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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 10, Iss. 26 — Dec. 30, 2002
  • pp: 1526–1533
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Full distortion induced by dispersion evaluation and optical bandwidth constraining of fiber Bragg grating demultiplexers over analogue SCM systems

Alfonso Martínez, Daniel Pastor, and José Capmany  »View Author Affiliations


Optics Express, Vol. 10, Issue 26, pp. 1526-1533 (2002)
http://dx.doi.org/10.1364/OE.10.001526


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Abstract

We provide a full analysis of the distortion effects produced by the first and second order in-band dispersion of fiber Bragg grating based optical demultiplexers over analogue SCM (Sub Carrier Multiplexed) signals. Optical bandwidth utilization ranges for Dense WDM network are calculated considering different SCM system cases of frequency extension and modulation conditions.

© 2002 Optical Society of America

1. Introduction

Optical Add Drop Multiplexers (OADMs) based on fiber Bragg gratings (FBG) are a suitable technology for channel routing and switching tasks to be carried in the optical layer of future DWDM networks. Different works have addressed the limitations that the in-band dispersion [1–2

1. B.J. Eggleton, G. Lenz, N. Litchinitser, D.B. Patterson, and R. E. Slusher, “Implications pf Fiber Grating Dispersion of WDM Communication Systems,” IEEE Photonics Technol. Lett. 9, 1403–1405, (1997). [CrossRef]

] and the out-band dispersion [3–5

3. J Capmany, D. Pastor, and B. Ortega, “RIN induced by out-of-band dispersion in fiber Bragg Grating based Add-Drop multiplexers,” Electron. Lett. 35, 2220–2221, (1999). [CrossRef]

] of the uniform apodised FBG produce over the dropped out (in-band case) or transmitted (out-band case) channel. Over digital transmission systems the impairments manifest as a penalty increase depending on the spectral location of the signal with respect to the center Bragg position of the FBG. For the in-band cases this penalty increase can be translated immediately into an effective optical bandwidth reduction that can deteriorate the tolerance of optical network to frequency deviations of lasers and demultiplexers respect to the standard values. The frequency tolerance reduction can be especially important in Dense WDM systems with channel spacing of 25 and 12.5GHz as it has been proposed in future optical networks.

The induced dispersion effects over an analogue SCM (Sub Carrier Multiplexed) signal (i.e typically a set of RF sub-carriers transporting multiple and different signals formats and applications), is due to the rising of distortion and intermodulation terms that can lead into a deleterious effect over an arbitrary interfered channel. These distortion and intermodulation terms have to be limited in amplitude to a maximum level depending of the signal format transported by the RF channels. In a general case moreover the number of interfering terms “falling” over an interfered channel can grow dramatically with the number of SCM channels limiting the system feasibility.

In this paper we deal with the in-band dispersion effects over analogue SCM signals, obtaining as final results a set of effective bandwidth utilization factors of the optical filter (OADM based on FBG), under very different and common system situations as: ITU channel spacing ( 100, 50, 25GHz), frequency extension of the SCM plan, modulation characteristics, etc. In order to accomplish the study we have completed the analytical model of the distortion calculations of [6

6. S. Ih. Charles and Wanyi Gu, “Fiber Induced Distortion in a Sub Carrier Multiplexing Ligthwave System,” IEEE J. Selected Areas in Commun. 8, 1296–1303, (1990). [CrossRef]

] in order to include both combined first and second order dispersion effects. The FBG response and their dispersion characteristics have been numerically calculated solving their Coupled Wave Equations, and their fundamental parameters have been properly chosen to fit the ITU grid spacing maintaining also a low cross-talk ration between adjacent channels (<-35dB). Typically apodization windows have been employed also in order to obtain the closest similarity to a practical case.

