the theoretical value of B is 1.95, while the experiment value is 1.4). Besides, the data pattern and signal detuning from the gain line centre also affect the system performance [19

19. L. Zhang, T. Luo, W. Zhang, C. Yu, Y. Wang, and A. E. Willner, “Optimizing operating conditions to reduce data pattern dependence induced by slow light elements,” in proceedings of OFC 2006, paper OFP7.

].

Fig. 3. The maximum of storage bits versus bit rate (a) RZ pulses with different peak powers for B=2 (b) RZ pulses for different broadening factors for 10nw peak power (c) NRZ pulses with different peak powers for B=2 (d) NRZ pulses with different broadening factors for 10nw peak power

4. Conclusion

We have studied theoretically the SBS slow-light tunable optical buffer, and have highlighted its storage abilities. Our results show that the maximum storage capacity is around 1 bit. It is limited by not only gain saturation but also pulse broadening. This is maybe one possible reason why no delay over one bit was reported. The former limitation can be overcome by employing attenuators in cascaded schemes. However the latter, up to now, remains unsolved. To solve this problem, new methods need to be developed. In spite of small buffer capacity, the tunable SBS slow-light buffer can play important roles in some circumstances such as accurate data synchronization and data bit equalization. In addition, we believe similar method can be used to analyze the resonance induced slow-light buffers including stimulated Raman scattering, optical parametric amplification, electromagnetically induced transparency etc.

Acknowledgments

The authors acknowledge the support from National Natural Science Foundation of China under the grants 60577048, the Science and Technology Committee of Shanghai Municipal under the contracts 04DZ14001/05ZR14078, and the Program for New Century Excellent Talents in University of China.

References and links

1.

K. Y. Song, M. G. Herraez, and L. Thevenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82–88 (2005). [CrossRef] [PubMed]

2.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005). [CrossRef] [PubMed]

3.

K. Y. Song, M. G. Herraez, and L. Thevenaz, “Long optically controlled delays in optical fibers,” Opt. Lett. 30, 1782–1784 (2005). [CrossRef] [PubMed]

4.

M. G. Herraez, K. Y. Song, and L. Thevenaz, “Arbitrary-bandwidth Brillouin slow light in optical fibers,” Opt. Express 14, 1395–1400 (2006). [CrossRef]

5.

Z. M. Zhu, M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “12-GHz-Bandwidth SBS slow light in optical fibers,” in proceedings of OFC 2006, paper PDP1.

6.

K. Y. Song and K. Hotate, “25 GHz bandwidth Brillouin slow light in optical fibers,” Opt. Lett. 32, 217–219 (2007). [CrossRef] [PubMed]

7.

A. Minardo, R. Bernini, and L. Zeni, “Low distortion Brillouin slow light in optical fibers using AM modulation,” Opt. Express 14, 5866–5876 (2006). [CrossRef] [PubMed]

8.

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). [CrossRef] [PubMed]

9.

L. L. Yi, L. Zhan, W. S. Hu, and Y. X. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering With phase-modulated pump,” IEEE Photon. Technol. Lett. 19, 619–621 (2007). [CrossRef]

10.

M. D. Stenner and M. A. Neifeld, “Distortion management in slow-light pulse delay,” Opt. Express 13, 9995–10002 (2005). [CrossRef] [PubMed]

11.

T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, “Distortion reduction in cascaded slow light delays,” Electron. Lett. 42, 1110–1112 (2006). [CrossRef]

12.

Z. W. Lu, Y. K. Dong, and Q. Li, “Slow light in multi-line Brillouin gain spectrum,” Opt. Express 15, 1871–1877 (2007). [CrossRef] [PubMed]

13.

J. B. Khurgin, “Performance limits of delay lines based on optical amplifiers,” Opt. Lett. 31, 948–950 (2006). [CrossRef] [PubMed]

14.

Z. M. Zhu and D. J. Gauthier, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378–2384 (2005). [CrossRef]

15.

V. P. Kalosha, L. Chen, and X. Bao, “Slow and fast light via SBS in optical fibers for short pulses and broadband pump,” Opt. Express 14, 12693–12703 (2006). [CrossRef] [PubMed]

16.

E. Shumakher, N. Orbach, A. Nevet, D. Dahan, and G. Eisenstein, “On the balance between delay, bandwidth and signal distortion in slow light systems based on stimulated Brillouin scattering in optical fibers,” Opt. Express 14, 5877–5884 (2006). [CrossRef] [PubMed]

17.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2005), Chap. 9.

18.

