## 3R optical regeneration: An all-optical solution with BER improvement

Optics Express, Vol. 14, Issue 14, pp. 6414-6427 (2006)

http://dx.doi.org/10.1364/OE.14.006414

Acrobat PDF (524 KB)

### Abstract

We demonstrate that an optical regenerator architecture providing re-amplification, re-shaping, and re-timing based on the principle of spectral shift followed by filtering can lead to bit error ratio improvement of the signal passing through it. This is in contrast with typical regenerators based on the usual principle of power conversion from a transfer function, which are unable to improve the bit error ratio. At first, we provide the theoretical basis that explains this improvement. Then we present the regenerator architecture based on spectral shift followed by filtering and provide experimental evidence of bit error ratio improvement of a noisy signal from 3×10^{-6} without regenerator to 2×10^{-10} with regenerator.

© 2006 Optical Society of America

## 1. Introduction

*power transfer function*(

*f*) [1]–[8

8. J. Suzuki, T. Tanemura, K. Taira, Y. Ozeki, and K. Kikuchi, “All-optical regenerator using wavelength shift induced by cross-phase modulation in highly nonlinear dispersion-shifted fiber,” IEEE Photon. Technol. Lett. **17**, 423–425 (2005). [CrossRef]

*P*-(

*t*)) provides a deterministic output power

*P*+(

*t*)=

*f*[

*P*-(

*t*)], where

*t*is time. An important characteristic of regenerators providing an output power depending only on the instantaneous input power is that they do not improve the bit error ratio (BER) of a signal passing through them [9

9. M. Rochette, J. N. Kutz, J. L. Blows, D. Moss, J. T. Mok, and B. J. Eggleton, “Bit error ratio improvement with 2R optical regenerators,” IEEE Photon. Technol. Lett. **17**, 908–910 (2005). [CrossRef]

9. M. Rochette, J. N. Kutz, J. L. Blows, D. Moss, J. T. Mok, and B. J. Eggleton, “Bit error ratio improvement with 2R optical regenerators,” IEEE Photon. Technol. Lett. **17**, 908–910 (2005). [CrossRef]

## 2. Concepts of probability distribution function and bit error ratio

*E*that the power level

*P*

_{E}is found between levels a and b is

*P*) follows the statistics of the event

*E*, and

*P*represents possible power levels at sampling time. An important characteristic of pdfs is that the complete surface under a pdf, or equivalently the integral over all possible power values, always equals 1. From our previous example, the probability that

*P*

_{E}is comprised between power levels a=0 and b=∞ equals 100% - it is a

*certain*event because a power level is a real number that

*must*be comprised between 0 and ∞.

_{1}) and the logical zeros (

_{0}) following,

*T*is a power level that represents the decision threshold. Eq. (2) is valid for a signal that is equally composed of logical ones and logical zeros. The sampled bit which has a power level

*above*the decision threshold is interpreted as a

*logical one*whereas the sampled bit which has a power level

*below*the decision threshold is interpreted as a

*logical zero*. An error therefore arises when a bit is so noisy that its power at sampling time is on the wrong side of the decision threshold. The decision threshold must be carefully chosen from

_{1}and

_{0}to avoid inducing an artificially high

*BER*. The optimal decision threshold which minimizes

*BER*is found by differentiating Eq. (2) with respect to

*T*and setting

*dBER/dT*=0. This gives

_{1}(

*T*

_{O})=

_{0}(

*T*

_{O}) as the solution for the optimal decision threshold

*T*

_{O}. The optimum threshold is therefore found at the common power coordinate where

_{1}(

*P*) and

_{0}(

*P*) intersect. As a result, the BER as expressed in Eq. (2) represents the surface integral under the common area of

_{1}(

*P*) and

_{0}(

*P*).

*T*

_{O}=0.269 W as found from the crossing point of the two pdfs. For this signal, errors statistically occur at a ratio of BER=4.7×10

^{-9}, as can be evaluated from the common surface under

_{1}and

_{0}.

## 3. Signal conversion by power transfer functions

*Class I*regenerators. In contrast, we show that a second class of regenerators, referred to as

*Class II*regenerators, ruled by more than one power transfer function can improve the BER of a signal, if properly engineered.

