Performance optimization of Gaussian apodized fiber Bragg grating filters in WDM systems

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 8, AUGUST 2002 1537

Performance Optimization of Gaussian ApodizedFiber Bragg Grating Filters in WDM Systems

João L. Rebola and Adolfo V. T. Cartaxo, Member, IEEE

Abstract—Fiber Bragg gratings (FBGs) with Gaussian apodiza-tion profiles and zero dc index change are studied extensively andoptimized for optical filtering in 40-Gb/s single-channel and WDMsystems with channel spacing of 100 and 200 GHz, for a singlefilter and for a cascade of optical filters. In the single-filter case,the optimized FBG leads practically to the same performance forsingle-channel and WDM systems, due to its low crosstalk intro-duction. The optimized filter is nonflat-top, with delay distortionbelow 7 ps, 3 dB bandwidth between 60 and 90 GHz, and isvery robust to a variation of the grating length and the dc effectiveindex change. For a cascade of optical filters and a WDM systemwith channel spacing of 100 GHz, the FBG must be designed care-fully due to a tradeoff between crosstalk and accumulated distor-tion. This tradeoff leads to 1.2 dB of sensitivity degradation rela-tive to the single-filter case, and the optimized filter approaches theflat-top response with 3 dB bandwidth between 110 and 130 GHzand delay distortion of about 3 ps. For a 200-GHz channel spacing,that tradeoff is lessened and the FBG optimization is mainly ruledby the distortion accumulation.

Index Terms—Fiber Bragg gratings, Gaussian apodization, op-tical filter cascade, optical filtering, receiver performance, single-channel systems, wavelength-division multiplexing systems.

I. INTRODUCTION

THE demand for network bandwidth, communication ca-pacity, and the exponential increase of traffic has led to

the development of wavelength-division multiplexing (WDM)systems. The narrowing of channel spacing gave rise to theso-called dense WDM (DWDM) systems, where wavelength-selective devices or optical filters with high selectivity and lowinsertion loss are required to achieve a good system perfor-mance.

Fiber Bragg gratings (FBGs) are potential devices for channelfiltering in DWDM systems [1]–[7], due to their versatility andhigh optical filtering performance. Sharp and flat-top amplituderesponses, flat delay response, and low crosstalk (high isolationand sidelobe suppression) are usually the desired characteris-tics of the optical filter [2], [4]–[7]. Apodized FBGs offer thesedesired amplitude features for the optical filters. The delay dis-tortion is perhaps the most critical issue in the design of thesegratings [4], [6]–[8].

Manuscript received October, 10 2001; revised April, 22 2002. Thiswork was supported by Fundação para a Ciência e a Tecnologia (FCT)from Portugal under Grant SFRH/BD/843/2000 and POSI under ProjectPOSI/35576/CPS/2000—DWDM/ODC.

The authors are with the Optical Communications Group, Instituto de Tele-comunicações, Department of Electrical and Computers Engineering, InstitutoSuperior Técnico, 1049-001 Lisbon, Portugal (e-mail: [email protected];[email protected]).

Digital Object Identifier 10.1109/JLT.2002.800300

Several works have carried out the optimization of apodizedFBGs for optical filtering [5], [6]1 and dispersion compensation[9], [10] in WDM systems and found a better performance for aspecific apodization profile. However, in each apodization pro-file, they consider either a single type of FBG filter [6] or theyfix an FBG parameter, for example, the grating length [9], [10]or the optimization is performed using simplified methods to as-sess the system performance [5].

In this work, we consider the Gaussian apodization profile be-cause it leads to higher sidelobe suppression than other apodiza-tion profiles [1], [6] and, thus, it is more suitable for optical fil-tering in WDM systems. The FBG is optimized by varying itsmain features and by assessing the receiver sensitivity exhaus-tively and rigorously. This leads to an optimum set of FBG pa-rameters and allows us to effectively choose the best candidatefor optical filtering. This study is performed for single-channeland WDM systems and for optical filter cascades, different ex-tinction ratios, and nonreturn to zero (NRZ) and return to zero(RZ) signal formats. The impact of detuning of the optimizedFBG optical filter on system performance is also assessed.

