Numerical Analysis of GeO2-Concentration Effectsin Arc-Induced Long-Period Fiber Gratingsunder External Refractive-Index ChangesValentin GUZMAN-RAMOS, Daniel E. CEBALLOS-HERRERA

�, and Romeo SELVAS-AGUILAR

Universidad Autonoma de Nuevo Leon, Facultad de Ciencias Fısico Matematicas, Av. Universidad S/N, Cd. Universitaria,San Nicolas de los Garza, Nuevo Leon, Mexico

(Received November 14, 2013; revised January 19, 2014; Accepted February 4, 2014)

We present a numerical analysis of the response of arc-induced long-period fiber gratings (LPFGs) under ambientrefractive-index changes using standard fibers with SiO2 as cladding material and different GeO2 concentration in theSiO2–GeO2 doped core. We obtain that the LPFG-sensitivity is increased using lower GeO2 concentrations and itfollows a parabolic behavior. Also, we identify two linear regimes using an external index of 1.37: for GeO2

concentrations between 2 and 3.5mol%, the LPFG-sensitivity changes with a rate of 3.614 nm per mole fraction ofGeO2, while for higher concentrations the sensitivity changes with a rate of 1.39 nm/mol%. Additionally, for fiberswith 2mol% of GeO2, the sensitivity calculated is comparable to this obtained in previous works using corrugated andtapered LPFGs in SMF28 fibers. These results are of interest for the design of improved LPFG-sensors.# 2014 The Japan Society of Applied Physics

Keywords: long-period fiber gratings, GeO2 concentration, refractive index measurement

1. Introduction

Long-period fiber gratings (LPFGs) consist of a periodicperturbation of the refraction index of the fiber core thatcouples energy between two co-propagating modes, typicallythe fundamental core mode and a higher order cladding modeat discrete resonance wavelengths. The coupling betweenthese co-propagating modes must satisfy the following phasematching condition: � res ¼ ðnco � nclÞ�, where � res is theresonance wavelength, nco and ncl are the effective indexof the core and cladding modes, and � is the grating period.For their fabrication, different techniques like UV radiationand arc-induced radiation have been developed.1,2) LPFGsformed by arc-induced radiation have generated greatinterest due to its versatility and low cost in the process offabrication. They have high temperature stability, allow awide tuning, and can be implemented in almost any type offiber. Controlling the fabrication parameters like the arc-discharge power, one can obtain a mode coupling betweenthe fundamental core mode and symmetrical or asymmetricalcladding modes respectively.3–5)

On the other hand, LPFGs have been extensively used insensing applications due to the fact that the resonancewavelength can be shifted under external perturbations.These perturbations modify the refractive index of the core-and cladding-material by strain, stress or thermal expansion,and change the modal behavior of the core and claddingmodes nco and ncl, and the grating period �. Theseperturbations can be produced in the LPFG by temperature,torsion, bending, and external refractive-index changes.6–9)

As a consequence, several designs have been performed toimprove the performance of LPFGs in sensing area,especially to detect external refractive-index changes for

biochemical applications.10–14) In recent works, differenttaper profiles, corrugations on the fiber cladding, and fiberscoated with nano-particles and thin films have beensuggested.15–18) Using these methods, the LPFG sensitivityto external refractive-index changes is improved approxi-mately 10 nm. However, it is worth to mention that theseworks have been performed using different types of single-mode fibers, among them: SMF-28 fibers from Corning,photosensitive B–Ge co-doped fibers from Fibercore Ltd.,or Dispersion Shifted Fibers. Also, these works haveanalyzed the sensitivity of different resonant peaks in eachproposed LPFG-sensor, and they have used differentfabrication techniques like UV-radiation combined withhydrogenation and Arc-induced radiation to induce theLPFG-sensor.