*BER*-) such as

*T*

_{O}- as defined by the crossing point between the two pdfs, or

_{0}-(

*T*

_{O-})=

_{1}-(

*T*

_{O-})

### 3.1 Class I Regenerators

*P*-) into an output signal (

*P*+) by means of a power transfer function,

*f*(

*P*-+

*dP*)≥

*f*(

*P*-) for all

*P*->0 and

*dP*>0) and therefore has an inverse solution

*P*-=

*f*

^{-1}(

*P*+). From the power transfer function, an input pdf (

*BER*

^{I}+, is obtained by transforming the input pdfs of the logical ones and the logical zeros with the pdf transformation operator ℑ, using Eqs. (2) and (5)

*dBER*

^{I}+/

*dP*+=0 and leads to

_{1}+(

*T*

_{O}+)=

_{0}+(

*T*

_{O}

_{+}). We rewrite Eq. (6) in consequence,

_{1+}and

_{0+}to their pdfs before conversion. Equation (5) is used for this purpose

^{-1}) on Eq. (9) to convert back the expression of

*P*- space. We then find,

*f*(

*P*

_{+}) contains more than one local maximum and/or discontinuities- then

*BER*

^{I}+≥

*BER*

^{I}-.

*Therefore, the BER after conversion with a single power transfer function is worse (higher) or at most equal to the BER before conversion, independently of the shape of the power transfer function*. We keep this last result as a general result for both monotonic and non-monotonic power transfer functions of Class I.

9. M. Rochette, J. N. Kutz, J. L. Blows, D. Moss, J. T. Mok, and B. J. Eggleton, “Bit error ratio improvement with 2R optical regenerators,” IEEE Photon. Technol. Lett. **17**, 908–910 (2005). [CrossRef]

*T*

_{O}=0.269 W,

*T*

_{+}=0.171 W), the BER remains the same at BER=4.7×10

^{-9}in both cases.

### 3.2 Class II Regenerators

_{1}- and

_{0}- converted individually following their pdf transformation operator, that is ℑ

_{1}and ℑ

_{0}respectively,

*dP*

_{+}=0 and leads to

_{1+}(

*T*

_{O+})=

_{0+}(

*T*

_{O+}). We rewrite Eq. (12) in consequence,

*P*-space using the inverted ℑ

_{1}operator (i.e.,

_{1}(

_{1-})]=

_{1-}and therefore resembles the first integrand in Eq. (3). In contrast, the second integrand of Eq. (17) comprises a double transformation of pdf0- that does not equals the second integrand of Eq. (3) unless ℑ

_{0}=ℑ

_{1}. As a result, a Class II regenerator with non-similar power transfer functions affecting independently logical ones and logical zeros lead to

*f*

_{1}and

*f*

_{0}are just slightly different. In this limit, just the second integrals of Eqs. (17) and (3) need to be taken into consideration since

*T*

_{O+})~

*T*

_{O-}and the first integrals cancel each other. This leads to the condition

*f*

_{1}(

*P*

_{-})>

*f*

_{0}(

*P*

_{-}) for all input power values

*P*

_{-}>0 and independently of

_{0-}.

*f1*(

*P*

_{-})>

*f*

_{0}(

*P*

_{-}) (upper left graph). A pdf conversion using these power transfer functions leads to pdfs with different shapes and thresholds (

*T*

_{O-}=0.269 W,

*T*

_{O+}=0.126 W), but also leads to a BER improvement from

^{-9}before conversion to

^{-10}after conversion (upper right graph). An equivalent way to evaluate the BER is to compare

_{1-}with both

_{0}-and its double converted operation

_{0}(

_{0-})) (lower graph). The resulting graph shows a clear BER improvement, or surface area reduction, from

_{0}(

_{0-})) being at lower values than

_{0-}. Once again, the BER is improved from

^{-9}before conversion to

^{-10}after conversion.

*f*

_{1}(

*P*

_{-})<

*f*

_{0}(

*P*

_{-}) for all input power values

*P*

_{-}>0 and independently of

_{0}

_{-}. A pdf conversion using these power transfer functions leads to pdfs with different shapes and thresholds (

*T*

_{O-}=0.269 W,

*T*

_{O+}=0.874 W), but also a BER improvement from

^{-9}before conversion to

^{-10}after conversion (upper right graph). Using the comparison of

_{1}with both

_{0}and its double converted operation

_{0}(

_{0-})) provides a clear view of the BER improvement (lower graph). The BER improvement between the example of Fig. 4 and this example are identical because the same power transfer functions have been used, with the only difference that they have been flipped symmetrically around the horizontal axis to invert the bits in this example.