II. THEORY

The optical properties of an FBG are mainly determined bya perturbation in the refractive index, which is produced by ex-posing the fiber to a spatially varying pattern of ultraviolet in-tensity. The induced perturbation of the refractive index ofthe FBG is given by [1]

(1)

where is the apodization profile, is the fringe vis-ibility of the index change, describes the grating chirp,and is the Bragg grating nominal period, which is given by

, where is the Bragg wavelength.The optical fields’ evolution through the Bragg grating is de-

scribed by the following differential equations obtained throughthe coupled-mode theory [1], [2], [11], [12]:

(2)

(3)

1In these works, the optimization is performed considering only apodizedFBGs with no null dc index change. However, with a null dc index change, theFBG has enhanced sidelobe suppression [1], [4] and, hence, it is more suitablefor optical filtering.

0733-8724/02$17.00 © 2002 IEEE

1538 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 8, AUGUST 2002

with , where is the grating length, andare, respectively, the incident and reflected wave on the grating,and is the dc self-coupling coefficient given by [1]

(4)

where is the detuning which is given by, is the dc (period-averaged) coupling coefficient,

which for a single-mode Bragg reflection grating is given byand is the ac coupling coefficient

given by . The FBG reflectiontransfer function is obtained from (2) and (3) and is given by

, assuming the boundary conditions and.

III. FBG FILTER CHARACTERISTICS

In this section, the characteristics of the FBG filter are ex-haustively studied by varying its main parameters. Our goal isto find a suitable set of these parameters that leads to superiorperformance of the FBG as an optical filter in optically pream-plified receivers.

Apodized FBG filters are considered in this work. However,the nonuniform index change caused by the apodizationorigins resonances on the high-frequency side of the reflectionspectrum, which induce undesirable crosstalk between adjacentchannels [1], [4], [6]. An apodized FBG with zero dc indexchange has been proposed to overcome this problem [1],[4]. However, apodized structures with zero dc index changerequire a two-stage illumination process to be realized. Toovercome this problem, a new technique of designing FBGshas been proposed [4]. In this technique, the grating periodvariation is designed to follow the apodization profile, ensuringa constant Bragg condition along the structure. The resultis a chirped Bragg grating with strong sidelobe suppression,flat-top amplitude response, and low delay distortion. Althougha raised-cosine apodization profile has been considered in[4], other apodization profiles can be used in this technique,yielding similar results. The resulting chirped FBG has agrating chirp given by

(5)

It should be pointed out that, by substituting (5) into (4),the dc self-coupling coefficient is practically equal to thedetuning, . The same result is obtained for unchirpedapodized FBGs with zero dc index change. This means thatthe unchirped apodized FBG with zero dc index change andthe chirped apodized FBG proposed in [4] show basically thesame reflection transfer function although they have differentperturbations of the refractive index.

An unchirped apodized FBG with zero dc index change isconsidered in this work. The Gaussian apodization profile canbe written as

(6)

(a)

(b)

Fig. 1. FBG characteristics as a function of � for � � �� mm and ��

�� and for � � �� mm and �� . (a) Insertion loss(dashed line) and sidelobe suppression (solid line). (b) Delay distortion (dashedline) and � (solid line).

where is the peak value of the dc effective index changeand is the parameter that controls the degree of truncation ofthe apodization profile. By setting , the Gaussian apodiza-tion profile defined in [1] and [6] is obtained. A lower tightensthe apodization profile, while a higher enlarges the profile.

Fig. 1 shows the FBG insertion loss, sidelobe suppression[Fig. 1(a)], delay distortion,2 and optical filter 3 dB bandwidth

[Fig. 1(b)] as a function of , for mm andand for mm and .

The zero dc index FBG filter characteristics are obtained bysetting nm, and . Thedifferential equations (2) and (3) are solved by the adaptive-stepsize Runge–Kutta numerical integration method.

It is known that the reflection transfer function of an apodizedFBG with nonzero dc index change follows closely the Fouriertransform of its apodization profile [6], [9]. In this case, it is ex-pected that the tightening of the apodization profile will resultin enhanced sidelobe suppression [9]. Fig. 1(a) shows that this is

2The delay distortion is obtained by subtracting the maximum delay by theminimum delay in a bandwidth of 80 GHz centered at the optical carrier fre-quency (it is assumed that the central frequency of the optical filter is alignedwith the optical carrier frequency). The bandwidth of 80 GHz is chosen, becausea bit rate of � � �� Gb/s is considered in our analysis.

