Noise reduction in 2R-regeneration technique utilizing self-phase modulation and filtering

doi:10.1364/OE.14.001737

Noise reduction in 2R-regeneration technique utilizing self-phase modulation and filtering

Thanh Nguyen, Mathilde Gay, Laurent Bramerie, Thierry Chartier, Jean-Claude Simon, and Michel Joindot »View Author Affiliations

Optics Express, Vol. 14, Issue 5, pp. 1737-1747 (2006)
http://dx.doi.org/10.1364/OE.14.001737

View Full Text Article

Acrobat PDF (252 KB)

Journal Search
Article Lookup

Article Tools

Citations

Alert me when this article is cited
Export Citation/Save

Full Text
Article Info
References (15)
Cited By
Figures (10)
Metrics

Abstract

We numerically investigate the 2R-regeneration technique utilizing self-phase modulation and off-center filtering. Our numerical simulations take into account the incoherent nature of noise through its spectral representation. This approach allows to evaluate a Q-factor improvement of 2 dB for this regenerator. Furthermore, our study points out the role of both the input and the output filter of this regenerator. We show that the input filter must be suitably chosen in order to obtain the best Q-factor improvement. The output filter must also be suitably chosen in order to preserve the modulation format.

1. Introduction

All-optical signal regeneration technique utilizing self-phase modulation in fiber and subsequent filtering was first proposed by Mamyshev [1

P. V. Mamyshev, “All-optical data regeneration based on self-phase modulation effect”, in Proceedings of the 1998 European Conference on Optical Communications (ECOC, Madrid, 1998) 1, 475–476.

]. This 2R-regenerator design is very attractive because of its simplicity : it only uses a fiber and an optical bandpass filter located at the output. Moreover, this technique being based on the Kerr effect, it does not suffer of any time response limitation. Since its first demonstration, this kind of regenerator has been extensively studied, both experimentally [2

G. Raybon, Y. Su, J. Leuthold, R. Essiambre, T. Her, C. Joergensen, P. Steinvurzel, K. Dreyer, and K. Feder, “40Gbit/s Pseudo-linear transmission over one million kilometres,” in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2002), FD-10 1-3.

, 3

T. H. Her, G. Raybon, and C. Headley, “Optimization of Pulse Regeneration at 40 Gb/s Based on Spectral Filtering of Self-Phase Modulation in Fiber,” IEEE Photonics Technol. Lett. 16, 200–202 (2004). [CrossRef]

, 4

N. Yoshikane, I. Morita, T. Tsuritani, A. Agata, N. Edagawa, and S. Akiba, “Benefit of SPM-based all-optical reshaper in receiver for long-haul DWDM tranmission systems,” IEEE J. Sel. Top. Quantum Electron. 10, 412–420 (2005).

, 5

M. Rochette, J. L. Blows, and B. J. Eggleton, “An all-optical regenerator that descriminates noise from signal,” in Proceedings of the 2005 European Conference on Optical Communications (ECOC, Glasgow, 2005) 3, 403–404.

] and theoretically [6

S. Taccheo and K. Ensner, “Investigation of amplitude noise and timing jitter of supercontinuum spectrum-sliced pulses,” IEEE Photonics Technol. Lett. 14, 1100–1102 (2002). [CrossRef]

, 7

M. Matsumoto, “Performance analysis and comparison of optical 3R regenerators utilizing self-phase modulation in fibers,” J. Lightwave Technol. 22, 1472–1482 (2004). [CrossRef]

, 8

J. T. Mok, J. L. Blows, and B. J. Eggleton, “Investigation of group delay ripple distorted signals transmitted through all-optical 2R regenerators,” Opt. Express 12, 4411–4422 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4411. [CrossRef] [PubMed]

, 9

M. Vasilyev and T. I. Lakoba, “All-optical multichannel 2R regeneration in a fiber-based device,” Opt. Lett. 30, 1458–1460 (2005). [CrossRef] [PubMed]

, 10

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 Photonics Technol. Lett. 17, 908–910 (2005). [CrossRef]

In some experimental studies, a noise source is superimposed on the data stream to simulate degradation of the signal by accumulation of amplified spontaneous emission (ASE) from optical amplifiers. Experimental Q-factor improvements of 1.5 dB have been reported with this regenerator [3

, 4

]. In these experimental studies, an input filter is usually present [2

, 3

, 4

] but its role is not clearly identified.