Then, it is necessary to perform a comparative study abouthow the fabrication technique and the type of fiber canimpact the performance of a LPFG. In this case, some workshave started with this analysis comparing two LPFGsinduced in a same B–Ge co-doped fiber and using twodifferent fabrication techniques: UV-radiation and Arc-induced radiation, in order to analyze the external refrac-tive-index and temperature sensing properties of thegrating;19) additional works have induced LPFGs using asame fabrication technique like UV-radiation or Arc-electricradiation in different fibers in order to analyze their responseunder temperature, strain, and external refractive-indexchanges.20,21) Also, effects of Boron-concentration in LPFGsinduced by UV-radiation in B–Ge co-doped fibers have beenanalyzed for bending and temperature sensing, but not forrefractive-index sensing.22) These comparative studies haveshown that the type of fiber used in the experiment is theprincipal factor that determines the improved performanceof a LPFG as a temperature, bending or refractive-indexsensor.�E-mail address: de.ceballos.herrera@gmail.com

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In particular, for external refractive-index sensing, it isbetter to induce a LPFG on a fiber with lower refractive-index in the core,6–8) in this way higher-order claddingmodes, which are more sensitive to external environmentdue to their largest evanescent field portion outside fiber,can be excited easier using adequate grating periods. In thissense, B–Ge co-doped fibers could be a first option becausethe refractive-index of the core is reduced for higherconcentrations of boron. However, we have to take inaccount that LPFGs induced on B–Ge co-doped fibers showhigher temperature sensitivity than these induced in SMF-28fibers, and in some circumstances it may be a disadvantagefor chemical sensing applications. Then, LPFGs inducedwith arc-electric technique in SMF-28 fibers seem to be abetter platform for refractive-index sensing.18,19) However,for this type of single-mode fibers we have to consideragain the effect of GeO2 concentrations in the GeO2–SiO2

doped core, where for lower GeO2 concentrations therefractive-index of the core is reduced.23,24) Then, we areinterested in to quantify the GeO2-concentration effects inthe LPFG-sensitivity and to describe how this can impact inthe design of improved LPFG-sensors.

In this context, in this paper we quantify the sensitivity ofan arc-induced LPFG to external refractive-index changesfor step-index fibers with different mole fraction of GeO2,and we describe through a polynomial expression how thissensitivity is modified as the GeO2 dopant concentration isreduced. We perform this analysis numerically using thecoupling between the fundamental core mode and the LP14higher-order cladding mode which is a typical claddingmode excited in arc-induced LPFGs. We verify the modelingexperimentally fabricating a single LPFG and two-in-seriesLPFGs induced by electric arc in a SMF-28 fiber with3mol% of GeO2 in the core. According to our results, wecan identify a parabolic behavior of the LPFG-sensitivity fordifferent GeO2 concentrations. Additionally, for fibers with2mol% of GeO2, the wavelength shift of the resonantpeak are comparable to these obtained in previous worksusing corrugated and tapered LPFGs induced in SMF-28fibers.15,18)

2. Experiment and Modeling

First, we perform an arc-induced LPFG in a SMF-28 fiberwith a period of � ¼ 609 �m and a length of L ¼ 2 cm.The Ge-content in the GeO2–SiO2 doped core is equal to3mol%, and it has a core radius r1 ¼ 4:1 �m, and a puresilica cladding with radius r2 ¼ 62:5 �m.24) The experimen-tal configuration used to produce the grating is shown inFig. 1. A white light source (WLS), a Fiber Splicer MachineSumimoto with 10mA of discharge current and 0.5 s ofexposure time, and an optical spectral analyzer (OSA) wereused for the LPFG-fabrication and spectral measurements. Inorder to control the fiber position respect to the arc source,one end of the fiber was clamped externally to a translationstage (TS) with a precision of 1 �m, and the other endwas attached to a fixed mass (1 g) to keep the tensionapproximately constant. The translation stage moves thefiber to the desired point and then, the electric arc is applied,