R. S. Tucker, P. C. Ku, and C. J. Chang-Hasnain, “Slow-light optical buffers: Capabilities and fundamental limitations,” J. Lightw. Technol. 23, 4046–4066 (2005). [CrossRef]

19.

L. Zhang, T. Luo, W. Zhang, C. Yu, Y. Wang, and A. E. Willner, “Optimizing operating conditions to reduce data pattern dependence induced by slow light elements,” in proceedings of OFC 2006, paper OFP7.

OCIS Codes
(060.2330) Fiber optics and optical communications : Fiber optics communications
(290.5900) Scattering : Scattering, stimulated Brillouin

ToC Category:
Slow Light

History
Original Manuscript: May 14, 2007
Revised Manuscript: July 9, 2007
Manuscript Accepted: July 15, 2007
Published: July 27, 2007

Citation
Liang Xing, Li Zhan, Lilin Yi, and Yuxing Xia, "Storage capacity of slow-light tunable optical buffers based on fiber Brillouin amplifiers for real signal bit streams," Opt. Express 15, 10189-10195 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-16-10189


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References

  1. K. Y. Song, M. G. Herraez, and L. Thevenaz, "Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering," Opt. Express 13, 82-88 (2005). [CrossRef] [PubMed]
  2. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005). [CrossRef] [PubMed]
  3. K. Y. Song, M. G. Herraez, and L. Thevenaz, "Long optically controlled delays in optical fibers," Opt. Lett. 30, 1782-1784 (2005). [CrossRef] [PubMed]
  4. M. G. Herraez, K. Y. Song, and L. Thevenaz, "Arbitrary-bandwidth Brillouin slow light in optical fibers," Opt. Express 14, 1395-1400 (2006). [CrossRef]
  5. Z. M. Zhu, M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, "12-GHz-Bandwidth SBS slow light in optical fibers," in proceedings of OFC 2006, paper PDP1.
  6. K. Y. Song, and K. Hotate, "25 GHz bandwidth Brillouin slow light in optical fibers," Opt. Lett. 32, 217-219 (2007). [CrossRef] [PubMed]
  7. A. Minardo, R. Bernini, and L. Zeni, "Low distortion Brillouin slow light in optical fibers using AM modulation," Opt. Express 14, 5866-5876 (2006). [CrossRef] [PubMed]
  8. 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). [CrossRef] [PubMed]
  9. L. L. Yi, L. Zhan, W. S. Hu, and Y. X. Xia, "Delay of broadband signals using slow light in stimulated Brillouin scattering With phase-modulated pump," IEEE Photon. Technol. Lett. 19, 619-621 (2007). [CrossRef]
  10. M. D. Stenner and M. A. Neifeld, "Distortion management in slow-light pulse delay," Opt. Express 13, 9995-10002 (2005). [CrossRef] [PubMed]
  11. T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, "Distortion reduction in cascaded slow light delays," Electron. Lett. 42, 1110-1112 (2006). [CrossRef]
  12. Z. W. Lu, Y. K. Dong, and Q. Li, "Slow light in multi-line Brillouin gain spectrum," Opt. Express 15, 1871-1877 (2007). [CrossRef] [PubMed]
  13. J. B. Khurgin, "Performance limits of delay lines based on optical amplifiers," Opt. Lett. 31, 948-950 (2006). [CrossRef] [PubMed]
  14. Z. M. Zhu and D. J. Gauthier, "Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber," J. Opt. Soc. Am. B 22, 2378-2384 (2005). [CrossRef]
  15. V. P. Kalosha, L. Chen, and X. Bao, "Slow and fast light via SBS in optical fibers for short pulses and broadband pump," Opt. Express 14, 12693-12703 (2006). [CrossRef] [PubMed]
  16. E. Shumakher, N. Orbach, A. Nevet, D. Dahan, and G. Eisenstein, "On the balance between delay, bandwidth and signal distortion in slow light systems based on stimulated Brillouin scattering in optical fibers, " Opt. Express 14, 5877-5884 (2006). [CrossRef] [PubMed]
  17. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2005), Chap. 9.
  18. R. S. Tucker, P. C. Ku, and C. J. Chang-Hasnain, "Slow-light optical buffers: Capabilities and fundamental limitations, " J. Lightw. Technol. 23, 4046-4066 (2005). [CrossRef]
  19. L. Zhang, T. Luo, W. Zhang, C. Yu, Y. Wang, and A. E. Willner, "Optimizing operating conditions to reduce data pattern dependence induced by slow light elements," in proceedings of OFC 2006, paper OFP7.

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