From a theoretical point of view, the most commonly used theoretical approach to study the Mamyshev regenerator consists of solving the nonlinear Schrödinger equation for an input pulse [6

S. Taccheo and K. Ensner, “Investigation of amplitude noise and timing jitter of supercontinuum spectrum-sliced pulses,” IEEE Photonics Technol. Lett. 14, 1100–1102 (2002). [CrossRef]

, 7

M. Matsumoto, “Performance analysis and comparison of optical 3R regenerators utilizing self-phase modulation in fibers,” J. Lightwave Technol. 22, 1472–1482 (2004). [CrossRef]

, 8

, 9

M. Vasilyev and T. I. Lakoba, “All-optical multichannel 2R regeneration in a fiber-based device,” Opt. Lett. 30, 1458–1460 (2005). [CrossRef] [PubMed]

]. Noise is generally taken into account through variations of the input pulse peak power. This method leads to a nonlinear transfer function for the regenerator. This function is known to reduce noise but does not take into account the incoherent nature of ASE noise. In reference [7

M. Matsumoto, “Performance analysis and comparison of optical 3R regenerators utilizing self-phase modulation in fibers,” J. Lightwave Technol. 22, 1472–1482 (2004). [CrossRef]

], Matsumoto uses a more realistic approach of including ASE noise, but the paper is focused on performance comparison between several kind of 3R regenerators rather than on the physical understanding of the Mamyshev regenerator in the presence of incoherent noise.

Interesting work has been recently proposed by Rochette et al. both theoretically and experimentally [5

, 10

] to explain the bit-error-rate improvement observed with this kind of regenerators. The authors argue that the regenerator needs to have different transfer functions for the signal and the noise to make BER improvement possible. However, in these papers the role of the filters is not investigated.

The aim of our paper is to propose an accurate simulation of the Mamyshev regeneration technique. We demonstrate, for the first time in the best of our knowledge, that a maximum Q-factor improvement of about 2 dB is possible only if an input filter is present and suitably chosen. Our conclusion is that the Mamyshev regenerator can discriminate noise from signal only if ASE noise has been previously eliminated from the spectral region where the signal is transposed.

In section 2, we present the approach which consists of taking into account the incoherent nature of ASE noise through its spectral representation. In section 3 we briefly present the principle of this self-phase-modulation-based 2R-regeneration technique. Section 4 presents the results of the simulations leading to the evaluation of the Q-factor improvement in the presence of the regenerator while section 5 is focused on the role of optical filters in this regeneration technique.

2. Relation between Q-factor and white noise

In this section we give the relation between the Q-factor of a degraded data stream and its corresponding optical signal-to-noise ratio (OSNR). Our calculation technique is based on the spectral representation of white noise. We use the schematic diagram shown in Fig. 1 to model the acquisition process of an optical data stream degraded by the accumulation of amplified spontaneous emission (ASE) of erbium-doped fiber amplifiers (EDFA).

Fig. 1. Schematic bloc diagram used for simulation.

The data encoder gives a 40 Gb/s random sequence of 1024 Fourier-limited gaussian pulses at 1550 nm with a full width at half maximum (FWHM) of 6.25 ps. The extinction ratio ER of the signal is defined as the ratio (in dB) between the peak power of the pulses and the background level.

Let E_S (t) be the function representing the magnitude of the electrical field of the optical signal in the time domain. The spectral representation Ẽ_S (v) is numerically calculated from E_S (t) by using the discrete Fourier transform (DFT):

{\tilde{E}}_{S} (v) = \frac{1}{\sqrt{N}} \sum_{k = - N / 2}^{N / 2 - 1} E_{S} (\frac{k T}{N}) \exp (- 2 i π \frac{k T}{N} v)

(1)

where N is the number of points dividing the time window T.

