Format transparent, wide range and independent dispersion monitoring method based on four-wave mixing

Optics Communications 309 (2013) 180–186

Contents lists available at SciVerse ScienceDirect

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

Format transparent, wide range and independent dispersion monitoring method based on four-wave mixing Sheng Cui a,b,c, Sheng He a,b,c, Simin Sun a,b,c, Changjian Ke a,b,c,n, 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 30 May 2013 Received in revised form 6 July 2013 Accepted 8 July 2013 Available online 19 July 2013

In this paper we propose an improved all optical chromatic dispersion (CD) monitoring method based on highly nonlinear power transfer function (PTF) provided by four-wave mixing (FWM) in highly nonlinear fibers (HNLFs). This method can be applied for various modulation formats, including on–off keying and advanced multi-level modulation formats, without necessitating any changes of the hardware or software. Furthermore, it can expand the CD monitoring range beyond the limitation of Talbot effects and is insensitive to optical signal-to-noise ratio (OSNR) and polarization mode dispersion (PMD). These improvements are achieved by optimizing the profile of the PTF curve and utilizing a sweeping tunable dispersion compensator (TDC) in combination with an extremely simple digital signal processing (DSP) to find the zero residual dispersion point. Numerical simulations are then used to demonstrate the effectiveness of this method. & 2013 Elsevier B.V. All rights reserved.

Keywords: Fiber optics communications Chromatic dispersion monitoring Four-wave mixing Power transfer function Tunable dispersion compensator

1. Introduction In high speed optical transmission systems CD is an indispensible signal quality parameter to be monitored [1]. All-optical chromatic dispersion monitors based on ultra-fast nonlinear effects are attractive because they can accommodate different modulation formats and bit rates and are relatively simple, thus cost-effective to be deployed at optical nodes without coherent receivers [1–9]. By now, many all-optical CD monitors have been proposed [2–10]. For the all-optical monitors utilizing nonlinear effects to map the CD information onto the optical spectrum, prior knowledge of the input signal spectrum and delicate spectrum analysis of the output signal are required [2–5], which may not be feasible or convenient for practical applications. For the methods based on nonlinear power transfer function (PTF) provided by nonlinear effects [6–9], such as two-photon absorption (TPA) in semiconductor detectors and cascaded FWM in parametric amplifiers, the CD information of the input signal is mapped onto the output average optical power; thus, only a simple slow optical detector is required for the measurement. However, their sensitivity is low and only applicable to 33% RZ signals with high OSNR because of the lowly nonlinear quadratic PTFs obtained [6–9]. n Corresponding author at: Huazhong University of Science and Technology, School of Optical and Electronic Information, Luoyu Road 1037, Wuhan, Hubei, China. Tel.: +86 027 87559189x3094; fax: +86 027 87556188. E-mail address: [email protected] (C. Ke).

0030-4018/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2013.07.011

Recently, we proposed a method to obtain a highly nonlinear PTF by single stage FWM with phase-matching condition optimized [10]. By this method the sensitivity is greatly enhanced, while the required input power is reduced. The sensitivity enhancement is important for highly accurate dispersion compensation and makes the method effective for signals with different duty cycles and low OSNR. However, it is still sensitive to PMD and OSNR and the CD monitoring range is also limited by the temporal Talbot effects as previous all-optical CD monitors (for 40 Gb/s 33% RZ signals the monitoring range is about 39 ps/nm) [6,10]. Furthermore, with the application of advanced multi-level modulation formats [11], it is desirous for the monitors to accommodate such signals. In this paper we propose an improved monitoring method which can be applied for various modulation formats, including on–off keying (OOK) and advanced multi-level modulation formats, in a truly format-transparent fashion. No changes of the hardware or software are needed during the operation. Furthermore, it can expand the CD monitoring range beyond the limitation of Talbot effects and is insensitive to optical signal-to-noise ratio (OSNR) and polarization mode dispersion (PMD). These improvements are achieved by optimizing the profile of the PTF curve and utilizing a sweeping tunable dispersion compensator (TDC) in combination with extremely simple digital signal processing (DSP) to find the zero residual dispersion point. The operating principles are introduced in Section 2. In Section 3 numerical simulations are used to demonstrate the accuracy and robustness of the method.

