Analysis of inverse-Gaussian apodized fiber Bragg grating

Analysis of inverse-Gaussian apodizedfiber Bragg grating

Bo Lin,1 Swee Chuan Tjin,1,* Nam Quoc Ngo,1 Yufeng Song,1

Sheng Liang,2 Li Xia,3 and Meng Jiang4

1Photonics Research Centre, School of Electrical and Electronic Engineering, Nanyang Technological University,50 Nanyang Avenue, Singapore 639798, Singapore

2School of Instrument Science and Opto-electronics Engineering, Beihang University,37 Xueyuan Road, Beijing 100191, China

3National Engineering Laboratory for Next Generation Internet Access System, Department of OpticalCommunication and Optical Network Engineering, Huazhong University of Science and Technology,

Wuhan 430074, China4Center for Optical and Electromagnetic Research, State Key Laboratory of Modern

Optical Instruments, Zhejiang University, Hangzhou 310058, China

*Corresponding author: [email protected]

Received 4 June 2010; accepted 21 July 2010;posted 26 July 2010 (Doc. ID 129579); published 24 August 2010

Inverse-Gaussian apodized fiber Bragg gratings (IGAFBGs) are numerically studied using the transfermatrix method and fabricated by the commonly used phase-mask scanning technique in a single-stepscanning process. The IGAFBG can serve as a dual-wavelength passband filter, whose wavelength spa-cing can be continuously tuned by introducing a tunable chirp through applying a strain gradient inprinciple. Also, an IGAFBG with identical dual passbands having 0:144 nm wavelength spacing is ex-perimentally achieved. We also show that an IGAFBG can act as a multipassband filter with varied freespectral ranges (FSRs), and the largest FSR variation of this IGAFBG is nearly seven times more thanthat in a comparable FBG pair filter. An IGAFBG with varied FSRs of ∼16:125, ∼12:25, ∼8:5, and∼6:375 GHz is fabricated. This multipassband varying-FSR IGAFBG filter can find applications instep-tunable microwave generations. © 2010 Optical Society of AmericaOCIS codes: 060.2330, 060.3735, 060.4510.

1. Introduction

FiberBragg gratings (FBGs) arewidelyutilized in tel-ecommunication and sensing due to their excellentproperties, such as all-fiber nature, low cost, smallsize, and compatibility with fiber-optics networks[1–6]. Six fundamental FBG structures including uni-form, apodized, chirped, phase-shifted, superstruc-ture, and tilted gratings have been well studied [7].The uniform FBG is the simplest type of FBG witha narrowband reflection spectrum at the Bragg wave-

length.However, theuniformFBGhas large sidelobesdue to its finite length and cannot be used for certainapplications that require significant suppression ofthe sidelobes. It is well known that the sidelobescan be easily suppressed by using a Gaussian apodi-zation function [7] because the Fourier transform ofthe Gaussian apodization function yields a Gaussian-like reflection spectrum. In our previous work [8], weenhanced the sidelobes of a regular FBG by using aninverse-Gaussian apodization function to produce adual-wavelength passband filter, which is incorpo-rated into a linear fiber laser cavity to generatedual-wavelength lasing. This inverse-Gaussianapodized (IGA) FBG distinguishes itself from the

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six reported fundamental FBG structures and pos-sesses unique advantages over the phase-shifted(PS) FBG [9,10], polarization-maintaining (PM) FBG[11–13], equivalent phase-shift (EPS) FBG [14,15],and an FBG pair [16–18] as a dual-wavelength pass-band filter, which have already been explained indetail [8]. However, the structure and property ofthe IGAFBG is not well studied.

In this paper, the relationship between the spec-tral shape of an IGAFBG (including the 3 dB band-widths of the two passbands and their wavelengthspacing) and its grating characteristics (includingthe grating length and index modulation depth) isanalyzed. An IGAFBGwith identical dual passbandsis numerically simulated and experimentally fabri-cated. The wavelength spacing can be flexibly chan-ged by changing the grating length and indexmodulation depth. Also, the wavelength spacing canbe continuously tuned by applying a tunable chirp onthe grating in principle. Furthermore, anotherIGAFBG with varied “free spectral ranges” (FSRs),serving as a multipassband filter, is studied and fab-ricated. It shows that the largest FSR variation ofthis IGAFBG is nearly seven times more than thatin a comparable FBG pair filter. This multipassbandIGAFBG filter can find applications in step-tunablemicrowave generations [18].