REBOLA AND CARTAXO: PERFORMANCE OPTIMIZATION OF GAUSSIAN APODIZED FBG FILTERS IN WDM SYSTEMS 1539

Fig. 2. Isolation versus � and �� .

not true for the zero dc index change FBG. With the increase of(from ), the sidelobe suppression increases, achieves

a maximum for , and then decreases again with a fur-ther increase of . Fig. 1 reveals a compromise of the choice,where low results in greater insertion loss and larger 3 dBbandwidths (higher crosstalk) and high results in higher delaydistortion. This compromise is in agreement with the results andconclusions presented in [9] for different apodization profiles ofnonzero dc index change FBG. However, it fails to predict thesidelobe suppression behavior with the tightening variation forFBG with zero dc index change. We set to 0.75 to benefit fromthe maximal sidelobe suppression and to avoid the higher delaydistortion observed for higher and the higher insertion lossand large FBG 3 dB bandwidths obtained for lower .

We vary from 1 mm to 1.1 cm and from 10 to1.1 10 to assess the dependence of the optical filter isola-tion, insertion loss, 3 dB bandwidth, and delay distortion onthose parameters. These features are presented, respectively, inFigs. 2–5. For a WDM system with 100-GHz channel spacing,we define the isolation of the filter (in decibels) as

dBGHz

(7)

where is the maximum of the amplitude response of theFBG and GHz is the FBG amplitude response at the fre-quency where the nearest adjacent channel is centered.

Fig. 2 shows that, for a filter isolation greater than 30 dB,3

should be above 0.4 cm and should be roughly below5 10 . Fig. 3 shows that, for above 0.4 cm and below5 10 , optical losses can be as high as 10 dB for low .If is maintained above 3 10 , less than 5 dB of lossshould be expected. It has been also observed that, when thefilter has significant insertion loss, the filter amplitude responseis no longer flat-top. The reduction of the insertion loss leads toa more flat-top amplitude response and also to a sharper filtercutoff. Extensive analysis of FBG transfer functions has shown

3We have observed that the sidelobe suppression is always above 30 dB forgrating lengths larger than about 0.2 cm, and, for high � (above 0.4 cm), thesidelobe suppression is always above 80 dB. Hence, in this case, for � � ��,the sidelobe suppression is of minor concern for the FBG filter project.

Fig. 3. Insertion loss versus � and �� .

Fig. 4. The �3 dB bandwidth � versus � and �� .

that, for an insertion loss below 0.5 dB, the FBG can be con-sidered flat-top. Therefore, Fig. 4 shows that the FBG can beflat-top for a very wide range of bandwidths (between 50 and140 GHz).

For a 40-Gb/s signal, the delay distortion should be less than25 ps [2]. In Fig. 5, the delay distortion is always below 25ps. Therefore, for that range of parameters, the FBG filter doesnot seem to introduce delay distortion that is enough for severeperformance degradation. If a more strict design of the FBGis intended, the delay distortion is only considered acceptablefor 2.5 ps [2]. Hence, the range of parameters that leads to anoptimized optical filter is given approximately by cm

cm and 3 10 . The boundis taken from Fig. 3 to ensure an optical

loss below about 5 dB. The bound is chosenfrom Fig. 2 to ensure an isolation above 20 dB. For this range ofparameters, the filter bandwidth varies approximately between65 and 90 GHz.

Notice that the previous range of parameters has been derivedneglecting the FBG ability of noise filtering, which is also im-portant for ensuring an optimal performance of the FBG in op-tically preamplified receivers, where the signal-amplified spon-taneous emission (ASE) beat noise is usually dominant.


Fig. 5. Delay distortion versus � and �� .

IV. SINGLE-CHANNEL SYSTEM

In this section, the FBG performance as an optical filter in anoptically preamplified receiver is assessed and optimized for asingle-channel system. To assess rigorously the performance ofthe optical receiver with the FBG as the optical filter, the rig-orous formulation described in [13] and the Gaussian approx-imation (GA) described in [14] are used. These two formula-tions allow us to take into account the influence of arbitrary op-tical filters in the error probability. The saddlepoint approxima-tion (SA) is used to calculate the error probability from the mo-ment-generating function derived through the rigorous formu-lation. The GA is used because of its inherent simplicity, shortcomputational time, and its relative accuracy (a maximum ofabout 1 dB of discrepancy [14] in comparison with the rigorousmethod).

