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Flat-top pulse generation based on a fiber Bragggrating in transmission

Miguel A. Preciado* and Miguel A. Muriel

ETSI Telecomunicacion, Universidad Politecnica de Madrid (UPM), 28040 Madrid, Spain*Corresponding author: ma.preciado@upm.es

Received October 27, 2008; revised January 23, 2009; accepted January 30, 2009;posted February 8, 2009 (Doc. ID 103231); published March 6, 2009

We propose and analyze a flat-top pulse generator based on a fiber Bragg grating (FBG) in transmission. Asis shown in the examples, a uniform period FBG properly designed can exhibit a spectral response in trans-mission close to sinc function (in amplitude and phase) in a certain bandwidth, because of the logarithmHilbert transform relations, which can be used to reshape a Gaussian-like input pulse into a flat-top pulse. 2009 Optical Society of America

OCIS codes: 060.3735, 200.4740, 230.1150, 320.5540, 320.7080.

The generation of well-defined pulse forms and pulsesequences is required for a wide range of applica-tions. Particularly, flat-top pulses are highly desiredfor various important applications: optical gating,nonlinear optical switching, and a wide range of ul-trafast pumpprobe experiments [13]. Fiber grat-ings offer their inherent advantages (all-fiber ap-proach, low insertion loss, and the potential for lowcost), and approaches based on fiber Bragg grating(FBG) in reflection [1,2], and long period Bragg grat-ings (LPBGs) in transmission [3] have been proposedfor flat-top pulse generation. The main drawback ofFBGs in reflection is that it requires an optical circu-lator, or similar device, to separate the incident inputsignal from the reflected output signal. RegardingLPBGs, they present two codirectional modes in theoutput.

In this Letter, we propose a flat-top pulse generatorbased on an FBG operating in transmission. Several

applications-based FBGs in transmission approacheshave been previously proposed, such as the disper-sion compensator [46], optical integrator [7,8], andoptical differentiator [9]. It is worth noting thatFBGs in transmission are not suitable for many ap-plications because of the amplitudephase relationsof their spectral response [6]. However, using them intransmission offers interesting properties. Besidesnot requiring the use of a coupler or circulator, thesystem is easily scalable, the energy efficiency is in-creased, the cost and complexity of the system are re-duced, and FBGs in transmission have less sensitiv-ity of the phase response than in reflection to gratingfabrication errors [4,6]. Moreover, the output signal

includes not only the processed signal within theFBG resonant band but also the rest of the input sig-nal (which is transmitted without any distortion),which may be interesting in WDM systems. Figure 1shows a schematic of the proposed system, where thecapabilities of this approach in WDM processing areshown.

In the remainder of this Letter, we explain the the-oretical basis of this method and design and simulatetwo FBGs and apply them in transmission, in singleand concatenated configuration, to several inputwaveforms. Finally, we summarize and conclude ourwork.

Let us suppose fint and foutt as the complex en-velopes of the input and output of the system, respec-tively, with t as the time variable. We can obtain aflat-top pulse foutt from a narrow-enough Gaussian-like pulse fint if they are related by fouttfint

rectt/T, where rectt is the rectangular function,T is the rectangle full width, denotes the convolu-tion operator, and denotes proportionality. The cor-responding spectral functions Fin and Fout arerelated by FoutsincT/ 2Fin, where sinc isthe sinc function; is the base-band angular pulsa-tion, i.e., =opt0, opt is the optical angular pul-sation; 0 is the central angular pulsation of the sig-nals; and j = 11/2 is the imaginary unit. Thus, thespectral response (SR) of the FBG in transmissionshould meet HTHT,ideal=Fout/FinsincT/ 2, where HT can never exactly reach

HT,ideal, since an FBG has no zeros in transmis-sion. It is well known that the SR magnitude andphase of a FBG in transmission are related by meansof the logarithmic Hilbert transform (LHT), since itsimpulse response is a minimum phase function [6].Thus, we cannot simultaneously impose arbitraryHT and HT, in general. Fortunately, neglect-ing linear phase terms, we can assume thatsincT/ 2 and sincT/ 2 are LHT pairs, sincethe rectangular function can be practically consid-ered a minimum phase function [10]. Indeed, if we

Fig. 1. (Color online) Schematic of the system. An FBGworking in transmission shapes a flat-top pulse in the cor-responding WDM channel. The output signal also includesthe signal in other WDM channels.

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have an FBG with HT HT,ideal sincT/2,we automatically obtain HTHT,ideal=sincT/2, where we neglect constant and lin-ear phase terms.

Since the SRs in reflection and transmission are re-lated by HR=1 HT2, the objective SR of theFBG in reflection must locally satisfy HR1 C sincT/ 22, where C 1 is a real constant.

Several approximations have to be done to obtainHR with a feasible FBG. First, we have to apply awindow function, since a FBG has a finite bandwidth.Moreover, we have to take into account that a reflec-tivity of 100% is impossible, but we can obtain a re-flectivity close to it. These approximations lead to

HR = WRmax1 C sincT/22 , 1

where Rmax1 is the maximum reflectivity of theFBG, and W is a window function. Finally, in thegrating design, we have to apply an inverse scatter-ing algorithm [11,12] to obtain the grating profile. Itis worth noting the independence of this design on

HR, which is a degree of freedom and can be ar-bitrarily chosen. However, we want to remark thatwe have obtained the best results of the inverse scat-tering algorithm by choosing HR as the maxi-mum phase corresponding to HR.