## 4. Principle and operation of the 3R regenerator with BER improvement

*et al*. [8

8. J. Suzuki, T. Tanemura, K. Taira, Y. Ozeki, and K. Kikuchi, “All-optical regenerator using wavelength shift induced by cross-phase modulation in highly nonlinear dispersion-shifted fiber,” IEEE Photon. Technol. Lett. **17**, 423–425 (2005). [CrossRef]

_{XPM}proportional to the slope of the superimposed signal,

*L*

_{Eff}is the effective fiber length,

*P*(

*t*) is the input signal, and

*t*is time. The output filter BPF2 filters out the spectral components that have been shifted by XPM and keeps the original frequency components at wavelength λc. Take note that this regeneration architecture is inverting the bits, i.e., logical ones are transformed into logical zeros and vice-versa. A non-inverting mode can also be achieved by offsetting the center frequency of BPF2 away from the original clock wavelength, in order to transmit only XPM generated frequencies. In both case, the power transferred from the input to the output of the regenerator depends on

*δω*

_{XPM}and hence the power transfer function depends on the temporal characteristics – namely the derivative - of the instantaneous input power, as expressed in Eq. (20). As a consequence, this 3R regenerator has the interesting capability to discriminates an abruptly varying signal from a slowly varying signal. This is in contrast with conventional regeneration schemes, or Class I regenerators, into which the power transfer function converts solely the instantaneous input power as expressed in Eq. (4), without regard to its derivatives. The capability of discriminating the slope (and therefore the width) of a pulse is a first step leading to the discrimination between noisy pulses and ASE noise alone. The second and last step to achieve signal discrimination is provided from the temporal shape of noisy pulses and ASE noise alone, as explained below.

## 5. Experimental demonstration of BER Improvement

*et al*. [8

8. J. Suzuki, T. Tanemura, K. Taira, Y. Ozeki, and K. Kikuchi, “All-optical regenerator using wavelength shift induced by cross-phase modulation in highly nonlinear dispersion-shifted fiber,” IEEE Photon. Technol. Lett. **17**, 423–425 (2005). [CrossRef]

^{23}-1 bits at a rate of 40 Gb/s. The bits are transformed by cascaded modulators into 8 ps pulses at a wavelength of 1534.25 nm and with a bandwidth of 0.5 nm, respectively. The pulsed signal and ASE noise from an EDFA are combined to a desired OSNR using a variable attenuator VA

_{1}and a 3 dB coupler. The ASE noise source and the pulsed signal are spectrally filtered in an identical fashion using a band-pass filter of 0.5 nm. The 3R architecture follows the schematic of Fig. 6(a) with the following parameters: the clock source sends pulses of 4 ps at a wavelength of 1558.0 nm, the HNLF has a length of 850 m and a nonlinearity γ=20 W

^{-1}Km

^{-1}, the bandpass filter BPF2 has a width of 0.5 nm and is centered at 1558.0 nm, the amplifier boosts the noisy pulses up to a peak power level sufficient (500 mW) to induce XPM on the clock. The regenerator is followed by a variable attenuator VA2 that ensures that the maximum peak optical power sent to the photodiode is maintained at a constant level of 2 mW. At this relatively high optical power level, shot noise and thermal noise have a negligible contribution over the total noise measured. For instance, the measured BER≪1×10

^{-13}(no errors) when measuring the 2 mW signal free from ASE at the photodiode input. In contrast, when ASE noise is superimposed to the signal, we obtain BER=1×10

^{-10}to 1×10

^{-2}depending on the OSNR adjustment. Signal-spontaneous beat noise is therefore the most prominent source of noise when ASE noise is present. The 2 mW optical signal converts into a 285 mV electrical signal at the photodiode output. A BER tester receives the noisy electrical signal with or without the 3R regenerator in the measurement setup and counts the number of errors for various levels of OSNR.

