Theoretical and experimental investigations of macro-bend Losses for standard single mode fibers

Transcription

1 Theoretcal and epermental nvestgatons of macro-bend Losses for standard sngle mode fbers Qan Wang Gerald Farrell and Thomas Frer ppled Optoelectroncs Center ubln Insttute of Technology Kevn Street ubln 8 Ireland Qan.wang@dt.e bstract: Modelng of macro-bend losses for sngle mode fbers wth multple claddng or coatng layers s presented. Macro-bend losses for standard sngle mode fbers SMF8 are nvestgated theoretcally and epermentally showng that the nner prmary coatng layer of SMF8 has a sgnfcant mpact on the bend losses and most of the radaton feld s absorbed n the nner prmary coatng layer of SMF8. The agreement between theoretcal calculatons and epermental measurements suggests that the so-called elastooptcal correcton n modelng s not reured for SMF8. 5 Optcal Socety of merca OCIS codes: 6.3 Fber optcs; 6.43 Fbers sngle-mode References. R. C. Gauther and C. Ross Theoretcal and epermental consderatons for a sngle-mode fber-optc bend-type sensor ppl. Opt Marcuse Curvature loss formula for optcal fbers J. Opt. Soc. m Marcuse end loss of slab and fber modes computed wth dffracton theory IEEE J. Quantum Electron C. Vassallo Perturbaton of an LP mode of an optcal fber by a uas-degenerate feld: a smple formula Opt. & Quantum Electron I. Valente and C. Vassallo ew formalsm for bendng losses n coated sngle-mode optcal fbers Electron. Lett Renner endng losses of coated sngle-mode fbers: a smple approach J. Lghtwave Technol L. Faustn and G. Martn end loss n sngle-mode fbers J. Lghtwave Technol J. arrs and P.F. Castle end loss measurement on hgh numercal aperture sngle-mode fbers as functon of wavelength and bend radus J. Lghtwave Technol R. Morgan J.S.arton P.G. arper and J..C. Jones wavelength dependence of bendng loss n mononmode optcal fbers:effect of the fber buffer coatng Opt. Lett Shama.. l-n and S. J. alme Constant-curvature loss n monomode fbers: an epermental nvestgaton ppl. Opt K. agano S. Kawakam and S. shda Change of the refractve nde n an optcal fber due to eternal forces ppl. Opt Introducton It s well known that a radaton loss occurs when a sngle mode fber s bent. ccurate modelng of ths bend loss s essental for the desgn of fbers employed n optcal communcatons or optcal devces based on a bent fber such as some forms of optcal sensor []. The smplest model treats a bent fber as a core-nfnte claddng structure [3]. In fact a practcal fber wth coatng layers offerng mechancal protecton shows ute dfferent bend loss characterstcs to those predcted by the smplest model. Estng theoretcal calculatons of fber bend losses treat a fber as a core-claddng-nfnte coatng structure when consderng the mpact of coatng layer [4-7]. s we know most fbers have double coatng layers or some fbers themselves have more than one claddng layer such as depressedcladdng fbers but no estng formulas have been presented for modelng bend losses of #7 - $5. US Receved 8 prl 5; revsed 9 May 5; accepted 3 May 5 C 5 OS 3 June 5 / Vol. 3 o. / OPTICS EPRESS 4476