S. Cui et al. / Optics Communications 309 (2013) 180–186

analytical ones using Eq. (1), except the deviations at P πs and the high power region because the fiber loss induced suppression of destructive interference and gain saturation is not considered in the analytical model [10]. We stress that FWM is a quasi-instantaneous effect [12]; thus, P s;i in Eqs. (1) and (2) refers to the instantaneous pulse power. For OOK formats the signal pulses have only one peak power level while for multi-level advanced modulation formats like m-ary quadrature amplitude modulation (mQAM) the signal pulses have multiple peak power levels. For example, the 16QAM signals have three levels of peak power and the ratio is 1:5:9, as shown in Fig. 3. The ratio between the lowest and the highest levels is 9.5 dB and after taking the CD into account the peak power variations may be even larger. Although the PTF with P πs 40 has a larger SPTF , the dynamic range is relatively smaller because of the uncontinuous profile and power saturation in high power regions, as seen in Fig. 2. Thus, the PTF with a smooth profile and wide dynamic range is more desirous to accommodate such signals because a relative large SPTF can be maintained with the whole range. Fig. 3(a–c) shows the variations of the idler power against CD for OOK signals with different duty cycles (33%, 66% and 100%) when the PTF with SPTF ¼ 5.5 is employed. To demonstrate the performance that can be achieved by the methods proposed before results obtained by the quadratic PTF (SPTF ≈2) is also shown [6–9]. The output power is scaled by the value at 0 ps/nm. As we can see, there is always an obvious symmetric center at 0 ps/nm because for ideal signal pulses the peak power change is the same for opposite-signed CD. Furthermore, using the smooth PTF with SPTF ∼5.5, the monitoring sensitivity is greatly improved. As we can see from Fig. 2(a), for 33% RZ signals the scaled idler power changes from 0 to  11 dB for 0∼7 40 ps/nm CD. The sensitivity and dynamic range is around 0.25 dB/(ps/nm) and 11 dB near the symmetric center at 0 ps/nm. While with quadratic PTF the sensitivity and dynamic range is around 0.075 dB/(ps/nm) and 3 dB. This improvement is important because it makes the symmetric center at 0 ps/nm more prominent and identifiable, even

2. Operating principles The setup of the monitor is shown in Fig. 1. The signal to be monitored (ωs ) is amplified and launched into the HNLF with a continuous probe wave ωpb . A new idler wave at ωi ¼ 2ωs ωpb is generated from the FWM in the HNLF. In the undepleted condition the output power of the idler wave P i is given by [10] P i ¼ P pb PTFðP s Þ ¼ P pb ðγP s LÞ2 ½sinhðgLÞ=gL2 ;

ð1Þ

with g 2 ¼ ΔβðΔβ=4 þ γP s Þ, where γ, L and Δβ are the nonlinear coefficient, fiber length and linear phase mismatch, respectively. P s;pb is the input power of the signal and probe waves. As demonstrated in our previous work, the CD information of the input signal is mapped onto the average idler power by the PTF and the sensitivity is proportional to the slope (SPTF ) of the PTF. A PTF with a larger SPTF can be obtained when Δβ o0 and the phase matching condition as follows is satisfied [10] P s 4 P πs ¼ P 0s 

π2 2

γL jΔβj

;

