Simultaneous chromatic dispersion monitoring and optical modulation format identification utilizing four wave mixing

Optics Communications 354 (2015) 59–65

Contents lists available at ScienceDirect

Optics Communications journal homepage: www.elsevier.com/locate/optcom

Simultaneous chromatic dispersion monitoring and optical modulation format identification utilizing four wave mixing Sheng Cui a,b,c, Chen Qiu a,b,c, Changjian Ke a,b,c,n, Sheng He a,b,c, Deming Liu a,b,c a

School of Optical and Electronic Information, Huazhong University of Science and Technology, Hubei, China National Engineering Laboratory for Next Generation Internet Access System, Wuhan, Hubei, China c Wuhan National Laboratory for Optoelectronics, Wuhan, Hubei, China b

art ic l e i nf o

a b s t r a c t

Article history: Received 27 July 2014 Received in revised form 21 April 2015 Accepted 22 April 2015 Available online 25 April 2015

This paper presents a method which is able to monitor the chromatic dispersion (CD) and identify the modulation format (MF) of optical signals simultaneously. This method utilizes the features of the output curve of the highly sensitive all-optical CD monitor based on four wave mixing (FWM). From the symmetric center of the curve CD can be estimated blindly and independently, while from the profile and convergence region of the curve ten commonly used modulation formats can be recognized with simple algorithm based on maximum correlation classifier. This technique does not need any high speed optoelectronics and has no limitation on signal rate. Furthermore it can tolerate large CD distortions and is robust to polarization mode dispersion (PMD) and amplified spontaneous emission (ASE) noise. & 2015 Elsevier B.V. All rights reserved.

Keywords: Nonlinear optics Four-wave mixing Chromatic dispersion monitoring Modulation format identification Advanced modulation formats

1. Introduction In order to support a wide range of data traffic and enhance operation flexibility optical networks are nowadays becoming more heterogeneous [1,2]. In such networks optical performance monitoring (OPM) and modulation format identification (MFI) are essential techniques for intelligent network management and optimal optical signal acquirement and demodulation [3–7]. Such techniques can provide key information of the optical signals such as the CD, polarization mode dispersion (PMD), optical signal to noise ratio (OSNR), modulation format and the number of multiplexed polarizations. Among the many CD monitors proposed by now [8,9], the alloptical chromatic dispersion monitors based on ultra-fast nonlinear effects are attractive because they can be used to monitor the CD distortions in a modulation format and bit rate transparent manner and are relatively simple, thus cost-effective to be deployed at low cost optical nodes or transmission systems without coherent receivers. In previous works, we proposed a highly sensitive all optical CD monitor based on exponential power transfer function (PTF) provided by FWM in highly nonlinear fibers (HNLFs) [9]. This method is then improved to expand the CD monitoring range, be robust to PMD and OSNR influence, and n Corresponding author at: School of Optical and Electronic Information, Huazhong University of Science and Technology, Hubei, China. Fax: þ 86 27 87556188. E-mail address: [email protected] (S. Cui).

http://dx.doi.org/10.1016/j.optcom.2015.04.060 0030-4018/& 2015 Elsevier B.V. All rights reserved.

accommodate on–off keying (OOK) and advanced modulation formats [10]. In this paper it is demonstrated that the highly sensitive all-optical CD monitor can also be used to realize MFI function. The topic of MFI has been well explored for radio communications. Nonetheless, MFI for fiber optic communications still remains underdeveloped. By now four different optical MFI methods have been proposed: (1) MFI from the constellation diagram with the use of k-means [3]; (2) MFI from signal cumulants [4]; Both of the two methods rely on very complicated blind demodulation process, and require costly full-fledged coherent receivers; (3) MFI from the asynchronous amplitude histograms or asynchronous delay-tap plots, which has limited CD tolerance (about 500 ps/nm) because these features are distorted by CD [5,6]; (4) MFI from signal Stokes space representation [7], which is developed for polarization multiplexed signals and also requires coherent receivers for CD compensation. Furthermore these methods have a single function of MFI and are not able to monitor CD distortions. Thus it is desirous to aggregate CD monitoring and MFI functions in a single device to enhance the operational efficiency and reduce the cost. In this paper, we propose a simple CD monitoring and MFI method without using high cost coherent receivers or any high speed optoelectronic devices. The highly sensitive all optical CD monitor [9] is used to monitor the variations of the signal instantaneous power distribution against CD which are unique for signals with different MFs. The features of the output curve of the CD monitor including its symmetric center, profile and