2. Analysis of the Inverse-Gaussian Apodized FBGUsing the Transfer Matrix Method

The transfer matrix method (TMM) [7] is employedin this work for the analysis and design of the pro-posed IGAFBG. All the parameters shown here havethe same definitions as in [7]. For an FBG with chirp,the main design equations are given below. The dcself-coupling coefficient is given by

�σðz; λÞ ¼ 2πneff

�1λ −

1λD

�þ 2π

λ δneff ðzÞ þ4πneffzðcrÞ

λ2D:

ð1Þ

The ac coupling coefficient is given by

κðz; λÞ ¼ πλ vδneff ðzÞ; ð2Þ

where δneff ðzÞ ¼ δneffAðzÞ, and AðzÞ is defined as theapodization function.

In our case, the apodization function is given by

AðzÞ ¼ 1 − expf½−4ðln 2Þz2�=ðL=3Þ2g: ð3Þ

In the above equations, neff is the effective refrac-tive index, δneff is the dc index change spatiallyaveraged over a grating period, which is also knownas the index modulation depth, cr is the chirp rate, vis the fringe visibility of the index change, λD is thedesigned wavelength, L is the grating length, and thegrating starts from −L=2 to L=2 in the dimension z.

3. Simulation Results

A. Unchirped IGAFBG as a Dual-Wavelength PassbandFilter

To recognize the special property of an IGAFBG, wecompare the spectral shapes of a uniform FBG andan IGAFBG. Figure 1 shows the calculated reflectionspectrum of a typical uniform grating without apodi-zation, and the parameters used are neff ¼ 1:45,L ¼ 1:2 cm, λD ¼ 1550 nm, and δneff ¼ 2:5 × 10−4.Figure 2 and its inset show the calculated reflectionand transmission spectra of an IGAFBG using Eq. (3)with the same parameter values as the uniform FBGin Fig. 1.

For the IGAFBG, three lobes (main lobe, þ1, andþ2 order lobes in Fig. 2) with high almost-equal re-flectivity occur in the reflection spectrum. Comparedwith Fig. 1, Fig. 2 shows that the main lobe becomesnarrower and its 3 dB bandwidth (BW) is about 1=3of the one shown in Fig. 1, which illustrates that theIGAFBG not only enhances the sidelobes but alsosqueezes the main lobe of a typical uniform FBG.The sidelobes can be enhanced in such a conditionthat the gaps between the lobes can produce two deepand ultranarrow passbands, as shown in the inset ofFig. 2. The 3 dB bandwidths of the two passbands arecalculated to be around 4.6 and 5:7 pm, respectively.The wavelength spacing between peak 1 and peak 2is approximately 0:137 nm.

Here, we show that, by changing the grating lengthL or the index modulation depth δneff , the 3 dB band-widths of the two transmission bands and the wave-length spacing between them can be changed. Asshown in Fig. 3, where neff ¼ 1:45, λD ¼ 1550 nm,and δneff ¼ 2 × 10−4, the 3 dB bandwidths of thetwo transmission bands decrease and the wave-length spacing also decreases, as L increases from1.4 to 1:9 cm. For example, the 3 dB bandwidthsare calculated at 5:19 pm (peak 1) and 6:64 pm (peak2) and the wavelength spacing is around 0:114 nmwhen L is 1:4 cm; Meanwhile, the 3 dB bandwidthsare 1:92 pm (peak 1) and 1:28 pm (peak 2) and thewavelength spacing is 0:096 nm when L is 1:9 cm.

Fig. 1. (Color online) Calculated reflection spectrum of a typicaluniform FBG without apodization, which means AðzÞ ¼ 1. Insimulation, neff ¼ 1:45, L ¼ 1:2 cm, λD ¼ 1550 nm, and δneff ¼2:5 × 10−4.

4716 APPLIED OPTICS / Vol. 49, No. 25 / 1 September 2010

It should be noted that, when L is less than 1:4 cm ata modulation depth of 2 × 10−4, the sidelobes cannotbe enhanced to form two high transmittivity pass-bands. In contrast, when L is greater than 1:9 cm,a triple-channel filter or a multichannel filter canbe realized as more sidelobes are enhanced due tothe increased grating length. This is discussed in de-tail in Subsection 3.C. In Fig. 4, where neff ¼ 1:45,λD ¼ 1550 nm, and L ¼ 1:5 cm, it can be seen thatthe 3 dB bandwidths of the two transmission bandsdecrease and the wavelength spacing increases asδneff increases from 2 × 10−4 to 2:5 × 10−4.