The spectral representation Ẽ_N (v) of ASE noise is assumed to be similar to white gaussian noise [11

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd Ed . (John Wiley & sons, Inc., 2002). [CrossRef]

] and can be written, in the frequency domain, as :

{\tilde{E}}_{N} (v) = A \exp (iϕ (v)),

(2)

where A is the magnitude of white noise. We take A constant over a frequency range B centered around the carrier frequency v ₀ (see Fig. 2(a)). Quantity ϕ is the random phase uniformly distributed between –π and π (see Fig. 2(b)). This simple formulation allows us to take into account the incoherent nature of the spontaneous emission from optical amplifiers.

The representation E_N (t) of the noise in the time domain can be obtained numerically by using the inverse discrete Fourier transform (IDFT) of the spectrum. Figures 2(c) and 2(d) represent respectively the real part r_N (t) and the imaginary part i_N (t) of E_N (t). By virtue of central limit theorem [12

J. W. Goodman, Statistical Optics (John Willey & sons, Inc., 1985).

], both r_N (t) and i_N (t) can be approximated by gaussian random variables. Figures 2(e) and 2(f) represent the probability density function of r_N (t) and i_N (t) assuming a gaussian law with a zero mean and a variance σ ² = A ² B/2T. Let us mention that this method to generate gaussian noise is similar to the method which consists to decompose the electric field in Fourier series [13

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989). [CrossRef]

In the frequency domain, the signal arriving at the optical bandpass filter input is written as :

{\tilde{E}}_{1} (v) = {\tilde{E}}_{S} (v) + {\tilde{E}}_{N} (v) .

(3)

Before detection, we evaluate the OSNR, defined as the ratio (in dB) between the signal power and the noise power for a given spectral range.

The detection stage generally includes a bandpass optical filter to reduce noise. We use a flat-top filter represented by a fifth-order supergaussian transfer function F ₁(v). The central frequency of the filter is the carrier frequency of the signal and its 3 dB-bandwidth is 150 GHz. After the filter, the signal is written as:

{\tilde{E}}_{2} (v) = F_{1} (v) {\tilde{E}}_{1} (v) .

(4)

Fig. 2. Description of white noise gaussian : (a) Magnitude and (b) phase of the bandwidth-limited white noise in the frequency domain, (c) real and (d) imaginary part of noise in the time domain and probability density functions of (e) real and (f) imaginary part of noise in the time domain. In this figure A = 10^-10 √W/Hz and B = 100 GHz. For numerical simulations, we have devided the total frequency range v_max = 1000 GHz in N = 2¹⁸ points, leading to a sampling frequency v_s = v_max/N = 3.8 MHz and a time window T = 1/v_s = 260 ns.

The photodetector converts the optical intensity, proportional to |E ₂(t)|², into a voltage v ₁(t):

v_{1} (t) = R {∣ E_{2} (t) ∣}^{2},

(5)

where R is the photodetector responsivity. In the following, R will be set to unity and we will neglect shot noise and thermal noise of the detector. The IDFT is used to obtain E ₂(t) from Ẽ₂(v).

Fig. 3. (a) Eye diagram and (b) intensity histogram of the detected signal.

Fig. 4. Q-factor versus OSNR for different ER.

The finite bandwidth of the electronics is taken into account through a fifth-order Bessel lowpass filter of transfer function H(v) whose cutoff frequency is 32 GHz. After the filter, the voltage, in the frequency domain, becomes:

{\tilde{v}}_{2} (v) = H (v) {\tilde{v}}_{1} (v),

(6)

where ṽ₁(v) is the DFT of v ₁(t). To represent the eye-diagram of the signal we calculate the IDFT, v ₂(t), of ṽ₂(v).