60

S. Cui et al. / Optics Communications 354 (2015) 59–65

Fig. 1. Setup of the CD monitoring and MFI module. EDFA: Erbium-doped fiber amplifier, and PM: Power meter.

convergence region are utilized to realize blind CD estimation and MFI simultaneously. With this method ten widely used MF including on–off keying and advanced modulation formats with single and dual polarizations can be identified using a simple algorithm based on maximum correlation classifier. Furthermore the CD tolerance limit is also expanded as the features are not distorted by CD. This paper is organized as follows: Section 2 reviews the working principles of the all optical CD monitor. Section 3 describes the features of the output curves of the CD monitor for signals with different MFs and explains the physical mechanism behind. Based on these features the MFI method is proposed. The whole CD estimation and MFI algorithm are described and are carried out to validate the effectiveness of this method in Section 4 followed by a brief conclusion.

2. Principles of the CD monitor The setup of the FWM based CD monitoring and MFI module is shown in Fig.1. The optical signal with unknown CD and MF is tapped from the optical link and fed into the module. The tunable dispersion compensator (TDC) is used to apply a series of CD onto the signal. The signal is then amplified by the EDFA and input into the HNLF with a continuous probe wave ωpb . A new idler wave at ωi = 2ωs − ωpb is generated from the FWM in the HNLF and extracted by the band pass optical filter at the fiber output. The output idler wave instantaneous power is given by

Pi = Ppb ⋅G (Ps ) = Ppb (γPs L )2 [ sinh (gL )/gL ]2 ,

(1)

with

g 2 = − Δβ (Δβ/4 + γPs ).

(2)

10 5 0 -5 -10 -15 -20

3. Principles of the MFI method The output curves of the CD monitor for signals with different MFs are shown in Figs. 2 and 3. Ten modulation formats are considered and the device parameters used are the same as that reported previously [10]. The FWM based nonlinear PTF has an order of about 5.5. The TDC sweeping range is 0–320 ps/nm. The results are obtained by numerical simulations using VPI TransmissionMaker V8.6 based on nonlinear Schrödinger equation and splitstep Fourier method. There are two noteworthy points. First, only 40 GBaud signals are considered, but all of the curves can be rescaled to any baud rate using the (1/baud rate)2 scaling along the

Idler average power (dBm)

Idler average power (dBm)

Here Ppb ,γ L, g and Δβ are the input probe wave power, fiber nonlinear coefficient, fiber length, parametric gain and linear

phase mismatch, respectively. When the linear phase mismatch Δβ satisfies −4γPs ≤ Δβ ≤ 0, exponential gain occurs [11]. The exponential gain G (Ps ) provides an exponential PTF between the signal and idler wave instantaneous powers. For the same input average power the nonlinear PTF gives preferential gain to signals with higher peak power, thus results in higher output average power P¯i . In other words the CD monitor output is sensitive to the input signal instantaneous power distribution which, as we know, changes with CD distortions. So CD can be monitored by simple average power measurement with cheap slow optical detectors. As demonstrated in our previous works, using the exponential PTF the output contrast of the CD monitor can be greatly improved compared to the previous monitors using a quadratic PTF [9]. The output curve of the CD monitor is symmetric about the zero-dispersion point, as CD induced optical pulse distortions are the same for CDs with the same magnitude but opposite sign. Thus using a simple symmetric center search algorithm in combination with a TDC, the zero CD point and the residual CD can be easily identified [10]. The position of the symmetric center is only determined by CD and is insensitive to PMD and OSNR, thus CD can be monitored independently. Numerical simulation shows that CD can be accurately estimated for signals with OSNR larger than 10 dB and differential group delay (DGD) smaller than 10 ps. It is noteworthy that the optical signals consist of random symbol sequence and the output idler average power P¯i which is measured with a slow optical detector is actually the averaged result over a large number of symbols, thus independent on the specific symbol sequence pattern. In other words P¯i is only determined by the statistical distribution of the signal instantaneous power which, in turn, is dependent on the signal MF, as will be shown later.