ð2Þ

where P 0s ¼ jΔβj=ð4γÞ. Eq. (2) indicates that P πs is proportional to jΔβj and may be positive or negative for different ranges of jΔβj, while the corresponding PTF also takes on different types of profiles, as shown in Fig. 2 and summarized in Table 1. When jΔβj 4 2π=L, P πs 4 0 and as we can see there is an obvious concave point at P πs dividing the PTF into two distinct sections with different slopes. In the section below, P πs , SPTF ≈2 because when in the low power region PTF∝ðγP s LÞ2 , noting that the PTF is drawn on a log–log plot. While the section above P πs has a much higher SPTF it was demonstrated in our previous work that a much higher monitoring sensitive can be obtained regarding to OOK signals in this section [10]. When 0 o jΔβj o 2π=L, P πs o 0 and the PTF has a smooth profile with increasing slope. When Δβ ¼ 0, PTF ¼ ðγP s LÞ2 and SPTF ¼2. The numerical results agree very well with the

TDC

EDFA

Table 1 Types of PTFs.

Filter

Filter Coupler

Signal

TDC Control & DSP

PM HNLF

Δβ

Filter

ω pb ω s

ω pb

ωs

PTF slope (in dB/dB scale)

Δβ 4 2π=L 0 o Δβ o 2π=L Δβ ¼ 0 or P s ⪡ Δβ =4γ

LD cw probe

181

ωi

Fig. 1. Setup of the monitor. EDFA: Erbium-doped fiber amplifier, TDC: tunable dispersion compensator, PM: power meter, LD: laser diode.

P πs 4 0, two sections with different slopes P πs o 0, smooth profile with increasing slope Constant slope of 2

Scaled output power (dB)

100 80 5.5 60

6.4

40

10

20

2

2 Saturation

0

3

-20 10

15

20

Input pump power (dBm)

2

25

Fig. 2. (a) PTFs under different Δβ obtained by analytical (thin line) and numerical methods (thick line). 2π=L is set at 4.5103 and Δβ is set at 0 (dotted line), 4103 (solid 3 line) and 510 (dashed line) respectively. The corresponding slopes are 2, 5.5 and 6.4. The data is scaled by the first value on the left. (b) The constellation of the 16QAM signals. Note that the power ratio is the square of the amplitude ratio.

S. Cui et al. / Optics Communications 309 (2013) 180–186

Scaled output idler power (dB)

182

5 0 -5 -10 -15 -1500

-1000

-500

0

500

1000

1500

Scaled output idler power (dB)

Residual CD of the signal (ps/nm) 6 4 2 0 -2 -4 -6 -8 -1500

-1000

-500

0

500

1000

1500

Scaled output idler power (dB)

Residual CD of the signal (ps/nm) 10 8 6 4 2 0 -2 -1500

-1000

-500

0

500

1000

the behavior of the idler power is still different for the OOK and advanced modulation format signals, as will be shown in Section 4. This is because, for the latter, the data driven multi-level amplitude and phase modulation change the way of the interference between the neighboring pulses. Because the symmetric center at 0 ps/nm indicates the point at which the residual CD is totally compensated, we can utilize a sweeping tunable dispersion compensator (TDC) in combination with simple digital signal processing (DSP) to estimate the residual CD. The output average power of the idler is recorded during the sweeping process, digitalized and processed by the DSP unit. In the DSP unit the evaluation function as follows can be used to identify the symmetric center at 0 ps/nm,   symðiÞ ¼ 10 log10 ∑m ð3Þ j ¼ 1 jyðijÞyði þ jÞj ; where i is the point to be evaluated and 2m (from the i  m point to the i+m point except the ith point) is the number of points used to calculate the degree of symmetry (DOS) with respect to the ith point. The accumulated CD of the signal is equal to the opposite signed TDC dispersion at that symmetric center. Thus, by this method the monitoring range is not limited by the Talbot effect anymore and it is only dependent on the sweeping range of the TDC. The CD measurement resolution is equal to the minimum sweeping step of the TDC. For LCOS-TDC it can be very small (o10 ps/nm) because the phase distribution generated by the device is very flexible [13,14]. In practical applications fast tunable CD compensators based on liquid crystal on silicon (LCOS) can be used to reduce the sweeping time [13]. Its reconfiguration time is on the scale of less than 100 ms and the tuning range can reach 71200 ps/nm with a 3 dB bandwidth of 30 GHz, which is suitable for 40 Gb/s signals [14]. By cascading several TDCs or using TDC in combination with a static dispersion compensation module based on dispersion compensation fiber (DCF), even larger tuning range can be obtained. The other advantage of this method is that the position of the symmetric center is only determined by the CD and is insensitive to PMD and OSNR; thus, the CD can be monitored independently by our method.