after this, the mechanical stage moves the fiber to the nextgrating period, and the process is repeated until the LPFG isformed. As a result, we obtain four resonant peaks located at1363, 1391, 1460, and 1610 nm as it can be observed inFig. 2. According to the modeling based in a fast-Fouriertransform (FFT) mode solver,25) these peaks correspond tothe mode coupling between the fundamental core mode, andthe first asymmetrical higher-order cladding modes LP11,LP12, LP13, and LP14 respectively. It implies that theperiodic perturbation induced in the fiber core is highlyasymmetric. In Fig. 3 we can observe the effective-indexcurve of the fundamental core mode and the four asymmetriccladding modes above mentioned, as well as, we show theresonance-wavelength curve obtained using the formula� res ¼ ðnco � nclÞ� for different grating periods. We notethat for � ¼ 609 �m, the resonance wavelengths for thesecladding modes adjust with the experiment. Also, it is worthto mention that although we use a splicer machine withAC discharges, which in theory produces a symmetricaltemperature distribution between electrodes, we obtain acoupling with asymmetrical cladding modes. With respectto the origin of coupling of asymmetrical cladding modesin our experiment we can deduce that our splicer machineproduces in some way an asymmetrical temperaturedistribution, and we can attribute this to several factors likedifferent degradation of electrodes in the splicer machine,and misalignment between electrodes, or a misalignment of

Fig. 1. Schematic of the experimental set up to fabricate arc-induced LPFGs.

Fig. 2. (Color online) Spectral response of the arc-induced LPFGwith � ¼ 609 �m. Insets indicate the simulated electric-field of thehigher-order cladding modes involved in the resonant peaks.

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the fiber with respect to the electrodes. In Ref. 4, a splicermachine with DC discharge that produces an asymmetricaltemperature distribution between electrodes is used, and theyobtain resonance peaks which correspond to couplings withasymmetrical cladding modes LP01, LP02, LP03, and LP04.These resonant peaks shown in Fig. 11 of Ref. 4 agreeperfectly with the resonant peaks shown in Fig. 2 of thismanuscript, confirming in this way our results.

For purposes of external refractive-index sensing, the LP14mode is more attractive because their external field is longerthan the others cladding modes. In this sense, we focus in theresonant peak at 1610 nm which corresponds to the LP14cladding mode. In order, to characterize this resonant peak,we fabricate two LPFGs in series with a separation of 8 cm toform a Mach–Zehnder interferometer (MZI). The result isshown in Fig. 4(a), where we can observe that the averageseparation of the spectral fringes is 8.2 nm. To verify oursimulations, we perform numerically both gratings with thesame conditions and we reproduce the spectral behavior ofthe MZI as it can be observed in Fig. 4(b).

In order to characterize the response of the LPFG toexternal refractive-index changes, we analyzed the spectralbehavior of the LPFG and the MZI submerged in aqueoussolutions composed by 10ml of distilled water with differentsugar concentrations between 0 and 8 g. Figure 5 shows thespectral response of the LPFG and MZI for some sugarsolutions, where we can observe that the LPFG-resonantpeak and the MZI-spectral fringes are shifted to shorterwavelengths with different rates. To visualize in a better waythe sensitivity of both LPFG and MZI for different sugarsolutions, we plot in Fig. 6 the wavelength shift for theresonant peak and the spectral fringes observed in Fig. 5respectively. In this figure we observe that the MZIsensitivity is approximately 3 nm higher than this obtainedfor the LPFG. This increment in sensitivity is expecteddue to the fact that the interaction length of the LPFGwith the solved sugar is 2 cm, which correspond to thegrating length, while for the MZI this interaction length islonger.

(a)

(b)

Fig. 3. (Color online) Modeling of the arc-induced LPFG: (a)Calculated effective index of the fundamental core mode LP01 andthe LP11, LP12, LP13, and LP14 cladding modes; (b) Calculatedresonant wavelengths. For points 1, 2, 3, and 4 the resonantwavelength are: 1363, 1391, 1460, and 1610 nm respectively.

(a)

(b)

Fig. 4. Spectral behavior of a single LPFG and two LPFGs-in-series (MZI) with a grating separation of 8 cm; (a) experiment and(b) modeling.

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Once the resonant peak of to the LP14 cladding mode ischaracterized experimentally in a single and a MZI format,we proceed to model its sensitivity to external refractive-index changes for different GeO2 concentrations. In themodeling we have considered the sellmeier formula forrefractive index of the GeO2–SiO2 doped core for differentmole fraction of GeO2 given in Ref. 23. We considerdifferent concentrations between 2–5mol% of GeO2 inorder to try keeping the single-mode behavior of the step-index fiber in the 1–1.7 �m wavelength range. In Fig. 7 it isshown the effective index of the core and cladding modesnco and ncl for different mole fraction of GeO2. We observethat as the GeO2 concentration is increased, the effective-index of the core-mode increments with higher proportionthan the effective-index of the cladding mode, it producesconsequently an increment of the difference nco � ncl forhigher values of GeO2 concentration and it affects directlythe phase matching condition � res ¼ ðnco � nclÞ�; in thiscase, if we want to keep the resonant peak at 1610 nm for 2,3, 4, and 5mol% of GeO2, the corresponding gratings

periods have to be � ¼ 958, 609, 448, and 343 �m,respectively.