2. Analogue SCM system definition and FBG dispersion description

We will assume the SCM system conveyed by an optical wavelength placed inside the band pass of an Uniform (non-chirped) and apodized fiber Bragg grating (UAFBG). We will follow the classical analysis carried out by Ih et al. [6

6. S. Ih. Charles and Wanyi Gu, “Fiber Induced Distortion in a Sub Carrier Multiplexing Ligthwave System,” IEEE J. Selected Areas in Commun. 8, 1296–1303, (1990). [CrossRef]

], to obtain the values of intermodulation (IMD) and harmonic distortion (HD) in the system. As developed in [6

6. S. Ih. Charles and Wanyi Gu, “Fiber Induced Distortion in a Sub Carrier Multiplexing Ligthwave System,” IEEE J. Selected Areas in Commun. 8, 1296–1303, (1990). [CrossRef]

] we will start from the modulated optical signal described by its electric field as:

e(t)=[2(1+micos(Wm))]1/2cos(wot+mfsin(wmt))
(1)

where mi, and mf are the intensity and frequency modulation indexes, wo is the optical carrier, and wm is the sub-carrier.Following a similar procedure as in [6

6. S. Ih. Charles and Wanyi Gu, “Fiber Induced Distortion in a Sub Carrier Multiplexing Ligthwave System,” IEEE J. Selected Areas in Commun. 8, 1296–1303, (1990). [CrossRef]

] but in this case including also the second order dispersion term, the detected photocurrent at the receiver can be written as:

I(t)=Co+k=1{Cckcos[k(wmtφ1)]+Csksin[k(wmtφ1)]}=Co+k=1Ckcos[k(wmtφ1+ϕk)]
(2)

where (Ck)2 = (Cck)2 + (Csk)2 and ϕk=arctan((Cck)2/(Csk)2). The coefficients C 0, Cck and Csk are formed by multiple terms given by:

Co=ao2+(1/2)i=1(ai2+bi2)
Cck=2aoakcos[k2φ2]cos[k3φ3]2a0bksin[k2φ2]sin[k3φ3]+
+(1/2)k1i=1(aiakibibki)cos[(k22ik)φ2]cos[(k33ik2+3ik3)φ3]+
+i=1(aiai+k+bibi+k)cos[(k2+2ik)φ2]cos[(k3+3ik2+3ki2)φ3]
k1i=1aibkisin[(k2+2ik)φ2]sin[(k33ik2+3ki2)φ3]
i=1(aibi+k+biai+k)sin[(k2+2ik)φ2]sin[(k3+3ik2+3ki2)φ3]
Csk=2aoakcos[k2φ2]sin[k3φ3]+2a0bksin[k2φ2]cos[k3φ3]+
+(1/2)k1i=1(aiakibibki)cos[(k22ik)φ2]sin[(k33ik2+3ik2)φ3]+
+i=1(aiai+k+bibi+k)cos[(k2+2ik)φ2]sin[(k3+3ik2+3ki2)φ3]+
+k1i=1aibkisin[(k22ik)φ2]cos[(k33ik2+3ki2)φ3]+
+i=1(aibi+k+biai+k)sin[(k2+2ik)φ2]cos[(k3+3ik2+3ki2)φ3]
(3)

The dispersion features β2Lg and β3Lg (Lg is the grating length) of the UAFBG under analysis are shown in Figs. 1–2, where we have assumed a proper apodisation profile of the coupling strength and device length to comply with the typically required parameters of the ITU DWDM grid spacing (AυC=100GHz, 50GHz and 25GHz) in terms of 3dB optical bandwidth (AυB=50GHz, 25GHz and 12.5GHz respectively) and cross-talk levels at the adjacent channel locations <-35 dB. Specifically the results shown in Figs. 1–2 correspond with a 50GHz bandwidth FBG The resulting required FBG lengths are under Lg=2.34 cm (narrowest case of 12.5GHz bandwidth).

Fig 1. First order dispersion of the apodized UFBG inside the band. 3dB optical bandwidth of 25 GHz. (1) Cosine apodization profile with C=1.2 ([7]), (2) Hiperbolic tangent apodization profile with α=1.75 y β=2 ([7]) and (3) hamming apodization profile with H = 0.8 ([7]). Lg is the grating length that in this case is Lg = 1.168 cm.