Another unique advantage of the IGAFBG is thatit can produce identical dual-passband filters [19]with a simpler scanning process in fabrication. Asseen in Fig. 3 at crossing point M, two transmissionpeaks (peak 1 and peak 2) have the same 3 dB band-widths of 3:1 pm and a wavelength spacing of0:104 nm at L ¼ 1:62 cm, and the correspondingtransmission spectrum is shown in Fig. 5(a). The rea-son for an IGAFBG to produce identical passbands isexplained as follows. At a specific index modulationdepth, e.g., 2 × 10−4, when the grating length is lessthan a threshold value of 1:62 cm, the þ2 order side-lobe is not sufficiently enhanced and the gap between

theþ1 and theþ2 order sidelobes is not so deep com-pared to the gap between the main lobe and the þ1order lobe, and thus the two passbands are not iden-tical (see the inset of Fig. 2, which shows a similarphenomenon). When the grating length is equal tothe threshold value of 1:62 cm, both the þ1 and þ2order sidelobes can be enhanced to such a conditionthat the þ2 order sidelobe has almost the same re-flectivity as the main lobe, and hence identical pass-bands can form, as shown in Fig. 5(a). Similarly,identical passbands occur when L is 1:5 cm andδneff is 2:16 × 10−4, which is indicated by N in Fig. 4,and the corresponding transmission spectrum isshown in Fig. 5(b). The wavelength spacing is

Fig. 2. (Color online) Calculated reflection spectrum of anIGAFBG described by Eq. (3). The inset shows the correspondingtransmission spectrum of this IGAFBG. In simulation, neff ¼ 1:45,L ¼ 1:2 cm, λD ¼ 1550 nm, and δneff ¼ 2:5 × 10−4.

Fig. 3. (Color online) 3 dB bandwidths of peak 1 (solid line withdiamond joints) and peak 2 (solid line with square joints) andwavelength spacing between these two peaks (dashed line) versusL of an IGAFBG. In simulation, neff ¼ 1:45, λD ¼ 1550 nm, andδneff ¼ 2 × 10−4.

Fig. 4. (Color online) 3 dB bandwidths of peak 1 (solid line withdiamond joints) and peak 2 (solid line with square joints) andwavelength spacing between these two peaks (dashed line) versusδneff of an IGAFBG. In simulation, neff ¼ 1:45, λD ¼ 1550 nm, andL ¼ 1:5 cm.

Fig. 5. (Color online) Calculated transmission spectra of threedifferent IGAFBGs having two identical passbands with variedwavelength spacings: (a) Wavelength spacing of 0:104 nm and3 dB bandwidths of 3:1 pm. This spectrum corresponds to M inFig. 3. (b) Wavelength spacing of 0:113 nm and 3 dB bandwidthsof 3:5 pm. This spectrum corresponds toN in Fig. 4. (c) Wavelengthspacing of 0:17 nm and 3 dB bandwidths of 5 pm.


0:113 nm and the 3 dB bandwidths of the two pass-bands are 3:5 pm in this case. The wavelength spac-ing between the two identical passbands of anIGAFBG filter can be flexibly changed by selectinga proper grating length and a proper index modula-tion depth. For example, when δneff is 3:25 × 10−4 andL is 1 cm, the wavelength spacing becomes 0:17 nmand the 3 dB bandwidths of the two passbands are5 pm, as shown in Fig. 5(c).

B. Chirped IGAFBG as a Dual-Passband Filter with aTunable Wavelength Spacing

The wavelength spacing between the two passbandsof an IGAFBG can be continuously tuned by applyinga tunable linear chirp on the grating, which can berealized by introducing a strain gradient [20] in prin-ciple. By applying different chirp rates at 0, 0.1, 0.15,and 0:2 nm=cm, the wavelength spacings of the twopassbands become 0.164, 0.158, 0.15, and 0:14 nm,respectively, as shown in Fig. 6. In simulation,neff ¼ 1:45, λD ¼ 1550 nm, δneff ¼ 3 × 10−4, and L ¼1 cm. Because of the incorporated chirp on theIGAFBG, the shape of the transmission spectrumchanges slightly, and this can be seen in Figs. 6(a)–6(d). The 3 dB bandwidths of the two passbands in-crease slightly and the transmittivity of the twopeaksdecreasesa little, as reported inTable1.However, thiswill not affect the IGAFBG as a dual-passband filter.Only a regular uniform FBG whose 3 dB bandwidthcovering the wavelength spacing Δλ of the two pass-bands is needed to pick out the expected dual chan-nels. Since the wavelength spacing of the twopassbands can be continuously tuned, we believe thata continuously tunable microwave signal can be gen-erated by incorporating such an IGAFBG in a linear[17] or a ring [21] laser cavity. The generated micro-wave frequency ranges from ∼20:5 GHz (0:164 nmwavelength spacing) to ∼17:5 GHz (0:14 nm wave-length spacing) in this case. The tuning range canbe easily changed by using a different IGAFBG withdifferent wavelength spacing. A tunable microwavegeneration based on an IGAFBG filter is beyondthe scope of this work and will be reported elsewhere.