The sensitivity is calculated for the error probability of10 . The optically preamplified receiver is described in [13]and [14]. Rectangular pulse shapes filtered by a 16th-orderBessel filter with a bandwidth of 60 GHz are considered atthe optically preamplified receiver input. The length of thedeBruijn sequences is 2 b. The spontaneous emission factor isset to , the preamplifier gain to dB, the PINresponsivity to A/W, and the electronic circuitry ismodeled by a second-order Butterworth with a 3 dB band-width of 26 GHz. These values are kept constant throughoutthis work. The values of and defined in [13] for the rigorousmethod are continuously optimized for the different parameters

and considered in the performance evaluation.Fig. 6(a) and (b) shows the receiver sensitivity estimates as

a function of and for two different extinction ratiosand , respectively. The extinction ratio is de-

fined in accordance with the International TelecommunicationsUnion Telecommunications Standardization Sector recommen-dation [15]. The signal has an NRZ format. The SA is used forthe performance evaluation.4

Comparison of Fig. 6(a) and (b) reveals that the region ofbest sensitivities moves slightly, toward larger grating lengths

4The GA and SA estimates lead to practically the same sensitivities for � ��. When the extinction ratio is increased, higher sensitivity discrepancies anda slightly different set of parameters for best sensitivities are observed.

(a)

(b)

Fig. 6. Sensitivity versus � and �� for an NRZ signal at 40 Gb/s and anextinction ratio of (a) � � �� and (b) � � �.

and to lower , with the increasing extinction ratio.5 Thismeans that, for the optimal optical filter that leads to these bestsensitivities, the optical filter 3 dB bandwidth is decreasing[see Fig. 4], while the delay distortion remains practically thesame [see Fig. 5].

For a lower extinction ratio, the eye penalty is more sensi-tive to distortion introduced by the optical FBG filter. Hence,the filter must have a higher bandwidth (about 65–80 GHz) toavoid the amplitude distortion. When the extinction ratio is in-creased, the signal levels apart and the FBG 3 dB bandwidthshould be smaller (between 40 and 55 GHz), to decrease thesignal-ASE beat noise and improve the sensitivity. However, ifan FBG optimized for an extinction ratio of is assumed,a maximum degradation of about 0.6 dB will be observed for

, which is almost negligible. Otherwise, if the oppositeis considered, i.e., an FBG optimized for , higher degra-dations that can exceed 1 dB could be observed.

In both figures, it should be noticed that the values of and, which lead to the best sensitivities, correspond to an FBG

with insertion loss (about 3 dB), i.e., non flat-top filters.

5Extinction ratios between � � �� and � � � have been also investigatedand the referred behavior has been also observed.


Fig. 7. Sensitivity versus � and �� for a RZ signal at 40 Gb/s and anextinction ratio of � � ��.

Furthermore, Fig. 6 shows also that the FBG is very robust toa variation in its parameters, because the receiver sensitivityvaries only about 1 dB in a very wide range of and .This can be explained as follows. When the 3 dB bandwidthof the FBG filter decreases, the power penalty due to thesignal-ASE beat noise decreases in a way that compensates forthe increasing power penalty due to eye-closure. This leads toa small degradation of the power penalty in a very wide rangeof parameters.

The analysis performed in Section III led to an optimal filterin the range given by cm cm and 3 10

. Although rough, that simple analysis predictsan acceptable range of parameters, as can be observed in Fig. 6.

For a single channel at 40 Gb/s, the RZ format with 50% dutycycle has been shown theoretically and experimentally to leadto larger fiber transmission distances than the NRZ format does,because the RZ signals are less affected by fiber nonlinearities[16], [17]. It is interesting to compare the optimization of theFBG filter for RZ signals with the previous optimization per-formed for NRZ signals.

Fig. 7 shows the receiver sensitivity estimated through the SAfor a signal with RZ format with an extinction ratio of .The best sensitivities occur also for smaller grating lengths, anda sensitivity degradation of about 0.8 dB is observed in com-parison with the NRZ format [see Fig. 6(a)]. This degradationis observed because the sensitivity gain of RZ with respect toNRZ can be negative for extinction ratios of 10, when, as in thiscase, direct modulation RZ signals are considered [18]. The as-sumption of “nearly” rectangular pulse shape also reduces thisgain [18], [19] and demands optimal FBG bandwidths higherthan that shown in Fig. 6 for the NRZ signal [19]. It shouldbe pointed out that the optimal optical filters obtained for theRZ signal have very poor isolation and, hence, can lead to se-vere performance degradation in WDM systems. Therefore, forWDM systems, it is expected that FBG filters with larger gratinglengths should be chosen.