In order to reduce the results into an approachable quantity we will employ for the rest of the paper a single apodization window as Hiperbolic Tangent because it is commonly used for FBG fabrication, and as we can see in Figs. 1–2 the dispersion properties of the different apodization functions do not differ strongly in their shape or magnitude. Nevertheless a precise calculation developed for a specific system must to take this parameter into consideration.

Fig. 2. Second order dispersion of the apodised UFBG. Same conditions of Fig. 1.

3. Results and Discussion

Figure 3 shows the compared results of distortion for the three ITU standards (100, 50 and 25GHz of channel spacing). These results reveal that the ‘effective optical bandwidth’ free of distortion is not the whole 3dB bandwidth of the FBG, but a reduced region inside of it. We can define this ‘effective optical bandwidth’ as the spectral range inside de band presenting distortion levels lower than a maximum fixed level (in our case taken as -60dBc which is the common maximum distortion level for analogue CATV applications).

For instance considering the IM2 terms (i.e. the distortion term generated at f1+f2 ), and the ITU case of 50GHz channel spacing, the distortion level below -60 dBc can be only obtained for detuning ratios values (y) in between y=-0.3 and y=0.25 (55% of the 3dB total bandwidth). In the case of the 25GHz spacing the bandwidth available reduces to the 20% (i.e 12.5GHz∙0.2=2.5GHz). The strong increasing of the distortion level observed when the ITU spacing decreases, has a clear physical explanation. When the ITU spacing decreases (and also the optical bandpass bandwidth), the required physical length of the FBG is bigger and its dispersive behaviour increases proportionally (see Fig. 3). So in general, as observed from the results, the distortion level restriction from the FBG based OADMs employed in each time more and more Dense-WDM systems will represent a serious limitation.

As expected from the dispersion in-band features depicted in Figs. 1–2, the distortion levels increase rapidly as the optical carrier displace from the centre to the edges of the FBG spectrum. Moreover, the evolution of this distortion increase with the optical carrier location is not perfectly symmetric, yielding a notch near the centre of the FBG but displaced from it a quantity depending of the FBG optical bandwidth. This non-symmetric results is due to the combined effect or interaction between the first and second order dispersion phase terms that are all included in (3). In this way, it is interesting to point out how the results predicts a better distortion behaviour if we situate the carrier displaced from the centre. For example in the trace of 25GHz of spacing the optimum displacement is about of 9% of the total bandwidth.

Fig. 3. IM2(f1 + f2)/C2 and IM3(2f2 - f1)/C2 versus the detuning parameter y for different channel spacing, ΔυC =100, 50 , 25 GHz (3dB optical bandwidths are 50GHz (Lg=0.584 cm), 25GHz (Lg=1.168 cm) and 12.5GHz (Lg=2.336 cm) respectively). Hiperbolic tangent apodization profile with α=1.75 and Β=2, 100 MHz for the common frequency. mi=0.05 and mf =0.2 indexes (directed modulated systems). Results from analitical expressions (3) (continuous line) and numerical simulation (dots).

The IM3 terms present smaller levels and of symmetric nature respect to FBG centre. Mainly they come dominated by the second order dispersion of the FBG (considering only the first order dispersion in (3) the IM3 values fall drastically). However, despite the low levels, they increase rapidly from -120 to -90 dBc (at the centre of the band if the ITU spacing decrease) and increase by 10dB from the centre to the edges of the spectrum.

The intermodulation results presented were concentrated on particular beating combinations (IM2(f1 + f2)/C2 and IM3(2f2 - f1)/C2) for sake of simplicity. In any case the method proposed is completelly indepented and applicable to other different terms as (f2-f1, or triple beating from three different carriers). The distortion level results of IM3 generated by three different frequencies present exactly the same evolution versus the detunning parameter (y) to that shown for IM3(2f2 - f1), and their levels can differ between zero and almost +12 dB depending strongly of the specific frequency plan employed. In order to validate our analytical formulation incorporating second order dispersion we have made the numerical simulation to obtain the distortion values of Fig. 3 (dots), resulting in a perfect agreement.