C. IGAFBG as Triple-Wavelength and MultiwavelengthPassband Filters

By selecting proper index modulation depth andgrating length, we can decide the number of thesidelobes that can be enhanced. Hence a triple-wavelength and even a multiwavelength passbandfilter can be produced. For example, a triple-

wavelength passband filter based on an IGAFBGis realized and shown in Fig. 7. In simulation,neff ¼ 1:45, λD ¼ 1550 nm, δneff ¼ 3 × 10−4, and L ¼1:5 cm in Eq. (3). The 3 dB bandwidths of the threetransmission bands λ1, λ2, and λ3 are approximately1.8, 0.6, and 1:6 pm, respectively. The wavelengthspacings Δλ12, Δλ23, and Δλ34 are 0.13, 0.096, and0:07 nm, respectively.

A multiwavelength passband filter with variedFSRs can also be obtained by choosing neff ¼ 1:45,λD ¼ 1550 nm, δneff ¼ 4 × 10−4, and L ¼ 2 cm. The si-mulated result is shown in Fig. 8, where theþ1 orderdip has a wavelength spacing of FSR1, and the þ2order dip has FSR2, and so on. It should be notedthat, FSR is not a strict definition for an IGAFBG

Fig. 6. (Color online) Calculated transmission spectra ofIGAFBGs at (a) 0 (b) 0.1 (c) 0.15, and (d) 0:2 nm=cm chirp rate.In simulation, neff ¼ 1:45, λD ¼ 1550 nm, δneff ¼ 3 × 10−4, andL ¼ 1 cm.

Table 1. Calculated Parameters of an IGAFBG Under Different Chirp Ratesa

Chirp Rate (nm=cm)WavelengthSpacing (nm)

3 dB BWof Peak 1 (pm)

3 dB BWof Peak 2 (pm)

Transmittivityof Peak 1 (dB)

Transmittivityof Peak 2 (dB)

0 0.164 5.95 6.76 0 00.1 0.158 8.15 8.7 −1 −1:30.15 0.15 11.89 11.89 −2 −2:50.2 0.14 11.89 17.3 −3:5 −3:5

aSee Fig. 6.


and only refers to the relevant wavelength spacingbetween adjacent passbands. 3 dB bandwidths ofλ1, λ2, λ3, λ4, λ5, and λ6 are 0.021, 0.017, 0.026,0.119, 0.681, and 2:979 pm, respectively. FSR1,FSR2, FSR3, FSR4, and FSR5 are 0.098, 0.081,0.066, 0.053, and 0:041 nm, corresponding to∼12:25,∼10:125, ∼8:25, ∼6:625, and ∼5:125 GHz frequency,respectively. This IGAFBG can be incorporated into afiber laser cavity to generate a step-tunable micro-wave [18] from ∼12:25 GHz down to ∼5:125 GHzusing only a uniform FBG (e.g., having a 3 dB band-width of 0:1 nm) tuned by applying a strain along itsfiber axis to select the expected adjacent dual wave-lengths from the IGAFBG filter.

4. Experimental Results

The fabrication of an IGAFBG as a dual-wavelengthpassband filter with different wavelength spacings of0.146, 0.1, and 0:07 nmhas been demonstrated in ourprevious work [8]. However, these IGAFBGs do notconsist of identical dual passbands. In this work, anIGAFBG with identical dual passbands is success-fully achieved in experiment. By using the phase-mask scanning technique, the UV light from a248 nm frequency-doubled argon laser is focused by

a cylindrical lens through a uniform phasemask witha 1065:7 nmpitch onto a single-mode fiber core that ishydrogen loaded for five days. The inverse-Gaussianapodization function is realized by varying the scan-ning speed of the laser beam, where a high scanningspeed yields a low δneff at a particular grating positionand vice versa. By adjusting the laser beam power,beam size, the position of the fiber relative to thephase mask, and the laser exposure time at differentpositions along the grating, we can achieve differentindex modulation depth distribution.