0

50

100

150

200

CD (ps/nm/km)

250

5 0 -5 -10 -15 -20 -25

0

50

100

150

200

250

300

CD (ps/nm/km)

Fig. 2. (a) The CD monitoring curves of 33% RZ (solid), CSRZ (dashed), NRZ (dotted) and ODB (dash dotted) signals. (b) The curves of single (solid) and dual (dashed) polarization 33% RZ (black)/CSRZ (blue) /NRZ (red) 16-QAM (solid) signals for CD¼ 0 ps/nm, OSNR ¼ 30 dB and DGD ¼ 0 ps. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

5

Idler average power (dBm)

Idler average power (dBm)

S. Cui et al. / Optics Communications 354 (2015) 59–65

0

-5

-10

-15

0

50

100

150

200

250

300

CD (ps/nm/km)

61

0 -2 -4 -6 -8 -10 -12 -14 -16

0

50

100

150

200

250

300

CD (ps/nm/km)

Idler average power (dBm)

Fig. 3. (a) The CD monitoring curves of 33% RZ (solid), CSRZ (dashed), NRZ (dotted) and ODB (dash dotted) signals. (b) The curves of single (solid) and dual (dashed) polarization 33% RZ (black)/CSRZ (blue) /NRZ (red) 16-QAM (solid) signals for CD ¼0 ps/nm, OSNR ¼ 14 dB and DGD¼ 4 ps. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 5 0 -5 -10

NRZ-16QAM CSRZ-16QAM 33% RZ-16QAM PM-NRZ-16QAM PM-CSRZ-16QAM PM-33%-16QAM

-15 -20 -25

0

200

400

600

800

1000

1200

1400

1600

CD (ps/nm) Fig. 4. The CD monitoring curves of single and dual polarization 16-QAM signals.

x axis because the dispersion effect scales inversely proportional to the squared baud rate [12]. Second, as the curve is symmetric about the zero-dispersion point, only the parts on the positive x-axis are shown. As we can see from Fig. 2 the curves are unique for signals with different MFs. This phenomenon can be explained as follows. Firstly, as shown in Fig. 2(a), when CD begins to increase, the curves of 33% RZ signals first descends and then ascends, while those of the carrier suppressed return to zero (CSRZ) and not return to zero (NRZ) signals first ascend and then descend. This is because the pulse peak power of the 33% RZ signals first drops as the pulse width is broadened by CD, while the pulse peak power of the CSRZ and NRZ signals first increase because of the phase discontinuity between adjacent bits of CSRZ signals and the well-