We have to point out in this point a very important consideration that it has to be done for the proper extension of the distortion level results to a practical system. This consideration is that the distortion levels depicted have to be multiplied by the proper “number of distortion terms” that they could follow over a specified channel in a complete SCM frequency plan. For example the NTSC-79 frequency plan leads into NCSO=70 (second order terms count) (i.e.+18dB) and NCTB=2350 (the third order terms count) (i.e.+34dB)).

We present in Fig. 4 a summary of distortion results as a function of the common frequency fu, evaluated for different modulation sceneries which adjust with three different practical possibilities. Those are: 1) mi = 5% and mf = 20% (case of direct modulation of a DFB laser, valid for low frequency plans), 2) mi =5% and mf =5% (case of externally modulated with a non-perfect balanced EOM (Electro Optical Modulator) or a MQW laser direct modulated), and finally 3) mi = 5% and mf = 0 (perfectly balanced dual-drive EOM). The 2° and 3° case allow the assumption of wider frequency plans due to the modulation bandwidths of the EOMs. So the the fu range of analysis have been extended up to 2 GHz, corresponding with the cases of systems transmitting SCM channels from 8 to 10GHz.

Fig. 4. IM2/C2 and IM3/C2 terms versus the common frequency. ITU spacing of AυC=50GHz (AυB=25GHz), Hiperbolic tangent apodization profiles with α=1.75 and β=2 , and y = 0 (centre of the FBG). Indexes of modulation mf = 0.2 (continuous line), mf = 0.05 (dashed line) and mf = 0 (dotted line), all traces mi= 0.05.

Fig. 5. Free of distortion optical bandwidth (BWfd) versus the common frequency for IM2 and HD terms (continuous line) and IM3 terms (dashed line). Hiperbolic tangent apodization profiles with α=1.75 y β=2, Intensity modulation indexes mi = 2 , 4 , 8, 16 % . (a) Low/Medium chirped modulation mf = mi, (b)High chirped modulation mf = 4mi.

Figure 5 provides design limits for the maximum channel detuning, or equivalently, the maximum channel wavelength tolerance for optical filters and sources depending on the concrete application. The results in Fig. 5 show some impacting examples like those for systems operating over D-WDM(ΔυC=50GHz), with common frequency equal to 300MHz (f1=1.2GHz, f2=1.5Ghz), and with medium/low chirped modulation and mi=[4–8%]. These will be limited to around the y=30% of the optical bandwidth. If the same system is operated over a U-WDM(ΔυC=12.5GHz), the optical bandwidth will be limited to y<10%. This two cases translate into a catastrophic results is the high chirped modulation is considered so we have y around 10% for D-WDM and y=0 for U-WDM (i.e all the FBG bandwidth provide high distortion levels than the -60dBc fixed).

4. Conclusions

Acknowledgements

The authors wish to acknowledge the financial support of the Spanish CICYT projects TEL 99-0437, TIC2001-2969-C02-01 and TIC2001-2895-C02-01 and the European projects NEFERTITI IST-2001-32786 , INTAS 97-30748 and LABELS IST-2001-37435. Alfonso Martinez acknowledges the funding of a FPI grant from the Universidad Politécnica de Valencia.

References and links

1.

B.J. Eggleton, G. Lenz, N. Litchinitser, D.B. Patterson, and R. E. Slusher, “Implications pf Fiber Grating Dispersion of WDM Communication Systems,” IEEE Photonics Technol. Lett. 9, 1403–1405, (1997). [CrossRef]

2.

G. NyKolak, B.J. Eggleton, G. Lenz, and T.A. Strasser, “Dispersion Penalty Measurements of Narrow Fiber Bragg Gratings at 10 Gb/s,” IEEE Photonics Technol. Lett. 10, 1319–1321, (1998). [CrossRef]

3.