V. WDM SYSTEM

In this section, the FBG is optimized for use in a three-channelWDM system with a channel spacing of 100 GHz. Three chan-

(a)

(b)

Fig. 8. Sensitivity versus � and �� for a WDM system at 40 Gb/s. (a) NRZsignal and (b) RZ signal for an extinction ratio of � � ��.

nels are enough to assess the WDM system performance be-cause the FBG has, in general, high isolation and sidelobe sup-pression.

In this section, all sensitivity estimates are obtained throughthe SA for an extinction ratio of .6 The rigorous formula-tion presented in [13] allows the consideration of only specificsequences in adjacent channels. Hence, complementary (to thesequence in the central channel) sequences are considered in theadjacent channels.

The study of the WDM system considers two cases of signalformats. Fig. 8(a) and (b) refers, respectively, to NRZ and RZsignals. A comparison of Fig. 8(a) with Fig. 6(a) reveals thatthe FBG chosen for a single channel is very good for channelselection, because the best sensitivities differ only slightly fromthe ones observed in Fig. 6(a) and are obtained practically forthe same and values. The sensitivities of an FBG withlarge 3 dB bandwidths ( lower than 0.3 cm) are much worsethan the ones obtained for the single-channel system due to thehigher linear crosstalk introduced by the optical filtering of the

6For WDM systems, a comparison between the GA and SA estimates hasbeen also performed considering the extinction ratio variation. It has been alsoobserved that the estimates provided by the two methods become closer withthe reduction of the extinction ratio. For � � ��, the estimates are practicallyequal.


adjacent channels. A comparison of Fig. 8(b) with Fig. 7 revealsthat the best sensitivities have moved to a region of parameterswhere the isolation and sidelobe suppression are higher and theoptical filter 3 dB bandwidth is smaller. This occurs to reducethe linear crosstalk introduced by the optical filtering of the RZsignal.

Fig. 8 shows that the performance degradation of a WDMsystem relative to a single-channel system is practically negli-gible for NRZ and RZ signals. The comparison of Fig. 8(a) withFig. 8(b) reveals that the two areas of parameters that lead to thebest sensitivities for the NRZ and RZ signals intersect. Hence,with only one FBG filter, the receiver performance is optimizedfor the two signal formats and for the extinction ratio, takinginto account the conclusion presented in Section IV. Notice alsothat, in this intersection area and for lower than 3 10 ,the FBG optical filter can have optical losses above 3 dB.

A channel spacing of 200 GHz has also been investigated,and the crosstalk introduced by the optical filtering is so smallthat Figs. 6(a) and 7 (for a single-channel system) practicallyrepresent the results achieved in this case.

VI. CASCADE OF OPTICAL FILTERS

In this section, a cascade of ten FBG filters is considered.Each FBG works as an add-drop filter present in the network.The signal is considered to be selected by the last add-drop filter.

All the FBG filters in the cascade are assumed to have thesame properties (same and ), and the assumptions pre-sented in [20] are considered. All sensitivity results are obtainedby using the GA proposed in [14]. The extinction ratio is ,and, for the WDM system, complementary sequences are trans-mitted in the two adjacent channels. All signals have an NRZformat. Fig. 9(a) and (b) shows the receiver sensitivities ob-tained, respectively, for a single-channel system and a WDMsystem.

A comparison of Fig. 9(a) with Fig. 6(a) reveals that the bestsensitivity achieved for the single filter and for the cascade ofoptical filters is the same and is about 28.3 dBm. The area ofbest sensitivities changed to lower and higher than thosevalues observed in Fig. 6(a). This area corresponds to individualfilters with 3 dB bandwidths above about 180 GHz and verylow delay distortion. The concatenation of the ten filters leads toan equivalent filter with 3 dB bandwidth and delay distortionsimilar to those observed for the optical filters that lead to thebest sensitivities for single-channel systems [Fig. 6(a)]. How-ever, if the signal is selected by the first add-drop filter of thecascade, a filter with a 3 dB bandwidth above 180 GHz wouldlead to a receiver performance degradation that can achieve 0.8dB [see Fig. 6(a)]. By cascading the optical filter that gives thebest sensitivities in Fig. 6(a), degradations between 0.8 and 10dB are observed [see Fig. 9(a)].