1500

Residual CD of the signal (ps/nm) Fig. 3. Variations of idler power against CD for signals with duty cycles of 33% (a), 66% (b) and 100% (c). PTFs with slopes of 5.5 (thick line) and 2(thin line), as shown in Fig. 2, are used for CD monitoring.

for signals with large duty cycles and low OSNR [10]. For other modulation formats similar results can be obtained and are not shown here. Another important point to note is that comparing Fig. 3(a–c), we can see that the behavior of the idler power with respect to the variations of CD are different for different duty cycles. This phenomenon has been reported and explained in Ref. [6]. For 33% RZ signals, the signal pulse peak power first falls because of the CD induced pulse broadening, while for 66% CSRZ or NRZ signals the pulse peak power first increases because of the phase discontinuity between adjacent bits or the “ear” formation at the pulse edge [6]. Furthermore, the pulse peak power swings periodically due to the temporal Talbot effect [6] which results in the limited CD monitoring range of the power-level measurement based monitoring methods [2–10]. As shown in Fig. 3, the variation of the idler power just presents the same kind of, but exaggerated, behavior as the result of the PTF mapping. Numerical simulations not presented here show that for advanced modulation formats (e.g. QPSK and 16QAM) a similar phenomenon exits. But it is noteworthy that even if the duty cycle is the same

3. Monitoring results The numerical simulations use VPI TransmissionMaker 8.6 based on the nonlinear Schrödinger equation and split-step Fourier method with the simulation setup as Fig. 1. The parameters used in the simulation are listed in Table 2. In the table L, λ0 , S, α and γ are the length, zero dispersion wavelength, dispersion slope, attenuation and nonlinear coefficient of the HNLF, respectively. λsig and λprob are Table 2 Parameters used in the simulations. L λ0 (km) (nm) 1.5

S α γ Idler filter λsig (ps/nm2/km) (dB/km) (W  1/km) BW (nm)

1534.0 0.0771

0.6

9.9

1

λprob

1536.5 1541.6

Table 3 PAPR and input power for different signals with 33% duty cycle. Formats

PAPR

Signal average power/peak power (mw)

33%-RZ DQPSK 16QAM

5.7 2.9 0.56/2.8/5.1

26.3/150 51.7/150 53.6/150

S. Cui et al. / Optics Communications 309 (2013) 180–186

and numerical simulations show that for signals with other duty cycles similar results can be obtained and thus are not shown here. The bandwidth of the filter extracting the idler wave is 1 nm. The bandwidth of the filter extracting the idler wave is 1 nm. Note that the bandwidth is optimized for high sensitivity and dynamic range. When the bandwidth is too large the output contrast will be degraded because the ASE noise power (coming for the EDFA, see Fig. 1) is large and can drown the idler at some level. While when the bandwidth is too small the performance will also be degraded because the idler power is attenuated by the filter, noting that the

the signal and probe wavelengths, respectively. Here, we choose the PTFs with SPTF ≈5.5, as shown in Fig. 2 for CD monitoring and thus operate the monitor around P s ¼21 dBm. Note that P s is the instantaneous pulse power and the theoretic pulse peak to average power ratio (PAPR) for RZ, quadrature phase shift keying (QPSK) and 16QAM signals are shown in Table 3. The average signal powers at the input of the HNLF are chosen according to the PAPR ratios. For 16QAM signal the PAPR of the middle power level with eight symbols and thus the highest occurrence probability are selected to calculate the input average power. Note that the signal duty cycle is set at 33%