An example of an eye diagram is given in Fig. 3(a) for ER= 15 dB and OSNR=20 dB/0.1nm. As expected, noise induces variations in the level of detected pulses. The corresponding intensity histogram is presented in Fig. 3(b). From this histogram we calculate the unregenerated Q-factor, Q ₁ defined by:

Q_{1} = \frac{V_{1} - V_{0}}{σ_{1} + σ_{0}},

(7)

where V ₁, V ₀, σ ₁ and σ ₀ are shown explicitly in Fig. 3(b).

Fig. 5. Schematic diagram of the regenerator.

By varying the white noise magnitude, A, and the extinction ratio, ER, of the pulse train we can plot the evolution of the Q-factor as a function of the OSNR for different ER. The results are shown in Fig. 4.

3. Self-phase-modulation-based 2R-regeneration technique

The schematic diagram of the regenerator is presented in Fig. 5 [1

P. V. Mamyshev, “All-optical data regeneration based on self-phase modulation effect”, in Proceedings of the 1998 European Conference on Optical Communications (ECOC, Madrid, 1998) 1, 475–476.

]. The principle of the Mamy-shev regenerator is usually explained as following. Due to the effect of self-phase modulation (SPM), the spectral bandwidth of the pulses broadens during propagation along the fiber of length L. The spectral broadening is proportional to the input peak power. The frequency of the filter is shifted of δv_f with respect to the input carrier frequency. Low peak power pulses do not induce enough SPM and are rejected by the filter. When the pulse peak power is high enough, a part of the SPM-broadened spectrum passes through the filter. This results in a nonlinear transfer function that can reduce noise in the signal. The output filter has usually a gaussian shape with the same spectral bandwidth as the input spectrum. Thus, the output pulsewidth is the same as the input pulsewidth but with a shift in wavelength from λ₀ to λ_f.

To study this regenerator, a single-pulse approach, which consists of studying the nonlinear propagation and filtering of a single pulse and plotting the ouptut intensity as a function of the input intensity, is generally used [1

P. V. Mamyshev, “All-optical data regeneration based on self-phase modulation effect”, in Proceedings of the 1998 European Conference on Optical Communications (ECOC, Madrid, 1998) 1, 475–476.

]. In Fig. 5, Ẽ₂(v) is obtained from Ẽ(v) by numerically solving the nonlinear Schrödinger equation (NLSE) [14

G. P. Agrawal, Nonlinear Fiber Optics, 2nd Ed. (Academic Press, Inc., 1995).

]. :

i \frac{\partial E}{\partial z} + \frac{β_{2}}{2} \frac{\partial^{2} E}{\partial t^{2}} + \frac{i α}{2} E = γ {∣ E ∣}^{2} E,

(8)

where E is the slowly-varying envelope of the electric field in the time domain, z the propagation distance, t the time (in a frame of reference moving with the pulse at the group velocity v_g ), β ₂ the second-order dispersion parameter, α the fiber loss and γ the nonlinear coefficient. Filtering of Ẽ₂(v) is achieved by multiplying it by the transfer function F ₂(v) of the filter to give the filtered signal Ẽ₃(v):

{\tilde{E}}_{3} (v) = F_{2} (v) {\tilde{E}}_{2} (v) .

(9)

We performed the simulation, using this method, for a 6.25 ps Fourier-limited gaussian pulse at 1550 nm. The NLSE is solved using the fourth-order predictor-corrector split-step Fourier method [15

X. Liu and B. Lee, “A fast method for nonlinear Scrhödinger equation,” IEEE Photonics Technol. Lett. 15, 1549–1551 (2003). [CrossRef]

] for the following parameters : β ₂ = +0.89 ps²/km, α = 1.4 × 10^-4 m^-1 (0.6 dB/km), γ = 8.4 W^-1m^-1, L = 2.5 km, δv_f = 280 GHz. Figure 6 represents the output peak power of the filtered pulse as a function of its corresponding input peak power.

Fig. 6. Transfer function of the regenerator and notation used.