_{2}. The extreme case of a continuous wave signal, with no power slope, does not induce any XPM and the clock is therefore completely transmitted through BPF

_{2}. The situation is different for 8 ps and 16 ps pulses where the amount of power transmitted through BPF

_{2}depends both on the peak pulse power and width of the input signal. The regenerator clearly discriminates pulses of different widths, and therefore discriminate logical ones (8 ps pulses, synchronized with the clock) from logical zeros (>8 ps pulses, asynchronized with respect with the clock). As shown in Fig. 4 and Fig. 5, even a small difference between power transfer function profiles associated to logical ones and logical zeros is expected to significantly affect the BER. The only difference between examples of Fig. 4, Fig. 5 and the actual demonstration is that in this case, logical zeros follow more than one power transfer function, depending on the many possible noise shape that superimpose with the clock. Of all the possible power transfer function, the noise shape always have a width larger than 8 ps and will therefore follow a power transfer function having

*f*

_{1}(

*P*

_{-})<

*f*

_{0}(

*P*

_{-}) for every

*P*

_{-}. Taking into consideration that the 3R regenerator is inverting the bits and that we experimentally measured that

*f*

_{1}(

*P*

_{-})<

*f*

_{0}(

*P*

_{-}) for every

*P*

_{-}ensures a BER improvement.

*BER*

_{-}=3×10

^{-6}without regenerator to

*BER*

_{+}=2×10

^{-10}with regenerator. This represents nearly four orders of magnitude in BER improvement at an OSNR=15 dB. Alternatively, the regenerator provides an OSNR margin of 4 dB at a BER of 10

^{-10}. To test the reproducibility, the experiment was repeated a few times (twice on Fig. 9(b)) and gave identical results. We believe that further improvement of the BER is possible by optimizing the regenerator parameters such as the length of nonlinear medium, the nominal peak power in the regenerator, and the spectral shift of BPF

_{2}.

## 6. Conclusion

## Acknowledgments

## Footnotes

* | As a recall from variable changes into integrals, one can convince himself by taking an example like x=y
^{1/2}, dx=dy/2y
^{1/2}, upper bound x=b changed for y=b
^{2} and lower bound x=a changed for y=a
^{2}) does not affect the final result. |

## Reference and links

1. | P. V. Mamyshev, “All-optical data regeneration based on self-phase modulation effect,” in Proc. |

2. | T. Her, T. Leng, G. Raybon, J. C. Bouteiller, C. Jorgensen, K. Feder, K. Brar, P. Steinvurzel, D. Patel, N. M. Litchinitser, P. S. Westbrook, L. E. Nelson, C. Headley, and B. J. Eggleton, “Enhanced 40 Gbit/s OTDM receiver sensitivity with all-fiber optical 2R regenerator,” in |

3. | G. Raybon, Y. Su, J. Leuthold, R. J. Essiambre, T. Her, C. Joergensen, P. Steinvurzel, and K. D. K. Feder, “40 Gbit/s Pseudo-linear Transmission Over One Million Kilometers,” in |

4. | M. Meissner, K. Sponsel, K. Cvecek, A. Benz, S. Weisser, B. Schmauss, and G. Leuchs, “3.9-dB OSNR gain by an NOLM-based 2-R regenerator,” IEEE Photon. Technol. Lett. |

5. | P. Z. Huang, A. Gray, I. Khrushchev, and I. Bennion, “10-Gb/s transmission over 100 Mm of standard fiber using 2R regeneration in an optical loop mirror,” IEEE Photon. Technol. Lett. |

6. | D. Rouvillain, F. Seguineau, L. Pierre, P. Brindel, H. Choumane, G. Aubin, J. L. Oudar, and O. Leclerc, “40 Gbit/s optical 2R regenerator based on passive saturable absorber for WDM long-haul transmission,” in |

7. | F. Ohman, S. Bischoff, B. Tromborg, and J. Mork, “Semiconductor devices for all-optical regeneration,” in |

8. | J. Suzuki, T. Tanemura, K. Taira, Y. Ozeki, and K. Kikuchi, “All-optical regenerator using wavelength shift induced by cross-phase modulation in highly nonlinear dispersion-shifted fiber,” IEEE Photon. Technol. Lett. |

9. | M. Rochette, J. N. Kutz, J. L. Blows, D. Moss, J. T. Mok, and B. J. Eggleton, “Bit error ratio improvement with 2R optical regenerators,” IEEE Photon. Technol. Lett. |

10. | M. Rochette, J. L. Blows, and B. J. Eggleton, “An All-Optical Regenerator that Discriminates Noise from Signal,” in |

11. | M. Rochette, L. B. Fu, V. Ta’eed, D. J. Moss, and B. J. Eggleton, “2R Optical Regeneration: An All-Optical Solution for BER Improvement,” to be published in J. Sel. Topics in Quant. Electron.12(6), (2006). |