The comparison of Fig. 9(b) with Fig. 9(a) reveals that thearea leading to the best sensitivities is much smaller, and, forgrating lengths close to 1 mm, power penalties exceeding 0.7 dBcan be observed. This is attributed to the crosstalk introduced bythe optical filtering of the signal in the adjacent channels, be-cause these cascaded filters show very high 3 dB bandwidths(about and above 180 GHz). When the central channel is se-

(a)

(b)

Fig. 9. Sensitivity versus � and �� for a cascade of ten optical filters. (a)Single-channel system and (b) WDM system at 40 Gb/s and for an extinctionratio of � � ��.

lected, for example, by the first add-drop filter of the cascade,the sensitivity degradation exceeds 8 dB [see Fig. 8(a)]. Thus, anFBG with these characteristics should be disregarded for WDMsystems. Also, sensitivity degradations that can achieve 10 dBare observed in Fig. 9(b) for the cascade of an FBG optimizedfor the single-filter case.

Therefore, the optimization of an FBG filter forsingle-channel and WDM systems, and also for the opticalfilter cascade, requires a compromise to achieve a satisfactoryperformance.7 This compromise results from two effects: onthe one hand, from the severe accumulated amplitude and delaydistortion introduced by the cascade of optical filters; on theother hand, from the high crosstalk introduced by the opticalfilter for lower grating lengths. The range of parameters thatgives sensitivities of about 27 dBm leads to a good choice ofthe FBG (only about 1.2 dB of degradation in comparison withthe single-filter case). This region is depicted in Fig. 9(b) (thearea inside the bold line). In this area, the FBG has a 3 dBbandwidth between about 110 and 130 GHz and is “almost” aflat-top filter. This can be seen in Fig. 10. This figure depicts

7For a WDM system with a channel spacing of 200 GHz, this performancecompromise is not as relevant. In this case, when the first add–drop filter selectsthe signal, a power penalty of only 0.5 dB is observed.


Fig. 10. Amplitude transfer functions of the two optimized FBG filters: � �

�� mm and �� (thin line) and � � �� mm and ��

�� (bold line).

the amplitude transfer functions of two FBG filters.8 The firstfilter, with mm and , is inside theoptimized parameters region depicted in Fig. 9(b). The secondfilter, with mm and , correspondsto the individual FBG optimized for single-channel and WDMsystems [see Figs. 6(a) and 8(a)]. The delay distortion of the twofilters is about 3 ps.

Fig. 10 shows the amplitude response of the filter that shouldbe used as an optical filter in an optically preamplified receiverfor single-channel and WDM systems and for a cascade of op-tical filters. As can be noticed, these optimized FBG filters donot have a steep cutoff, which is usually a requirement for thiskind of application [2], [4], [6], [7]. This assumption resultsfrom considering only the crosstalk introduced by the imperfectoptical filtering of adjacent channels. However, it disregards theaccumulation of distortion caused by cascading optical filters.As sharper amplitude responses lead to higher delay distortion[7],9 the optimization leads to a filter without steep cutoff inorder to introduce lower distortion.

VII. OPTICAL FILTER MISALIGNMENT

In Sections IV–VI, the FBG has been optimized for use as anoptical filter in single-channel and WDM systems and for op-tical filter cascades. This optical filter should be tuned to thecarrier wavelength to achieve an optimal performance. In thissection, the impact of the optimized FBG filter misalignmenton the system performance is investigated. We choose an FBGwith mm and , which is insidethe optimized parameters region depicted in Fig. 9(b). All sen-sitivity results are obtained by using the GA proposed in [14].The extinction ratio is , and, for the WDM system witha channel spacing of 100 GHz, complementary sequences areconsidered in the two adjacent channels. All signals have anNRZ format.

Fig. 11 shows the sensitivity as a function of the optical filterdetuning for four cases: two single-channel systems (one with

8Notice that Fig. 10 shows the low-pass equivalent transfer functions of theoptimized FBG filters.

9This conclusion can be drawn from Figs. 3 and 5.