0 6

-1200

4 2 0

-400

-4

400

-6

800

-8

1200

-10 0

2

4

6

8

10

-5 -10 -15 -1600

-2

0

Scaled Idlerpower [dB]

CD[ps/nm]

-800

Scaled Idlerpower[dB]

OSNR=30dB -1600

1600

-12

0

-10 -1600

-1200

4

-800

2

-400

0

Scaled Idlerpower [dB]

6

-4 -6

800

-8

1200

-10 0

2

4

6

8

0

2 0

-400

Scaled Idlerpower[dB]

-800

800

1600

-5

-800

0

800

1600

-4 400

-6

800

-8

1200

-10 6

8

10

-5

-10

-15 -1600

-2

0

Scaled Idlerpower[dB]

CD[ps/nm]

4

DGD[ps]

0

0

6

4

-800

Chromatic Dispersion [ps/nm]

Chromatic Dispersion [ps/nm]

OSNR=10dB

2

1600

-10

-10 -1600

10

-1200

1600 0

800

-5

DGD[ps]

-1600

0

0

-15 -1600

-2 Scaled Idlerpower [dB]

CD[ps/nm]

OSNR=20dB

400

-800

Chromatic Dispersion [ps/nm]

-1600

0

-800 0 800 1600 Chromatic Dispersion [ps/nm]

-5

DGD[ps]

1600

183

-800

0

800

1600

-800

0

800

1600

Chromatic Dispersion [ps/nm]

0

-5

-10 -1600

Chromatic Dispersion[ps/nm]

Fig. 4. Output power against CD under different DGD and OSNR for 33% RZ signals.

184

S. Cui et al. / Optics Communications 309 (2013) 180–186

the effectiveness of the method the residual CD of the input signal is set at 600 ps/nm and the DOS is calculated for every point on the curve. Fig. 5 shows the monitoring results for ideal and signals degraded by ASE noise and PMD. As we can see, the CD can always be correctly estimated for signals with OSNR not smaller than 10 dB and DGD not larger than 10 ps. Even larger degradation tolerance can be achieved if a more complex identification algorithm is used, which will be a future research topic. Finally, it is noteworthy that the HNLF used is long and the fiber fabrication

idler spectrum has a relative large width because of the modulated signal acting as the pump. Figs. 4–6 show the monitoring results for 40 GBaud OOK, QPSK and 16QAM signals under different OSNR and DGD. As we can see, the position of the symmetric center is always fixed near 0 ps/nm and insensitive to OSNR and DGD. The contrast around the symmetric center is high even when the signal is degraded by ASE noise and PMD, so the symmetric center can be correctly identified by the simple algorithm using Eq. (3). To demonstrate

15

-1200 10

-400

400

0

800 1200 1600

-5 0

2

4

6

8

10 5 0 -5 -10 -1600

5

0

Scaled Idlerpower [dB]

CD [ps/nm]

-800

Scaled Idlerpower [dB]

OSNR=30dB

-1600

15

5

0

400 800

-5

1200 1600

0

2

4

6

8

10

Scaled Idlerpower [dB]

0

-400

5 0 -5

15

-5

400 800

-10

1200 4

6

DGD [ps]

-800

0

800

1600

Chromatic Dispersion [ps/nm]

10 5 0 -5 -1600

-800

0

800

1600

5 0 -5 -10 -1600

0 Scaled Idlerpower [dB]

CD [ps/nm]

-800

2

1600

10

5

0

800

Chromatic Dispersion [ps/nm]

OSNR=10dB

-1200

1600

0

10

DGD [ps]

-1600

-800

0

-10 -1600

0 Scaled Idlerpower [dB]

CD [ps/nm]

-800

Scaled Idlerpower [dB]

10

-400

1600

Chromatic Dispersion [ps/nm]

OSNR=20dB

-1200

800

5

DGD [ps]

-1600

0

10

-5 -1600

10

-800

Chromatic Dispersion [ps/nm]

8

10

15

-800

0

800

1600

Chromatic Dispersion [ps/nm]

10 5 0 -5 -1600

-800

0

800

Chromatic Dispersion [ps/nm]

Fig. 5. Output power against CD under different DGD and OSNR for QPSK signals.