known “ears” formation on the edges of NRZ signals [12]. In particular, the curve profiles of the CSRZ and 33% RZ are nearly reversed. When CD keeps increasing, the curves begin to show periodic-like oscillations due to the temporal Talbot effect [12] which damps to some extent because of the random symbol sequence modulated onto the optical pulses. For signals with 100% duty cycle, such as NRZ and ODB signals, the oscillations are small and almost damp out. The profile difference between the four OOK MF curves is thus very obvious. Secondly, Fig. 2(b) shows the curves of the single and dual polarization 16-QAM signals with different duty cycles. As we can see they are different from the curves of the OOK signals. For 16-QAM signals, the Talbot effect induced oscillations damp much more quickly and after about one Talbot period DT (DT ≈80 ps/nm for 40 Gbaud signals at 1550 nm) the oscillations almost damp out. This is because, compared to simple OOK modulation, the multilevel phase and amplitude modulation applied onto the optical pulses have much more damping effect on the Talbot effect which is strongest for periodic pulse sequence. Thus the curves of the 16-QAM signals can be easily distinguished from those of the OOK signals. From Fig. 2 (b) we can see that the curves of the dual polarization 16-QAM signals are identical with their single polarization counterparts. But with increasing CD, the curves of the dual and single polarization signals tend to converge to different power (Pconv ). To demonstrate this feature more clearly, Fig.4 shows the curves over a broader CD range (20 DT s). It shows that the curves of the single and dual polarization signals tend to converge to different Pconv s with 10 dB interval. The significant power gap makes it possible to

Fig. 5. Statistical power distribution of single (left) and dual polarization (right) 16-QAM signals with the same average power at CD ¼10DT s. The instantaneous power is scaled by the input average power.

62

S. Cui et al. / Optics Communications 354 (2015) 59–65

Tx RZ-OOK

Tx CSRZ-OOK SMF Tx NRZ-OOK

Tx ODB-OOK

SMF CD/PMD emulator

Switch

Coupler

EDFA Receiver

EDFA Attenuator OBPF

Tx (PM)-RZ-16QAM

CD esti. & MFI module

Tx (PM)-CSRZ-16QAM

Tx (PM)-NRZ-16QAM Fig. 6. System setup for CD estimation and MFI based on the monitoring curves. OBPF: Optical band pass filter.

Obtain monitoring curve

Idlerpower (dBm)

40 20

CD esti.

0 -20

curve scaling and truncation

-40 -60 10

15 20 Signalpower (dBm)

25

Fig. 7. The PTF provided by FWM with an order of about 5.5 obtained by numerical simulation (solid line) and analytic method (dashed line).

identify single and dual polarization signals by simple power measurement. The different Pconv s can be explained by the statistical instantaneous power distribution of the single and dual polarization signals at large CD values. Fig. 5 shows the power distribution of the two kinds of 16-QAM signals at CD ¼ 10DT s. As we can see with sufficient CD, the single and dual polarization signals tend to follow different kinds of power distributions. This is because with increasing CD more and more optical pulses overlap and interfere with each other, causing strong inter symbol interference (ISI). From the central limit theorem, under strong ISI the optical field real and imaginary part of a long pulse sequence (noting that a slow optical detector is used in the CD monitor) follow Gaussian distributions. Hence, the amplitude of the single polarization signal has a Rayleigh distribution, and the instantaneous power follows exponential distribution [14]. In contrast, the instantaneous power of the dual polarization signals consisted of two independent channels follows chi-squared distribution with four degrees of freedom. Because the power distributions evolve into different types, and thus, the signals receive different gain from the nonlinear PTF, resulting in different Pconv s. In practical applications the PMD and ASE noise influence on the CD monitor must be considered. Fig. 3 shows the curves of signals with OSNR ¼14 dB and DGD ¼ 4 ps. As we can see in the presence of large link distortions the curve contrast is reduced to

OOK MFs: NRZ,CSRZ,RZ or ODB;

Max Corr. classifier duty cycle Yes

No

16QAM with certain duty cycle

PM-16QAM with certain duty cycle

Fig. 8. The flow chart of the CD esti. And MFI process (PTconv represent the power thresholds for the judgment of single and dual polarization signals).