Fig. 11. Sensitivity versus optical filter detuning for a system at 40 Gb/s and anextinction ratio of � � ��.�: single-channel/single filter; : WDM/single filter;: single-channel/optical filters cascade; �: WDM/optical filters cascade.

a single optical filter and the other with a cascade of ten op-tical filters) and two WDM systems (one with a single opticalfilter and the other with a cascade of ten optical filters). Fig. 11shows that the single filter is very tolerant to the carrier detuningfor single-channel systems. A sensitivity degradation of 3 dBis observed only for detunings of about 80 GHz. This result isdue to the high 3 dB bandwidth of the optimized FBG (above100 GHz). For a WDM system, the single filter leads to a sen-sitivity degradation of 3 dB for a detuning of about 25 GHz.The significant reduction of the maximum detuning is due tothe crosstalk.10

For the cascade of optical filters, a sensitivity degradation of3 dB is observed for a detuning of about 20 GHz for single-channel and WDM systems. The accumulated amplitude anddelay distortions are responsible for this behavior.11 Therefore,all detunings that lead to 3 dB of sensitivity degradation exceedhalf of the bit rate magnitude. Hence, we can consider that theoptimized FBG is robust to the carrier misalignment.

VIII. CONCLUSION

In this work, FBGs with Gaussian apodization profile andzero dc index change have been proposed for use as opticalfilters in single-channel and WDM systems at 40 Gb/s, andthe characteristics have been studied extensively. High sidelobesuppression, high isolation, and low delay distortion have beenobserved. Through the combination of these properties, a roughanalysis of the optimal FBG to be used as an optical filter in anoptically preamplified receiver has been performed and has ledto an acceptable prediction of the optimal FBG.

Exhaustive optimization of the FBG has been performedthrough the assessment of the sensitivity for single-channeland WDM systems. It has been shown that the optimizedFBG can lead practically to the same receiver performance,for single-channel and WDM systems, due to its low crosstalkintroduction. The FBG has been optimized for RZ and NRZtransmission and is very robust to variations in extinction ratio.

10For a channel spacing of 200 GHz, the tolerance to the detuning is almostthe same as that observed for the signal-channel system due to the low crosstalkintroduced.

11This conclusion holds also in a cascade of optical filters for a WDM systemwith channel spacing of 200 GHz.


The parameters and of the optimized FBG are betweenabout 0.3 cm and 0.65 cm and 3 10 and 6.5 10 ,respectively. This leads to the conclusion that the optimizedFBG is very robust to a variation in those parameters.

The cascade of the optimized FBG optical filters has been in-vestigated for single-channel and WDM systems. For a WDMsystem with a channel spacing of 100 GHz, 1.2 dB of sensitivitydegradation with respect to the single-filter case is obtained inthe optimization of the filter to ensure its good performance asan add-drop filter in a network. This good performance resultsfrom a compromise between the high crosstalk introduced bythe FBG, due to its higher bandwidth for lower grating lengths,and the severe accumulated amplitude and delay distortion in-troduced by the cascade of optical filters. For a WDM systemwith channel spacing of 200 GHz, this compromise is unneces-sary to achieve a good performance of the filter. The compro-mise leads to an optimized FBG with a bandwidth between 110and 130 GHz, an isolation of about 20 dB, a delay distortion ofabout 4 ps, and a nearly flat-top amplitude response, however,without a steep cutoff.

The optimized FBG filter tolerance to the detuning has beenalso investigated, and results show that, for a sensitivity degra-dation of 3 dB with respect to the tuned case, a detuning of20 GHz is allowed, even for a cascade of ten optical filters.

REFERENCES

[1] T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol., vol. 15, pp.1277–1294, Aug. 1997.

[2] A. Othonos and K. Kalli, Fiber Bragg Gratings—Fundamentals and Ap-plications in Telecommunications and Sensing. Norwell, MA: ArtechHouse, 1999, ch. 3.

[3] M. Zervas, “New generation DWDM fiber grating devices,” Proc. SPIE,vol. 4087, pp. 162–166, 2000.

[4] A. Carballar, M. Muriel, and J. Azana, “Fiber grating filter for WDMsystems: An improved design,” IEEE Photon. Technol. Lett., vol. 11,pp. 694–696, June 1999.

[5] M. Lima, A. Teixeira, and J. Rocha, “Simultaneous filtering and dis-persion compensation in WDM systems using apodised fiber gratings,”Electron. Lett., vol. 36, no. 16, pp. 1412–1414, Aug. 2000.

[6] , “Optimization of apodized fiber grating filters for WDM sys-tems,” in Proc. IEEE LEOS Annu. Meeting, vol. 2, 1999, pp. 876–877.

[7] G. Lenz, B. Eggleton, C. Giles, C. Madsen, and R. Slusher, “Dispersiveproperties of optical filters for WDM systems,” IEEE J. Quantum Elec-tron., vol. 34, pp. 1390–1402, Aug. 1998.