J Capmany, D. Pastor, and B. Ortega, “RIN induced by out-of-band dispersion in fiber Bragg Grating based Add-Drop multiplexers,” Electron. Lett. 35, 2220–2221, (1999). [CrossRef]

4.

L.R. Chen, “Relative Intensity noise enhancement due to out-of-band dispersion in cascaded fiber Bragg Gratings,” Optics Communications 184, 157–160, (2000). [CrossRef]

5.

D. Pastor, A. Martinez, J. Capmany, and B. Ortega, “Impact of Fiber Bragg Grating based OADM outband dispersion in DWDM-SCM systems,” IEEE Photonics Technol. Lett. 14, 567–569, (2002). [CrossRef]

6.

S. Ih. Charles and Wanyi Gu, “Fiber Induced Distortion in a Sub Carrier Multiplexing Ligthwave System,” IEEE J. Selected Areas in Commun. 8, 1296–1303, (1990). [CrossRef]

7.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” IEEE Journal of Lightwave Technol. 14, 2581–2588 (1996). [CrossRef]

8.

M. Ibsen and M.N. Zervas, “99,9% reflectivity dispersion-less square-filter fiber bragg grating for high speed DWDM networks,” Conf. Opt. Fiber. Comm., Baltimore, OSA Tech. Dig. Paper PD21, (2000)

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.4510) Fiber optics and optical communications : Optical communications
(230.1480) Optical devices : Bragg reflectors

ToC Category:
Research Papers

History
Original Manuscript: November 12, 2002
Revised Manuscript: December 14, 2002
Published: December 30, 2002

Citation
Alfonso Martinez, Daniel Pastor, and Jose Capmany, "Full distortion induced by dispersion evaluation and optical bandwidth constraining of fiber Bragg grating demultiplexers over analogue SCM systems," Opt. Express 10, 1526-1533 (2002)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-26-1526


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References

  1. B.J. Eggleton, G. Lenz, N. Litchinitser, D.B. Patterson and R. E. Slusher, �??Implications pf Fiber Grating Dispersion of WDM Communication Systems,�?? IEEE Photonics Technol. Lett. 9, 1403-1405, (1997). [CrossRef]
  2. G. NyKolak, B.J. Eggleton, G.Lenz, and T.A. Strasser, �??Dispersion Penalty Measurements of Narrow Fiber Bragg Gratings at 10 Gb/s,�?? IEEE Photonics Technol. Lett. 10, 1319-1321, (1998). [CrossRef]
  3. J, Capmany, D. Pastor, B. Ortega, �??RIN induced by out-of-band dispersion in fiber Bragg Grating based Add-Drop multiplexers,�?? Electron. Lett. 35, 2220-2221, (1999). [CrossRef]
  4. L.R. Chen,�?? Relative Intensity noise enhancement due to out-of-band dispersion in cascaded fiber Bragg Gratings,�?? Opt. Commun. 184, 157-160, (2000). [CrossRef]
  5. D. Pastor, A. Martinez, J. Capmany and B. Ortega , �??Impact of Fiber Bragg Grating based OADM outband dispersion in DWDM-SCM systems,�?? IEEE Photonics Technol. Lett. 14, 567-569, (2002). [CrossRef]
  6. Charles S. Ih. and Wanyi Gu, �??Fiber Induced Distortion in a Sub Carrier Multiplexing Ligthwave System,�?? IEEE J. Selected Areas in Commun. 8, 1296-1303, (1990). [CrossRef]
  7. D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Marti, �??Design of apodized linearly chirped fiber gratings for dispersion compensation,�?? IEEE J. Lightwave Technol. 14, 2581-2588 (1996). [CrossRef]
  8. M. Ibsen and M.N. Zervas, �??99,9% reflectivity dispersion-less square-filter fiber bragg grating for high speed DWDM networks,�?? Conf. Opt. Fiber. Commun. OSA Tech. Dig. Paper (Optical Society of America, Washington, D.C., 2002) PD21.

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