1600

OSNR=30dB

-1600 -1200

5

-400 0

0 400

-5

800 1200 1600

-10 0

2

4

6

8

Scaled Idlerpower [dB]

CD [ps/nm]

-800

Scaled Idlerpower [dB]

S. Cui et al. / Optics Communications 309 (2013) 180–186

0

-5

-10

-15 -1600 15

6

2

0

0

400

-2

800

-4 -6

1200 1600

-8 0

2

4

6

8

Scaled Idlerpower[dB]

CD [ps/nm]

4

-400

Scaled Idlerpower [dB]

8

-800

2

-400

0 -2 -4

800

-6

1200 1600

0

2

4

6

8

10

-8

DGD [ps]

Scaled Idlerpower [dB]

CD [ps/nm]

-800

Scaled Idlerpower [dB]

4

400

0

800

1600

-5

-10

-15 -1600

-800

0

800

1600

-800

0

800

1600

Chromatic Dispersion [ps/nm]

15 10 5 0

Chromatic Dispersion [ps/nm]

OSNR=10dB

0

-800

0

-5 -1600

10

-1200

1600

0

DGD [ps]

-1600

800

Chromatic Dispersion [ps/nm]

OSNR=20dB

-1200

0

5

DGD [ps]

-1600

-800

Chromatic Dispersion [ps/nm]

10

-5 -1600

10

185

0

-5

-10 -1600

-800

0

800

1600

-800

0

800

1600

Chromatic Dispersion [ps/nm]

10

5

0

-5 -1600

Chromatic Dispersion [ps/nm]

Fig. 6. Output power against CD under different DGD and OSNR for 16QAM signals.

process inevitably results in undesirable variation of λ0 along the fiber. This will cause a reduction in the phase matching accuracy and thus change the idler power with different sections of the HNLF. Furthermore, it may also degrade the monitoring sensitivity [15]. Nevertheless, because this method is not based on simple power measurements the CD monitoring accuracy will not be affected as long as the nonlinearity of the PTF and the resulted output contrast are high enough for correctly identifying the symmetric center at 0 ps/nm by using Fig. 7, Eq. (3).

4. Conclusion We proposed a method to expand the CD monitoring range of the highly sensitive FWM based on all-optical monitors utilizing TDC and very simple DSP. This method is insensitive to PMD and OSNR and applicable to both OOK and advanced multi-level modulation formats in a truly format and bit rate transparent operation. Thus, this method is desirous for high speed reconfigurable optical networks encompassing multiple modulation formats.

10

0.8

5

0.4

0

0

-5

-0.4

-10

-0.8 0

800

4

0.8

2

0.4

0

0

-2

-0.4

-4

-0.8

-6 -1600

-1.2 1600

20

0.6

10

0 -0.6

-800-600

0

800

Scaled idler power (dB)

1.2

Scaled DOS (dB)

Scaled idler power (dB)

30

-10 -1600

10

0.6

5

0

0

-0.6

5

0.4

0

0

-5

-0.4

-10

-0.8 -1.2 1600

The CD applied by TDC (ps/nm)

Scaled idler power (dB)

0.8

Scaled DOS (dB)

Scaled idler power (dB)

1.2

800

-800-600

0

800

-1.2 1600

The CD applied by TDC (ps/nm)

10

0

-1.2 1600

1.2

-5 -1600

-1.2 1600

15

-800-600

800

15

The CD applied by TDC (ps/nm)