some extent but the curve profiles are maintained thanks to the exponential PTF. As for the CD distortion which is a troublesome issue for the other MFI methods, it can only shift the curve along the CD-axis without changing its profile. From the above analysis we can see that the CD monitoring curve profiles are unique for signals with different MFs and are almost maintained in the present of different distortions. Thus the curves shown in Fig. 2 can be used as templates in the maximum correlation classifier to realize MFI. The chosen seven templates include the four curves of the OOK MFs shown in Fig. 2(a) and the three curves of the single polarization 16-QAM MFs shown in Fig. 2(b) which are also shared by the dual polarization 16-QAM signals because their curves are similar. Note that all of the seven

S. Cui et al. / Optics Communications 354 (2015) 59–65

63

Fig. 9. The CD monitoring curves for 40GBaud NRZ-OOK (a) and 33%-RZ-16-QAM (b) signals with CD equal to 600 and –600 ps/nm, respectively.

33%RZ -OOK

33%RZ -16-QAM

OSNR (dB)

ODB

OSNR (dB)

OSNR (dB)

CSRZ -16-QAM

CSRZ -OOK

The templates are represented by NRZ -OOK CSRZ -OOK

33%RZ -OOK NRZ -16-QAM CSRZ -16-QAM 33%RZ -16-QAM OSNR (dB)

OSNR (dB)

NRZ -OOK

ODB

NRZ -16-QAM

OSNR (dB)

OSNR (dB) Fig. 10. Variations of corrn (n¼ 1 7) against OSNR when DGD¼ 0 ps.

curve templates consists of 4DT s which is enough for MFI. In the classifier, the correlation function used to evaluate the similarity between the template (MCn ) and the curve to be recognized (MCs ) is given by

DMCs, n = Diff (MCs, n ) corrn =

E [(DMCs −μs )(DMCn −μn )] σs σn

(n = 1, 2, ⋯7) (3)

where DMCs, n represent the first derivatives of MCs, n , and μs, n and σs, n are the means and standard deviations of DMCs, n . MCn that gives the highest corrn value is declared a match and n indicates

the specific MF. On this basis the single and dual polarization 16QAM signals can be distinguished from Pconv . In practice, the fiber parameters may deviate from the nominal ones. But because exponential PTFs can be obtained when Δβ is in the range of −4γPs ≤ Δβ ≤ 0, the exponential PTF can still be retained when the deviation is small. When the deviation is large, which is a rare case, one can tune ωpb and Ps to keep −4γPs ≤ Δβ ≤ 0 satisfied, which is not difficult because the PTF can be measured easily. It is noteworthy that when measuring PTF both Ps and Pi are not modulated, so slow optical detectors can be used to measure Ps and Pi . When exponential PTFs can be obtained, similar monitoring

64

S. Cui et al. / Optics Communications 354 (2015) 59–65

33%RZ-OOK

ODB

33%RZ-16-QAM

OSNR (dB) CSRZ -16-QAM

OSNR (dB)

CSRZ -OOK

OSNR (dB)

The templates are represented by NRZ -OOK CSRZ -OOK

33%RZ-OOK NRZ-16-QAM CSRZ -16-QAM 33%RZ-16-QAM OSNR (dB) NRZ -OOK

OSNR (dB) NRZ -16-QAM

OSNR (dB)

OSNR (dB)

ODB

-4 -6 -8 -10 -12 30

26

22 18 OSNR (dB)

14

10

0

2

4

6

8

DGD(ps)

0 -2 -4 -6 -8 -10 -12 30

26

22 18 OSNR(dB)

14

10

0

2

4

6

8

DGD(ps)

Idler average power (dBm)

0 -2

Idler average power (dBm)

idler average power (dBm)

Fig. 11. Variations of corrn (n ¼1  7) against OSNR when DGD¼ 8 ps in the worst case.

0 -2 -4 -6 -8 -10 -12 30

26

22 18 OSNR(dB)

14

10

0

2

4

6

8

DGD(ps)

Fig. 12. The variations of Pconv for 33% RZ-16-QAM (a), CSRZ-16-QAM (b) and NRZ-16-QAM (c) signals when OSNR and PMD degradations are present simultaneously.

curves can be obtained. As the maximal correlation classifier based on statistical correlation functions is used to evaluate the similarities, small deviations will not affect the MFI results.