[8] B. Eggleton, G. Lenz, N. Litchinitser, D. Patterson, and R. Slusher,“Implications of fiber grating dispersion for WDM communicationsystems,” IEEE Photon. Technol. Lett., vol. 9, pp. 1403–1405, Oct.1997.

[9] K. Ennser, M. Zervas, and R. Laming, “Optimization of apodizedlinearly chirped fiber gratings for optical communications,” IEEE J.Quantum Electron., vol. 34, pp. 770–778, May 1998.

[10] D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Martí, “Design ofapodized linearly chirped fiber gratings for dispersion compensation,”J. Lightwave Technol., vol. 14, pp. 2581–2588, Nov. 1996.

[11] A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J.Quantum Electron., vol. QE-9, pp. 919–933, Sept. 1973.

[12] R. Kashyap, Fiber Bragg Gratings. New York: Academic, 1999, ch.4–5.

[13] E. Forestieri, “Evaluating the error probability in lightwave systems withchromatic dispersion, arbitrary pulse shape and pre- and postdetectionfiltering,” J. Lightwave Technol., vol. 18, pp. 1493–1503, Nov. 2000.

[14] J. Rebola and A. Cartaxo, “Gaussian approach for performance evalua-tion of optically preamplified receivers with arbitrary optical and elec-trical filters,” Proc. Inst. Elect. Eng., pt. J, vol. 148, no. 3, pp. 135–142,June 2001.

[15] “Optical interfaces for equipment and systems relating to the syn-chronous digital hierarchy,”, ITU-T recommendation G. 957, 1995.

[16] D. Breuer and K. Petermann, “Comparison of NRZ- and RZ-modula-tion format for 40-Gb/s TDM standard-fiber systems,” IEEE Photon.Technol. Lett., vol. 9, pp. 398–400, Mar. 1997.

[17] R. Ludwig, U. Feiste, E. Dietrich, H. Weber, D. Breuer, M. Martin, andF. Küppers, “Experimental comparison of 40 Gbit/s RZ and NRZ trans-mission over standard singlemode fiber,” Electron. Lett., vol. 35, no. 25,pp. 2216–2218, Dec. 1999.

[18] M. Pauer, P. Winzer, and W. Leeb, “Bit error probability reduction in di-rect detection optical receivers using RZ coding,” J. Lightwave Technol.,vol. 19, pp. 1255–1262, Sept. 2001.

[19] P. Winzer, M. Pfennigbauer, M. Strasser, and W. Leeb, “Optimum filterbandwidths for optically preamplified RZ and NRZ receivers,” J. Light-wave Technol., vol. 19, pp. 1263–1273, Sept. 2001.

[20] M. Kuznetsov, N. Froberg, S. Henion, and K. Rauschenbach, “Powerpenalty for optical signals due to dispersion slope in WDM filter cas-cades,” IEEE Photon. Technol. Lett., vol. 11, pp. 1411–1413, Nov. 1999.

João L. Rebola was born in Lisbon, Portugal, on March 29, 1976. He receivedthe “Licenciatura” degree in electrical engineering in telecommunicationsand computers from Instituto Superior Técnico, Lisbon Technical University,Lisbon, Portugal, in 1999. He is currently working toward the Ph.D. degree inelectrical engineering at the same university.

His main research interests currently include optical filtering and perfor-mance evaluation in dense wavelength-division multiplexing systems.

Adolfo V. T. Cartaxo (S’89–M’98) was born in Montemor-o-Novo, Portugal,on January 10, 1962. He received the “Licenciatura” degree in electrical engi-neering, the M.Sc. degree in telecommunications and computers, and the Ph.D.degree in electrical engineering from Instituto Superior Técnico (IST), LisbonTechnical University, Lisbon, Portugal, in 1985, 1989, and 1992, respectively.

From 1987 to 1990, he was an Assistant Lecturer at IST and from 1990 to1992, he carried out postgraduate research work at IST in the area of clock re-covery circuit optimization in direct detection optical communications. Since1992, he has been an Assistant Professor at IST where he has coordinated IST’sparticipation in several projects in the context of the European Union and Por-tuguese programs on research and development (R&D) in the telecommunica-tions area. In the past few years, he has acted as a Technical Auditor and Evalu-ator for projects included in European Union R&D Programs. His main researchinterests include fiber-optic communication systems and networks.

Documents

Performance optimization of Gaussian apodized fiber Bragg grating filters in WDM systems