To fit the inverse-Gaussian apodization functionEq. (3) into the fabrication process, after doing sev-eral trials of using different scanning speed distribu-tions, we choose the scanning speed profile VðzÞ ¼0:03 × ðAðzÞ þ 0:1Þ−1 mm=s, as shown in Fig. 9(a),in which the expected speed profile (dashed line) isconsistent with the experimental profile (solid line).Figure 9(b) shows the transmission spectra of anIGAFBG with identical dual passbands, where thelength of the grating is 12 mm and the argon laseroutput power is 66 mW in fabrication. The experi-mental result (solid line) and the simulatedresult (dashed line) are in a good agreement witheach other. In simulation, neff ¼ 1:447, L ¼ 12 mm,

Fig. 7. (Color online) Calculated transmission spectrum of anIGAFBG with three passbands. In simulation, neff ¼ 1:45,L ¼ 1:5 cm, λD ¼ 1550 nm, and δneff ¼ 3 × 10−4.

Fig. 8. (Color online) Calculated transmission spectrum of anIGAFBG having multipassbands with varied FSR values. Theþ1 order dip has FSR1, and the þ2 order dip has FSR2, and soon. In simulation, neff ¼ 1:45, L ¼ 2 cm, λD ¼ 1550 nm, andδneff ¼ 4 × 10−4.

Fig. 9. (Color online) (a) Scanning speed distribution of the trans-lation stage used in the fabrication of an IGAFBG. Solid line, ex-perimental speed distribution; dashed line, expected speeddistribution to best fit Eq. (3). (b) Transmission spectra of thisIGAFBG. Solid line, measured spectrum (the argon laser outputpower used is 66 mW and the grating length is 12 mm); dashedline, calculated spectrum. In simulation, neff ¼ 1:447,L ¼ 12 mm, Λ ¼ 532:85 nm, and δneff ¼ 2:7 × 10−4.


δneff ¼ 2:7 × 10−4, and the grating period Λ ¼532:85 nm. It can be seen that two identical trans-mission bands with very narrow 3 dB bandwidthsare realized. Due to the 0:01 nm resolution limit ofthe optical spectrum analyzer (OSA, Ando AQ6317B), the true 3 dB bandwidths of the twoidentical passbands cannot be measured and are es-timated to be 3:8 pm based on the simulation result,and the wavelength spacing is approximately0:144 nm.

A multiwavelength passband filter with variedFSRs based on an IGAFBG is also obtained in experi-ment. We used a laser output power of 80 mW and ascanning speed profile of VðzÞ to fabricate a 17 mmlong IGAFBG. The experimentally measured trans-mission spectrum is shown in Fig. 10(a) and thematched simulation result is shown in Fig. 10(b).In Fig. 10(a), the sharp transmission peaks are notfully resolved due to the limited resolution of theOSA, and the ripples occurring in the dips are dueto the high transmittivity of the passbands so thatunavoidable electrical noise occurs in the low powerdips. In simulation, neff ¼ 1:447, L ¼ 17 mm,δneff ¼ 4:5 × 10−4, and Λ ¼ 532:85 nm. The experi-

mental and theoretical FSR values are reported inTable 2, and they agree with each other. It can beseen from Table 2 that the fabricated IGAFBG hasvaried FSR values of 0.129, 0.098, 0.068, and0:051 nm, corresponding to ∼16:125, ∼12:25, ∼8:5,and ∼6:375 GHz in frequency, respectively.

5. Discussion

A uniform FBG having two separate π phase shifts[9,10] hardly achieves two identical passbands ex-perimentally because each phase shift is generatedindependently. An EPS FBG [14,15] and a π phase-shifted sampled FBG [19] can form identical dual-passband filters; however, the design of the samplingperiod is complex and the long grating length, due tothe inserted nongrating gap, causes the inconveni-ence in packaging. FBG pair [16–18] similarly hasa nongrating section between the two subgratings.The proposed IGAFBG with identical passbandscan overcome the above-mentioned limitations.

The distinction between an IGAFBG and an FBGpair (two identical FBGs separated by a spacing) isthat the IGAFBG is a continuous grating without aphysical gap [8]. The structures of an IGAFBG andan FBG pair have already been compared and ana-lyzed in [8]. Here, we focus on the transmission spec-tral shape of an IGAFBG to further explain itsunique advantages as compared with an FBG pair.