The nonlinear shape of this function allows for the reduction of both the level of undesirable low-level pulses and the fluctuations of high-level pulses. The peak power of high-level pulses must correspond to the flat-top area of the curve (around 1.5 W in our case).

However, even if the single-pulse approach allows the nonlinear behavior of the regenerator be described, we want to point out that it does not properly describe regeneration of an input signal degraded by EDFA noise. Indeed, in the single-pulse approach noise is taken into account through variations of the pulse peak power. In reality, the wave propagating in the fiber is the superposition of the coherent data stream and the incoherent ASE noise. Then, particular attention must be paid to the description of noise in such regeneration technique. Furthermore, the single-pulse approach cannot investigate the important role played by an input filter.

4. Q-factor improvement using the white noise approach

In this section we use the approach already presented in section 2 to describe more accurately the performance of the regenerator. The nonlinear fiber and the filter used in section 3 are inserted in front of the detector (Fig. 7). The detection process does not need any optical filter since the regenerator already includes one (filter # 2). However the previously used flat-top optical filter (filter # 1) is not removed but is now inserted in front of the regenerator. The role of this filter is to eliminate noise in the bandpass of the second filter. As we will show later, the performance of the regenerator depends now of the characteristics of this filter.

Fig. 7. Schematic bloc diagram used for simulation in the white noise approach.

Fig. 8. Q-factor improvement evolution versus peak power in the white noise approach.

The post-regeneration Q-factor Q ₂ can now be evaluated and compared with the Q-factor Q ₁ calculated previously. The Q-factor improvement Q_IM is defined as the ratio (in dB) of Q ₂ to Q ₁. An improvement of Q-factor occurs if Q_IM > 0. The Q-factor improvement of the signal has been calculated for different values of the peak power of high-level pulses by keeping the ER and the OSNR constant. The result is shown in Fig. 8 for ER = 20 dB and OSNR = 27 dB/0.1 nm.

Q-factor improvement occurs between 1.6 W and 2.1 W of peak power. The maximum value of Q_IM is about 2 dB and is obtained for 2 W of peak power. This value of Q_IM is comparable to the values of 1.5 dB previously reported in experimental studies [3

, 4

]. In Fig. 8, we have also plotted the transfer function of the regenerator using the single pulse approach (dashed line). The two approaches differ for the evaluation of the working power of high-level pulses : around 1.5 W for the single-pulse approach and around 2 W for the white noise approach. This difference can be partly attributed to the finite extinction ratio of the pulse train used in the white-noise approach.

In Fig. 8, we have also plotted Q_IM when the input optical bandpass filter is removed. In this condition we observe no improvement of the Q-factor. This means that, to properly regenerate a signal degraded by EDFA noise, the Mamyshev regenerator needs to include an input filter. In the best of our knowledge, no demonstration of this point has been proposed previously, even if, in experimental studies [2

, 3

, 4

], an input filter is systematically used.

5. Role of the filters

In the previous section we have shown that the Mamyshev regenerator improves the quality of a degraded data stream only if an input filter is included in front of the regenerator. We are now able to propose a new meaning of the Mamyshev technique. Figure 9 shows the magnitude of the spectrum of both signal and noise at different points of the regenerator : (a) before the input filter, (b) after the input filter, (c) after the nonlinear fiber and (d) after the output filter. In Fig. 9(a), spectra of both signal and noise are represented separately. The noise spectrum covers the whole frequency domain while the signal spectrum is located around the carrier frequency. After the input filter, the spectra of both signal and noise can still be represented separately since filtering is a linear process [Fig. 9(b)]. The role of the input filter is to suppress noise over the bandpass of the output filter while preserving the signal spectrum. After nonlinear propagation in the fiber, signal and noise are mixed together because of nonlinear coupling and the spectrum is broadened by SPM [Fig. 9(c)] . However, noise is less affected by SPM because of its relatively low instantaneous power. Due to SPM, higher-order harmonics components appear on both side of the initial spectrum. Figure 9(d) then represents the filtered output signal. This spectrum has the characteristics of the input spectrum but is frequency-shifted. Noise is reduced but not totally eliminated by this technique because of phase-amplitude coupling introduced during the nonlinear propagation in the fiber.