In Fig. 8 one can observe how the doped core affects theexternal field of the LP14 cladding mode. For an incrementof GeO2 concentration, the field penetrates more in theambient making the resonant peak more sensitive to externalrefractive-index changes. In our calculations, we solve forthe E-field in the entire domain of the optical fiber (core,cladding, and external media), and the solutions arenormalized for the entire domain as

R jEðx; yÞj2 dx dy ¼ 1.To quantify this sensitivity for both LFG and MZI, we modelthe wavelength shift of the resonant peak at 1610 nm and thespectral fringes under external refractive-index changes as itis shown in Fig. 9. In this figure, the negative wavelengthshifts indicate displacements of the resonant peak to shorterwavelengths. It is worth to mention that all these curveswere obtained using an external refractive-index lower thanthe cladding material (SiO2). The sensitivity behaviorobserved in Fig. 9 using different mole fraction of GeO2

(a)

(b)

Fig. 5. (Color online) Wavelength shift of: (a) the LPFG-resonant peak and (b) the MZI-fringes, for different sugar solutions.

Fig. 6. Sensitivities of the LPFG and the MZI for different sugarsolutions.

Fig. 7. (Color online) Effective index of the LP01-core mode andthe LP14-cladding mode for different GeO2 concentration.

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are similar for both LPFG and MZI; however the wavelengthshift values for the MZI are slightly higher than theseobtained for the LPFG. Also, in Fig. 9 we show theestimated refractive-index values of the sugar solutions usedin the experiment, which were obtained by comparing thewavelength shift of the resonant peak measured in theexperiment (Fig. 5), and the wavelength shift calculated inthe modeling respectively.

3. Discussion

According to the modeling shown in Fig. 7, we canobserve that the first principal effect to use fibers with highermole fraction of GeO2 is an increment of the effective indexof the core mode, being this increment higher than thisobserved in the LP14 cladding mode. Also, we can observethat the effective-index increment of the core mode is notlinear with respect to the GeO2 concentration. It impactsdirectly to the LPFG phase matching condition. Addition-ally, we observe in Fig. 8 that the external electric-field ofthe LP14 cladding mode is sensitive to the core refractive-index, but this sensitivity is also not linear, for example, inFig. 8 it is easy to note that the electric-field increases fasterfor lower GeO2 concentrations. As a consequence, theresults shown in Fig. 9 for both LPFG and MZI indicate anonlinear increment of the sensitivity to external refractive-index changes for lower GeO2 concentrations. It is worth toremember that numerical calculations shown in Fig. 9 wereobtained considering an initial resonant peak at 1610 nm,then we had to use different grating periods for each molefraction of GeO2.

To observe with more clarity the nonlinear behavior fordifferent mole fraction of GeO2 we plot in Fig. 10 thewavelength shift of the resonant peak at 1610 nm fordifferent GeO2 concentrations using a fixed externalrefractive-index of 1.37. We choose this value becauseaccording to Fig. 9, around this external refractive-index weobserve higher variations of the LPFG sensitivity. In this

Fig. 8. (Color online) External electric-field of the LP14 claddingmode for different GeO2 concentration.

(a)

(b)

Fig. 9. Calculated sensitivities of the LPFG and MZI for differentmole fraction of GeO2.

Fig. 10. (Color online) Behavior of the LPFG sensitivity for afixed external refractive-index (1.37) and different mole fraction ofGeO2.