4. Numerical simulations In order to validate the proposed CD estimation and MFI technique, extensive numerical simulations are performed using the VPI TransmissionMaker V8.6. Fig. 6 shows the system configuration used in our simulations. The device parameters are the

same as those used to obtain Fig. 2. The EDFA output signal average power is set at 50 mW. The PTF provided by FWM is shown in Fig. 7. The order of the PTF is about 5.5. The numerical results agree very well with the analytical ones using Eq. (1) except the roll off in high power region because gain saturation is not considered in the analytical model [11]. The OSNR is varied in the range of 10–30 dB (in steps of 4 dB) by using an EDFA with a variable optical attenuator in front. A CD and PMD emulator are used to introduce different CD and DGD. The signal's state-of-polarization is 45° with respect to the principal states-of-polarization of the PMD emulator.

S. Cui et al. / Optics Communications 354 (2015) 59–65

The flow chart of the CD estimation and MFI process is shown in Fig. 8. In the first step the monitoring curve is obtained. Fig. 9 shows the curves for 40 GBaud NRZ and 33% RZ-16-QAM signals with residual CD equal to 600 and  600 ps/nm, respectively. The x-axis denotes the CD applied onto the signal by the TDC. In the second step the symmetric center is found by simple search algorithm [10] and the CD is equal to the opposite signed TDC dispersion at that symmetric center. We note that the monitoring range is not limited by the Talbot effect, but by the tuning range of the TDC. In case that the signal CD is large, the tuning range can be expanded by using the TDC in combination with cheap static dispersion compensation modules based on dispersion compensation fiber (DCF). Furthermore fast TDCs can be used to reduce the sweeping time [15–17]. The reconfiguration time of the TDCs based on liquid crystal on silicon (LCOS) is on the scale of less than 100 ms and the tuning range can reach 71200 ps/nm with 3 dB bandwidth of 30 GHz which is suitable for 40 GBaud signals [16]. Recently it is reported that a fast TDC based on parametric process has response time of less than 17 ms [17]. After CD is estimated, Pconv can be obtained from the far end point away from the zero dispersion point (ZDP) as shown in Fig. 9. In the third step, the curve is scaled along the x-axis by a factor of (40/Bs )2, where Bs is the signal baud rate (in GBaud). The curve is then truncated to have a length of 4DT s from the symmetric center. In the fourth step, maximum correlation classifier is applied to distinguish the NRZ, CSRZ, 33% RZ OOK and 16-QAM signals with different duty cycles. The classifier is tested against different link impairments via extensive simulations. Fig. 10 shows corrn (n ¼1– 7) variations against OSNR from 10 to 30 dB when DGD ¼0. The part below zero is not shown to maintain focus on the positive part because the maximum corrn indicates the MF. As we can see, the correlation value between the curve of the distorted signals and the correct template only decreases slightly and remains much higher than the other ones, showing that the classifier is robust to ASE noise. The MF can be identified correctly even when OSNR as low as 10 dB. Fig.11 shows corrn variations against OSNR from 10 to 30 dB when DGD ¼8 ps. As we can see the correlation value between the curve of the distorted signals and the correct template remains the maximal one, and the MF can still be identified correctly when DGD ¼8 ps and OSNR ¼10 dB. The MFI results for the dual polarization 16-QAM MFs are similar to those shown in Fig. 11 and not shown here for concision. The fifth step is for the 16-QAM signals with determined duty cycles but unknown number of polarizations. As explained above the two kind of signals can be identified by choosing an appropriate power threshold (PTconv ). Fig.12 shows the variation ranges of Pconv when DGD is in the range of 0-8 ps and OSNR is in the range of 10–30 dB. As we can see there is an obvious power gap between single and dual polarization signals and PTconv can be set at  7.2 dBm. When Pconv is above PTconv , the signal is single polarization one, otherwise it is dual polarization one.