Fig. 9. Evolution of the spectrum of both signal and noise through the regenerator : (a) before the input filter, (b) after the input filter, (c) after the nonlinear fiber and (d) after the output filter.

To study the influence of the input filter, we have plotted the Q-factor improvement Q_IM as a function of the input peak power for different values of the input filter bandwidth. The results are shown in Fig. 10. Maximum Q-factor improvements occur for filter bandwidths around 150 GHz. For higher filter bandwidths, the noise power under the output filter increases and degrades the output Q-factor. For lower filter bandwidths, Q-factor improvement requires higher peak powers because the filter attenuates the input power. When the bandwidth is too small, no Q-factor improvement occurs because the filter degrades the signal too much. Our study shows that an appropriate choice of the input filter bandwidth allows to optimize the regenerator efficiency. This argument could be important for designing Mamyshev regenerators in the context of wavelength division multiplexing systems where optical demultiplexers play the role of input filters [2

Fig. 10. Q-factor improvement evolution versus peak power for different input filter band-widths.

Figure 9(d) also demonstrates the role of the output filter. By choosing the frequency shift δv_f of the output filter to be a multiple of the repetition rate, the spectrum shape and then the modulation format are preserved. When this is so, the carrier frequency component is centered in the spectrum. This is the case of our study where δv_f was chosen to be 7 times (280 GHz) the repetition rate. In comparison, we have also represented, in the inset of Fig. 9(d), the output spectrum for a frequency shift corresponding to an odd half multiple of the repetition rate (260 GHz). In this case, the carrier frequency component is suppressed. However, Q-factor improvement still occurs with a maximum value of Q_IM equal to 1.9 dB.

6. Conclusion

We have numerically investigated the 2R-regeneration technique utilizing self-phase modulation and filtering. We have proposed a slightly different interpretation of this technique by using the spectral representation of signal and noise. Indeed, the basic principle of the Mamyshev regeneration technique is to transpose more signal than noise to a spectral region where ASE noise has been previously eliminated. Q-factor improvement of 2 dB has been numerically evaluated. This value is in good agreement with the experimental values recently reported. This approach has allowed us to point out the role of the input filter which has to be suitably chosen. We have also demonstrated that the frequency shift of the output filter must be a multiple of the repetition rate to preserve the modulation format.

Acknowledgments

Authors thank Art O’Hare (School of Physics, Dublin Institute of Technology, Dublin, Ireland) for his comments on the manuscript. This work is supported by the Conseil Régional de Bretagne (convention No.1193).