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case, Fig. 10 only shows the sensitivity of a single LPFG.In this figure we can observe how the nonlinear behavioris more evident and follow a parabolic shape, also we notetwo quasi-linear regimens: for lower GeO2 concentrationsbetween 2 and 3.5%, the sensitivity changes with a rate of3.614 nm per mole fraction of GeO2, and for higher GeO2

concentrations, the LPFG sensitivity changes with a rate of1.39 nm per mole fraction of GeO2 respectively. Finally, it isimportant to mention that the wavelength resonant shiftobtained using 2mol% of GeO2 is comparable to theseobtained in previous works for similar external refractive-index changes.15–18) For example, in our case, the wave-length shift calculated is approximately 10 nm for anexternal refractive-index of 1.37, which corresponds to athird part of the values reported in Refs. 15 and 18 usingcorrugated and tapered LPFGs induced in a SMF28 fiberwith 3mol% of GeO2. It indicates that if we combine theseLPFGs designs with fibers that present a reduction of 1 molefraction of GeO2 in its doped core, we can improve thesensitivity with the same factor; that is approximately 30percent. In this context, it is very convenient to know thecapabilities of the LPFGs induced in SMF28 fibers usingdifferent GeO2 concentrations in the doped core. It allows usto interpolate how the sensitivity can be improved and alsoto establish a limit in which this sensitivity can beincremented or reduced. Then, to perform improved designsof arc-induced LPFG sensors in standard single-mode fibers,it is suggested to consider the parabolic modification of theLPFG-sensitivity to external refractive-index changes fordifferent GeO2 concentrations described in this work.

In addition, it is convenient to mention that numericalcalculations shown in Figs. 2 and 9 were obtained consider-ing a step-index profile of a SMF-28 fiber; however, studiesof phase microscopy confirm the presence of a dip on thecore and reveal that the refractive index profile of SMF-28fiber is not a staircase pattern.26,27) According to Ref. 27,the dip in the refractive index profile of a SMF-28 fiberdisappears after arc discharge application, and the indexprofile follow a quasi-staircase pattern. This effect isattributed to the diffusion of dopants in the fiber core duringthe arc discharge application. Taking in account thisinformation, we can consider in our modelling a step-indexprofile as an approximation of the quasi-staircase patternproduced after arc discharge.

Finally, we have to take in account that after an arcdischarge application on a SMF-28 fiber with 3mol% ofGeO2, the refractive index of the core and cladding ismodified and this refractive index change depends of thedischarge current and exposure time. In particular, for35mA with 75ms, and 100mA with 41ms of arc dischargeconditions, the refractive index of the core reduces2:8� 10�4 and 1:6� 10�4, while the refractive index ofthe cladding increases 2� 10�4 and 3� 10�4, respec-tively.27) Therefore, the refractive index difference betweenthe core and cladding is modified around 5� 10�4 for bothdischarge conditions. Then, for other mole fractions of GeO2

we can expect refractive index changes similar to thesevalues reported in Ref. 27.

4. Conclusions

We reported the numerical analysis of the response of arc-induced LPFGs to external refractive-index changes usingsingle-mode fibers with different GeO2 concentration in thedoped core. We compare these calculations with experi-mental measurements using a LPFG and a MZI induced in aSMF28 fiber with 3mol% of GeO2. Also, we evaluate thewavelength shift of the resonant peak that corresponds to themode coupling between the fundamental core mode and theLP14 cladding mode. We obtain that the wavelength shift ofthis resonant peak follow a parabolic behavior for differentmole fraction of GeO2. Also, for an external refractive-indexof 1.37 we note two quasi-linear regimens: for lower GeO2

concentrations between 2 and 3.5%, the sensitivity ismodified with a rate of 3.614 nm per mole fraction of GeO2,and for higher GeO2 concentrations, a change of 1.39 nm permole fraction of GeO2 is obtained. In addition, for this sameexternal refractive-index, the wavelength resonant shiftobtained with 2mol% of GeO2 corresponds to the thirdpart of the values obtained in previous works for similarexternal refractive-index changes. Then, a reduction of 1mole-fraction of GeO2 combined with corrugations andtapers in the LPFG sensor can improve the sensitivity withthe same factor, approximately 30%. These results arereproducible and contribute with important information forthe design of improved optical devices based in arc-inducedLPFGs for chemical sensing applications.

Acknowledgments

Authors thank to UANL and SEP for the financial support in theprojects PAYCIT CE757-11 and PROMEP 103.5/13/6644.

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