Figure 11 shows the calculated transmission spec-trum of a regular FBG pair. In simulation, the lengthof each subgrating is 5 mm, the separation betweenthe two FBGs is 7 mm (total length of the FBG pair is17 mm), neff is 1.447, Λ ¼ 532:85 nm, and δneff is4:5 × 10−4. This FBG pair has the same length and

Fig. 10. (Color online) Transmission spectra of an IGAFBG withvaried FSRs as a multiwavelength passband filter: (a) measuredspectrum (the argon laser output power used is 80 mW and thegrating length is 17 mm); (b) simulated spectrum. The þ1order dip has FSR1, and the þ2 order dip has FSR2, and so on. Insimulation, neff ¼ 1:447, L ¼ 17 mm, Λ ¼ 532:85 nm, andδneff ¼ 4:5 × 10−4.

Table 2. FSRs of an IGAFBG as a Multiwavelength Filtera

FSR1 FSR2 FSR3 FSR4

Measured (nm) 0.129 0.098 0.068 0.051Simulated (nm) 0.122 0.094 0.07 0.057aSee Figs. 10(a) and 10(b).

Fig. 11. (Color online) Simulated transmission spectrum of a reg-ular FBG pair. In simulation, neff ¼ 1:447, Λ ¼ 532:85 nm,δneff ¼ 4:5 × 10−4, the length of each subgrating is 5 mm, andthe separation between these two subgratings is 12 mm. The num-bers 1, 2, 3, 4, and 5 in the figure do not mean the dip order, andthey refer to FSR1, FSR2, FSR3, FSR4, and FSR5 only.


index modulation depth as the IGAFBG shown inFig. 10(b). The calculated FSR values of the FBG pairare reported in Table 3. It can be seen from Table 3that, the central FSR (FSR3) is larger than theothers. The reason has already been explained in[22,23]. The identical and separated FBGs act astwo reflectors, similar to the two massive mirrors ina bulk Fabry–Perot etalon. The FSR of an FBG pairvaries with wavelength λ as FSRðλÞ ¼ c=½2neff ðλÞLeff ðλÞ� [22], where c is the light velocity in vacuumand Leff is the effective cavity length. The effectiverefractive index neff can be treated as a constantwithin a small wavelength range. Off resonance,one can imagine that the grating reflectivity andthe Bragg scattering are weaker than those in theresonance condition, so that the light penetratesfarther into gratings [22]. Hence, Leff increases as re-sonance wavelength increases to the red edges anddecreases to blue edges in the spectrum. Therefore,FSR on resonance is larger than the others. The lar-gest FSR variation is equal to ðFSR3-FSR1Þ=FSR1 ¼16:9% in Table 3.

The principle behind IGAFBG is to enhance thesidelobes [8]. The enhanced þ1 order sidelobe mayhave the shortest effective cavity length, leading tothe largest FSR, followed by the þ2, þ3, þ4, andother higher order sidelobes (see Figs. 7, 8, and 10).Hence, we have FSR1 > FSR2 > FSR3 > FSR4 inFig. 10(b). The largest FSR variation in simulationis equal to ðFSR1-FSR4Þ=FSR4 ¼ 114:0% in Table2, which is nearly seven times more than the valueobtained in a comparable FBG pair (16.9%) with thesame grating length and index modulation depth.Zhou et al. [18] reported a work to generate step-tunable microwave signal using an FBG pair witha narrow tuning range of 0:58 GHz, correspondingto a wavelength range of ∼4:66 pm. We believe thestep-tuning range can be enlarged using an IGAFBGinstead of an FBG pair filter.

6. Conclusions

The property of an IGAFBG has been studied. Wehave demonstrated the effectiveness of using theIGAFBG as an identical dual-passband filter and amultipassband filter with varied FSRs. The experi-mental and simulated transmission spectra of theIGAFBG are in good agreement with each other.The wavelength spacing of an IGAFBG-based dual-passband filter can be continuously tuned by apply-ing a tunable chirp in principle. A multipassbandvarying-FSR IGAFBG filter has larger FSR variationthan a comparable FBG pair.

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Table 3. FSRs of a Regular FBG Paira

FSR1 FSR2 FSR3 FSR4 FSR5

Simulated (nm) 0.0865 0.0989 0.1011 0.1003 0.0938aSee Fig. 11.


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Analysis of inverse-Gaussian apodized fiber Bragg grating

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