-15 -1600

0

The CD applied by TDC (ps/nm)

The CD applied by TDC (ps/nm)

0

-800-600

Scaled DOS (dB)

-800-600

1.2

15

1.2

10

0.6

5

0

0

-0.6

-5 -1600

-800-600

0

800

Scaled DOS (dB)

-15 -1600

6

Scaled DOS (dB)

1.2

Scaled idler power (dB)

15

Scaled DOS (dB)

S. Cui et al. / Optics Communications 309 (2013) 180–186

Scaled idler power (dB)

186

-1.2 1600

The CD applied by TDC (ps/nm)

Fig. 7. CD estimation results (represented by +) using the extremely simple DSP algorithm based on the TDC sweeping results (solid line). The dashed line is the DOS of each point obtained by Eq. (3) scaled by the value at the symmetric center. The figures on the left and right columns are results for ideal and degraded signals with OSNR ¼ 10 dB and DGD ¼10 ps, respectively.

Acknowledgments This work is supported by the National Basic Research Program of China (973 Program, Grant no. 2010CB328305), the National High Technology Research and Development Program of China (863 Program, Grant nos. 2011AA01A110 and SS2012AA010407) and the Natural Science Foundation of China (Grant nos. 61007043 and 61107051). References [1] Z. Pan, C. Yu, A.E. Willner, Optical Fiber Technology 16 (2010) 10. [2] T. Luo, C. Yu, Z. Pan, Y. Wang, J.E. McGeehan, M. Adler, A.E. Willner, IEEE Photonics Technology Letters 18 (2006) 430. [3] J. Yang, L. Zhang, X. Wu, O.F. Yilmaz, B. Zhang, A.E. Willner, IEEE Photonics Technology Letters 20 (2008) 1642. [4] T.D. Vo, B. Corcoran, J. Schröder, M.D. Pelusi, D. Xu, A. Densmore, R. Ma, S. Janz, D.J. Moss, B.J. Eggleton, Journal of Lightwave Technology 29 (2011) 1790.

[5] C. Courvoisier, J. Fatome, C. Finot, IEEE Photonics Technology Letters 23 (2011) 537. [6] S. Wielandy, M. Fishteyn, B. Zhu, Journal of Lightwave Technology 22 (2004) 784. [7] T.T. Ng, J.L. Blows, M. Rochette, J.A. Bolger, I. Littler, B.J. Eggleton, Optics Express 13 (2005) 5542. [8] T.T. Ng, J.L. Blows, J.T. Mok, R.W. McKerracher, B.J. Eggleton, Journal of Lightwave Technology 23 (2005) 818. [9] K. Bondarczuk, P.J. Maguire, D.A. Reid, L.P. Barry, J. O′Dowd, W.H. Guo, M. Lynch, A.L. Bradley, J.F. Donegan, IEEE Journal of Quantum Electronics 45 (2009) 223. [10] S. Cui, L. Li, S. Sun, C. Ke, D. Liu, Optical Engineering 50 (075008) (2011) 1. [11] Sébastien Bigo, in: Proceedings of the Optical Fiber Communication Conference, Los Angeles, California, March 4–8, 2012, OTh3A. [12] G.P. Agrawal, Nonlinear Fiber Optics, second ed., Academic Press, New York, 1995. [13] M.A.F. Roelens, S. Frisken, J.A. Bolger, D. Abakoumov, G. Baxter, S. Poole, B.J. Eggleton, Journal of Lightwave Technology 26 (2008) 73. [14] K. Seno, N. Ooba, K. Suzuki, T. Watanabe, M. Itoh, S. Mino, T. Sakamoto, in: Proceedings of the Optical Fiber Communication Conference, Los Angeles, California, March 6–10, 2011, OWM5. [15] S. Cui, D. Liu, Y. Wang, F. Tu, Optics Express 17 (2009) 1454.