References and links

1.	P. V. Mamyshev, “All-optical data regeneration based on self-phase modulation effect”, in Proceedings of the 1998 European Conference on Optical Communications (ECOC, Madrid, 1998) 1, 475–476.
2.	G. Raybon, Y. Su, J. Leuthold, R. Essiambre, T. Her, C. Joergensen, P. Steinvurzel, K. Dreyer, and K. Feder, “40Gbit/s Pseudo-linear transmission over one million kilometres,” in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2002), FD-10 1-3.
3.	T. H. Her, G. Raybon, and C. Headley, “Optimization of Pulse Regeneration at 40 Gb/s Based on Spectral Filtering of Self-Phase Modulation in Fiber,” IEEE Photonics Technol. Lett. 16, 200–202 (2004). [CrossRef]
4.	N. Yoshikane, I. Morita, T. Tsuritani, A. Agata, N. Edagawa, and S. Akiba, “Benefit of SPM-based all-optical reshaper in receiver for long-haul DWDM tranmission systems,” IEEE J. Sel. Top. Quantum Electron. 10, 412–420 (2005).
5.	M. Rochette, J. L. Blows, and B. J. Eggleton, “An all-optical regenerator that descriminates noise from signal,” in Proceedings of the 2005 European Conference on Optical Communications (ECOC, Glasgow, 2005) 3, 403–404.
6.	S. Taccheo and K. Ensner, “Investigation of amplitude noise and timing jitter of supercontinuum spectrum-sliced pulses,” IEEE Photonics Technol. Lett. 14, 1100–1102 (2002). [CrossRef]
7.	M. Matsumoto, “Performance analysis and comparison of optical 3R regenerators utilizing self-phase modulation in fibers,” J. Lightwave Technol. 22, 1472–1482 (2004). [CrossRef]
8.	J. T. Mok, J. L. Blows, and B. J. Eggleton, “Investigation of group delay ripple distorted signals transmitted through all-optical 2R regenerators,” Opt. Express 12, 4411–4422 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4411. [CrossRef] [PubMed]
9.	M. Vasilyev and T. I. Lakoba, “All-optical multichannel 2R regeneration in a fiber-based device,” Opt. Lett. 30, 1458–1460 (2005). [CrossRef] [PubMed]
10.	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 Photonics Technol. Lett. 17, 908–910 (2005). [CrossRef]
11.	G. P. Agrawal, Fiber-Optic Communication Systems, 3rd Ed . (John Wiley & sons, Inc., 2002). [CrossRef]
12.	J. W. Goodman, Statistical Optics (John Willey & sons, Inc., 1985).
13.	N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989). [CrossRef]
14.	G. P. Agrawal, Nonlinear Fiber Optics, 2nd Ed. (Academic Press, Inc., 1995).
15.	X. Liu and B. Lee, “A fast method for nonlinear Scrhödinger equation,” IEEE Photonics Technol. Lett. 15, 1549–1551 (2003). [CrossRef]

OCIS Codes
(060.4510) Fiber optics and optical communications : Optical communications
(070.4340) Fourier optics and signal processing : Nonlinear optical signal processing
(230.1150) Optical devices : All-optical devices
(230.4320) Optical devices : Nonlinear optical devices

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: January 13, 2006
Revised Manuscript: February 17, 2006
Manuscript Accepted: February 19, 2006
Published: March 6, 2006

Citation
Thanh Nguyen, Mathilde Gay, Laurent Bramerie, Thierry Chartier, Jean-Claude Simon, and Michel Joindot, "Noise reduction in 2R-regeneration technique utilizing self-phase modulation and filtering," Opt. Express 14, 1737-1747 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-5-1737

Sort: Author | Year | Journal | Reset

References

P. V. Mamyshev, "All-optical data regeneration based on self-phase modulation effect", in Proceedings of the 1998 European Conference on Optical Communications (ECOC, Madrid, 1998) 1, 475-476.
G. Raybon, Y. Su, J. Leuthold, R. Essiambre, T. Her, C. Joergensen, P. Steinvurzel, K. Dreyer and K. Feder, "40Gbit/s Pseudo-linear transmission over one million kilometres," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2002), FD-10 1-3.
T. H. Her, G. Raybon, C. Headley, "Optimization of Pulse Regeneration at 40 Gb/s Based on Spectral Filtering of Self-Phase Modulation in Fiber," IEEE Photonics Technol. Lett. 16, 200-202 (2004). [CrossRef]
N. Yoshikane, I. Morita, T. Tsuritani, A. Agata, N. Edagawa, S. Akiba, "Benefit of SPM-based all-optical reshaper in receiver for long-haul DWDMtranmission systems," IEEE J. Sel. Top. Quantum Electron. 10, 412-420 (2005).
M. Rochette, J. L. Blows, B. J. Eggleton, "An all-optical regenerator that descriminates noise from signal," in Proceedings of the 2005 European Conference on Optical Communications (ECOC, Glasgow, 2005) 3, 403-404.
S. Taccheo, K. Ensner, "Investigation of amplitude noise and timing jitter of supercontinuum spectrum-sliced pulses," IEEE Photonics Technol. Lett. 14, 1100-1102 (2002). [CrossRef]
M. Matsumoto, "Performance analysis and comparison of optical 3R regenerators utilizing self-phase modulation in fibers," J. Lightwave Technol. 22, 1472-1482 (2004). [CrossRef]
J. T. Mok, J. L. Blows, and B. J. Eggleton, "Investigation of group delay ripple distorted signals transmitted through all-optical 2R regenerators," Opt. Express 12, 4411-4422 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4411. [CrossRef] [PubMed]
M. Vasilyev, T. I. Lakoba, "All-optical multichannel 2R regeneration in a fiber-based device," Opt. Lett. 30, 1458-1460 (2005). [CrossRef] [PubMed]
M. Rochette, J. N. Kutz, J. L. Blows, D. Moss, J. T. Mok, B. J. Eggleton, "Bit-error ratio improvement with 2R optical regenerators," IEEE Photonics Technol. Lett. 17, 908-910 (2005). [CrossRef]
G. P. Agrawal, Fiber-Optic Communication Systems, 3rd Ed. (John Wiley & sons, Inc., 2002). [CrossRef]
J. W. Goodman, Statistical Optics (John Willey & sons, Inc., 1985).
N. A. Olsson, "Lightwave systems with optical amplifiers," J. Lightwave Technol. 7, 1071-1082 (1989). [CrossRef]
G. P. Agrawal, Nonlinear Fiber Optics, 2nd Ed. (Academic Press, Inc., 1995).
X. Liu, B. Lee, "A fast method for nonlinear Scrh¨odinger equation," IEEE Photonics Technol. Lett. 15, 1549-1551 (2003). [CrossRef]