12. | A. Papoulis and S. U. Pillai, |

**OCIS Codes**

(060.7140) Fiber optics and optical communications : Ultrafast processes in fibers

(190.4360) Nonlinear optics : Nonlinear optics, devices

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: June 22, 2006

Revised Manuscript: July 27, 2006

Manuscript Accepted: June 27, 2006

Published: July 10, 2006

**Citation**

Martin Rochette, Justin L. Blows, and Benjamin J. Eggleton, "3R optical regeneration: an all-optical solution with BER improvement," Opt. Express **14**, 6414-6427 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-14-6414

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### References

- P. V. Mamyshev, "All-optical data regeneration based on self-phase modulation effect," in Proc. of 24th European Conference on Optical Communication, 1998 (IEE, UK, 1998), pp. 475-476.
- T. Her, T. Leng, G. Raybon, J. C. Bouteiller, C. Jorgensen, K. Feder, K. Brar, P. Steinvurzel, D. Patel, N. M. Litchinitser, P. S. Westbrook, L. E. Nelson, C. Headley, and B. J. Eggleton, "Enhanced 40 Gbit/s OTDM receiver sensitivity with all-fiber optical 2R regenerator," in Technical Digest of the Conference on Lasers and Electro-Optics, 2002, (Optical Society of America, Washington DC, 2002), pp. 534-535.
- G. Raybon, Y. Su, J. Leuthold, R. J. Essiambre, T. Her, C. Joergensen, P. Steinvurzel, and K. D. K. Feder, "40 Gbit/s Pseudo-linear Transmission Over One Million Kilometers," in Proceeding of the Optical Fiber Conference and Exhibit, 2002, (Optical Society of America and the Laser and Electro-Optics Society, Washington DC, 2002), pp. FD10-1 - FD10-3. [CrossRef]
- M. Meissner, K. Sponsel, K. Cvecek, A. Benz, S. Weisser, B. Schmauss, and G. Leuchs, "3.9-dB OSNR gain by an NOLM-based 2-R regenerator," IEEE Photon. Technol. Lett. 16,2105-2107 (2004). [CrossRef]
- P. Z. Huang, A. Gray, I. Khrushchev, and I. Bennion, "10-Gb/s transmission over 100 Mm of standard fiber using 2R regeneration in an optical loop mirror," IEEE Photon. Technol. Lett. 16, 2526-2528 (2004). [CrossRef]
- D. Rouvillain, F. Seguineau, L. Pierre, P. Brindel, H. Choumane, G. Aubin, J. L. Oudar, and O. Leclerc, "40 Gbit/s optical 2R regenerator based on passive saturable absorber for WDM long-haul transmission," in Proceeding of the Optical Fiber Conference and Exhibit, 2002, (Optical Society of America and the Laser and Electro-Optics Society, Washington DC, 2002), p. FD11-1. [CrossRef]
- F. Ohman, S. Bischoff, B. Tromborg, and J. Mork, "Semiconductor devices for all-optical regeneration," in Proceedings of the 5th International Conference on Transparent Optical Networks, 2003, (2003), pp. 41-46.
- J. Suzuki, T. Tanemura, K. Taira, Y. Ozeki, and K. Kikuchi, "All-optical regenerator using wavelength shift induced by cross-phase modulation in highly nonlinear dispersion-shifted fiber," IEEE Photon. Technol. Lett. 17, 423-425 (2005). [CrossRef]
- M. Rochette, J. N. Kutz, J. L. Blows, D. Moss, J. T. Mok, and B. J. Eggleton, "Bit error ratio improvement with 2R optical regenerators," IEEE Photon. Technol. Lett. 17, 908-910 (2005). [CrossRef]
- M. Rochette, J. L. Blows, and B. J. Eggleton, "An All-Optical Regenerator that Discriminates Noise from Signal," in Proceedings of the 31st European Conference on Optical Communication, 2005, (IEE, UK, 2005), We2.4.1.
- M. Rochette, L. B. Fu, V. Ta’eed, D. J. Moss, and B. J. Eggleton, " 2R Optical Regeneration: An All-Optical Solution for BER Improvement," to be published in J. Sel. Topics in Quant.Electron. 12(6), (2006).
- A. Papoulis, and S. U. Pillai, Probability, random variables, and stochastic processes, 4th ed (McGraw Hill science, New York, 2001).

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