65

5. Conclusion In summary, we have proposed a novel CD estimation and MFI method utilizing the highly sensitive CD monitor based on FWM. It is shown that the output curves of the CD monitor are unique for signals with different MFs because they have different statistical power distributions when CD changes. The difference is related to the pulse duty cycle, amplitude and phase modulation manner and number of multiplexed polarizations. The features of the curve including its symmetric center, profile and convergence region are utilized to realize CD estimation and MFI. With this method, ten widely used MFs can be recognized using simple algorithms based on maximum correlation classifier. This method does not require expensive coherent receivers or any high speed optoelectronic devices. Furthermore it can tolerate large CD distortions and is robust to PMD and ASE noise.

Acknowledgments This work is supported by the National High Technology Research and Development Program of China (863Program, Grant no. 2013AA013403), Major Equipment Development Project (Grant no. 2013YQ160487), National Natural Science Foundation of China (Grant no. 61475053) and the Fundamental Research Funds for the Central Universities (Grant no. 2015TS045).

References [1] A. Nag, M. Tornatore, B. Mukherjee, J. Lightw. Technol. 28 (2010) 466–475. [2] K. Roberts, C. Laperle, European Conference on Optical Communication, Amsterdam, Netherlands, September 16–20, 2012, pp. We.3.A.3. [3] N. G. Gonzalez, D. Zibar, I. T. Monroy, European Conference on Optical Communication, Torino, Italy, September 19–23, 2010, p. 6.11. [4] P. Isautier, A. Stark, K. Mehta, R. de Salvo, S. E. Ralph, Optical Fiber Communication Conference, Anaheim, USA, March 19–21, 2013, pp. OTh3B.4. [5] F.N. Khan, Y. Zhou, A.P.T. Lau, C. Lu, Opt. Express 20 (2012) 12422–12431. [6] F.N. Khan, Y. Zhou, Q. Sui, A.P.T. Lau, Opt. Fiber Technol. 20 (2014) 68–74. [7] R. Borkowski, D. Zibar, A. Caballero, V. Arlunno, I.T. Monroy, IEEE Photonics Technol. Lett. 25 (2013) 2129–2133. [8] Z. Pan, C. Yu, A.E. Willner, Opt. Fiber Technol. 16 (2010) 20–45. [9] S. Cui, S. Sun, L. Li, C. Ke, Z. Wan, D. Liu, IEEE Photonics Technol. Lett. 23 (2011) 1724–1726. [10] S. Cui, S. He, S. Sun, C. Ke, D. Liu, Opt. Commun. 309 (2013) 180–186. [11] G.P. Agrawal, Nonlinear Fiber Optics, second ed., Academic Press, New York, 1995. [12] S. Wielandy, M. Fishteyn, B. Zhu, J. Lightw. Technol. 22 (2004) 784–793. [14] L. Trutna, P. Spagon, D.E. del Castillo, Engineering Statistics Handbook, National Institute of Standards and Technology, United States, 2000. [15] B.J. Eggleton, B. Mikkelsen, G. Raybon, A. Ahuja, J.A. Rogers, P.S. Westbrook, T. N. Nielsen, S. Stulz, K. Dreyer, IEEE Photonics Technol. Lett. 12 (2000) 1022–1024. [16] K. Seno, N. Ooba, K. Suzuki, T. Watanabe, M. Itoh, S. Mino, T. Sakamoto, Optical Fiber Communication Conference, Los Angeles, USA, March 8–10, 2011, pp. OWM.5. [17] Ken Tanizawa, Hiroyuki Matsuura, Kensuke Ogawa et al., Optical Fiber Communication Conference, Los Angeles, USA, March 22–26, 2015, pp. M3F.3.