IEEE J. Sel. Top. Quantum Electron.

N. Yoshikane, I. Morita, T. Tsuritani, A. Agata, N. Edagawa, S. Akiba, "Benefit of SPM-based all-optical reshaper in receiver for long-haul DWDMtranmission systems," IEEE J. Sel. Top. Quantum Electron. 10, 412-420 (2005).

IEEE Photonics Technol. Lett.

S. Taccheo, K. Ensner, "Investigation of amplitude noise and timing jitter of supercontinuum spectrum-sliced pulses," IEEE Photonics Technol. Lett. 14, 1100-1102 (2002). [CrossRef]
M. Rochette, J. N. Kutz, J. L. Blows, D. Moss, J. T. Mok, B. J. Eggleton, "Bit-error ratio improvement with 2R optical regenerators," IEEE Photonics Technol. Lett. 17, 908-910 (2005). [CrossRef]
T. H. Her, G. Raybon, C. Headley, "Optimization of Pulse Regeneration at 40 Gb/s Based on Spectral Filtering of Self-Phase Modulation in Fiber," IEEE Photonics Technol. Lett. 16, 200-202 (2004). [CrossRef]
X. Liu, B. Lee, "A fast method for nonlinear Scrh¨odinger equation," IEEE Photonics Technol. Lett. 15, 1549-1551 (2003). [CrossRef]

Other

M. Rochette, J. L. Blows, B. J. Eggleton, "An all-optical regenerator that descriminates noise from signal," in Proceedings of the 2005 European Conference on Optical Communications (ECOC, Glasgow, 2005) 3, 403-404.
P. V. Mamyshev, "All-optical data regeneration based on self-phase modulation effect", in Proceedings of the 1998 European Conference on Optical Communications (ECOC, Madrid, 1998) 1, 475-476.
G. Raybon, Y. Su, J. Leuthold, R. Essiambre, T. Her, C. Joergensen, P. Steinvurzel, K. Dreyer and K. Feder, "40Gbit/s Pseudo-linear transmission over one million kilometres," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2002), FD-10 1-3.
G. P. Agrawal, Nonlinear Fiber Optics, 2nd Ed. (Academic Press, Inc., 1995).
G. P. Agrawal, Fiber-Optic Communication Systems, 3rd Ed. (John Wiley & sons, Inc., 2002). [CrossRef]
J. W. Goodman, Statistical Optics (John Willey & sons, Inc., 1985).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Click here to see a list of articles that cite this paper