As an example, we design a uniform-period FBG intransmission on the ideas introduced above, wherewe assume a central frequency 0/ 2=193 THz,and we will refer to this grating as FBG1. The desiredSR in reflection, HR, is defined by Eq. (1), withC =1, Rmax=0.9999, T=50 ps, and the window func-tion W used is a raised-cosine function with a roll-off factor of 1 / 3 and a total width of 400 GHz. To fullycharacterize the desired response in reflection, we as-sign HR as the maximum phase correspondingto HR (another phase could be arbitrarily as-signed). Using an inverse-scattering algorithm we ob-tain the corresponding coupling coefficient z,which is represented in Fig. 2. It is worth noting thatz is complex in general but can be assumed real foruniform-period FBGs. This is legitimate provided wetake a proper choice of the origin z =0 [13]. The re-quired grating profile has a length of L =10 cm, anaverage refraction index nav=1.452, a grating period

of 0 = 534.888 nm, and a maximum absolute cou-pling factor maxz=2858.87 m1. Each zerocrossing of z in Fig. 2 implies a spatial -phaseshift in the grating, which implies a significant num-ber (about 50) of-phase shifts, but it is within cur-rent technology, since FBGs have become extremelysophisticated [14].

Figure 3(a) shows the magnitude and phase of theFBG SR in transmission, obtained from numericalsimulation. It can be observed that the SR phasewithin the operative band, the width of which can beapproximately estimated as 120 GHz, consists of alinear phase term (pure delay), plus the -phaseshifts corresponding to sinc function.

To highlight the easy scalability of this approachand the potential for multiband WDM processing, weconsider a system composed by the concatenation ofFBG1 and FBG2, a grating equivalent to FBG1 butwith a different grating period and central frequency(0 =535.582 nm and 0 = 192.75 THz, respectively).The system SR in transmission, shown in Fig. 3(b),was obtained by using the transfer matrix method

[13] (it is not exact to calculate it by directly multi-plying the FBG SRs in transmission, since there is alittle overlapping band around 192.875 THz). Figure4 shows the numerically obtained output temporalwaveforms for different input temporal waveforms.In Fig. 4(a), we consider FBG1 with the input wave-forms of a transform-limited Gaussian optical pulseof 7 ps and spectral width of 126.08 GHz (bothFWHM width) with a central frequency of 193 THz.As can be observed, the output pulse exhibits the de-sired flat-top shape. In Figs. 4(b) and 4(c) we considera signal composed of four transform-limited Gauss-ian optical pulse pulses at different central frequen-cies (192.5, 192.75, 193, and 193.25 THz), each with a

temporal width of 7 ps (FWHM). In Fig. 4(b) we ap-ply the signal to FBG1. Note that FBG1 processesonly the pulse within its resonant band. In Fig. 4(c),we apply the signal to the concatenation of FBG1 andFBG2, and it can be observed that the resulting sys-tem processes only the pulses within the resonantband of the FBGs. In both cases, the shapes of theprocessed pulses are practically the same as shown inFig. 4(a), and the output also includes the rest of theunprocessed pulses, which remain undistorted.

Fig. 2. (Color online) Grating profile obtained by inversescattering in a positive and negative representation, whereeach zero crossing ofz implies a spatial -phase shift inthe grating.

Fig. 3. (Color online) Spectral response in transmission of(a) FBG1; (b) the system composed of FBG1 concatenatedwith FBG2.

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It is worth noting that the FBG spectral responseat the central frequency is the maximum for passivedevices, HT= 0=1, which implies optimum energyefficiency, which is unreachable for reflective FBGs,since a 100% of reflectivity is not possible. We alsowant to remark that the maximum reflectivity andspectral width of the FBG are related to the flat-toppulse quality in terms of edge sharpness and top flat-ness, and to the grating feasibility in terms of length,coupling strength, and profile complexity. It is sug-gested to use a trial and error design method withFBGs synthesis and simulation software to obtain atrade-off solution between grating feasibility andpulse quality, depending on the concrete limitationsof the technology used and the application require-ments.

In conclusion, in this Letter we have presented aflat-top pulse generator approach based on an FBG intransmission. As it has been shown, we can obtain anFBG SR in transmission close to the sinc function ina certain bandwith in amplitude and phase. Since theamplitude and phase of the FBG SR in transmissionare LHT pairs [6] and amplitude and phase of thesinc function can also be considered LHT pairs [10],when the SR amplitude is close to the sinc function

amplitude the SR phase also becomes close to thesinc function phase. We want to emphasize the highenergetic efficiency, simplicity, scalability, and suit-ability for WDM applications, obtaining a multibandprocessing by simply concatenating several FBGs intransmission at different resonant bands, withoutany additional element except fiber optics.

This work was supported by the Spanish Ministe-rio de Educacion y Ciencia under Project PlanNacional de IDI TEC2007-68065-C03-02.

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Fig. 4. (Color online) Temporal waveforms of the input sig-nal (dashed curve), and the output signal (solid curve) inthe examples: (a) FBG1 applied over a 7 ps Gaussian pulseat 193 THz; (b) FBG1, applied over a signal composed offour 7 ps Gaussian pulses at several frequencies, whereonly the pulse in the FBG1 resonant band is processed; (c)

FBG1 and FBG2 concatenated, applied over the same pre-vious signal, where only the pulses in the FBG1 and FBG2resonant bands are processed. Note that the output signalalso includes the unprocessed pulses outside the FBGresonant bands, which are hardly distinguishable from theinput signal pulses in (b) and (c).

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