2 these fbers ecept the predcton of mamum or mnmum bend losses condtons n relaton to fber parameters and nput wavelength [89]. Therefore calculaton of bend losses for a sngle mode fber wth multple claddng layers or coatng layers based on perturbaton theory s frstly presented n Secton whch can be used for smulaton and desgn of fber devces wth multple claddng layers or multple coatng layers when macro-bend losses are nvolved. Prevous publshed nvestgatons of fber bend loss have been focused on some specal fbers partcularly fbers wth small numercal apertures rather than standard sngle mode fbers such as SMF8 whch are wdely used n optcal communcatons. In the present paper the bend loss characterstcs of SMF8 are nvestgated theoretcally and epermentally. The mpact of three nterfaces: between claddng layer and nner prmary coatng layer; between the nner prmary coatng layer and outer prmary coatng layer and 3 between the outer prmary coatng layer and ar on bend losses are analyzed. etaled comparsons between the epermental measured results and theoretcal calculated bend losses based on dfferent models are carred out n Secton 4 whch ndcate that most of the radated feld s absorbed n the nner coatng layer and a theoretcal model wth only the nner coatng layer can predct bend losses wth a good agreement wth epermental results. n elastooptcal correcton or so-called effectve bendng radus was reured n prevous publshed nvestgatons n order to make the calculated bend losses agree wth epermental results due to the refractve nde change caused by the bendng stress. owever the agreement between theoretcal and measured results n the present paper suggests that ths elastooptcal correcton s not reured for SMF8.. Theoretcal calculatons of fber bend loss Total loss of a bent fber ncludes the pure bend loss n the bent secton and the transton loss caused by the msmatch of propagaton mode between the bent and the straght sectons. For a sngle mode bent fber of length L the pure bend loss can be calculated by [8] L s ep αl αL = log = where α s the so-called bend loss coeffcent whch s determned by the fber structure bendng radus and wavelength of the lght. Most theoretcal nvestgatons on fber bend losses are focused on calculatons of ths bend loss coeffcent. The smplest model treats the fber as a core-nfnte claddng structure and a smple formula was developed to calculate the bend loss coeffcent α []. practcal fber contans one or two coatng layers outsde to offer mechancal protecton. The estence of the coatng layers wll produce a so-called whsperng-gallery mode for a bent fber due to the reflecton of the radated feld at the nterface between the claddng layer and the coatng layer. In order to consder the effect of ths reflecton on the bend loss more complcated formulas for the bend loss coeffcent α have been developed. Calculaton of bend loss consderng the coatng layer was presented n Ref. [4] usng perturbaton theory and subseuently two straghtforward formulas were presented n Ref. [6] and [7] respectvely. owever all these calculatons are based on a fber contanng only one coatng layer. Many fbers have more than one coatng layer or the fber tself may have a multple claddng layer structure for whch the bend loss cannot be calculated wth these formulas. Therefore calculaton of bend losses for a fber wth multple claddng or coatng layers usng perturbaton theory s presented below through generalzng the approach employed n Ref. [4] and [7] and t can be used for modelng and desgn of fber devces wth mult-claddng layers nvolvng or utlzng bend loss. In common wth prevous models the outermost layer s consdered nfnte n present calculaton. Fgure gves the schematc cross-secton vew of a bent fber wth multple claddng or coatng layers. The bendng radus s denoted by R. For the -th claddng layer the refractve #7 - $5. US Receved 8 prl 5; revsed 9 May 5; accepted 3 May 5 C 5 OS 3 June 5 / Vol. 3 o. / OPTICS EPRESS 4477

3 n n n Core: n R n - - y Fg.. Cross-secton of a bent fber wth multple claddng layers. nde s n and the thckness s. ased on the appromatons made n Refs. [4-7] the feld n the claddng layers of the bent fber s [ ] = π ψ d y y ep where the notaton n Refs. [6] and [7] s used and = R n k n k R 3 β. and are ry functons respectvely. For the outermost nfnte layer there s a relatonshp between and namely j =. For any two adjacent layers accordng to feld-contnuous boundary condtons we have [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] = =. 3 Therefore = M M M M consderng all the claddng layers or n a short form G = conseuently. ased on the boundary condton between the frst claddng layer and the core layer [7] we have [ ] [ ] { } [ ] / / ep γ γ π = a G and wth the perturbaton theory the bend loss coeffcent can be calculated by [ ] = γ πβ κ α d a K V Im 4 The advantage of ths model s that t can not only be used to calculate bend losses of fbers contanng only one coatng layer as presented n Ref. [5-7] but also t s sutable for fbers wth multple claddng layers depressed-claddng fbers or coatng layers. The fber used n C 5 OS 3 June 5 / Vol. 3 o. / OPTICS EPRESS 4478 #7 - $5. US Receved 8 prl 5; revsed 9 May 5; accepted 3 May 5

4 Ref. [9] has two coatng layers and the presented epermental results and theoretcal nvestgatons predctng the mamum or mnmum bend losses condtons n relaton to fber parameters and nput wavelength n Ref. [9] show that for that fber the radated feld penetrates through both the nner and the outer prmary coatng layers. Wth the above formulas theoretcal modelng ncludng the outer prmary coatng shows a better agreement between the epermental and theoretcal results by comparson wth the case where only the nner layer s consdered. 3. Epermental nvestgatons about bend losses for SMF8 Fgure gves the epermental setup used for our measurement of fber bend losses. The optcal spectrum analyzer s used nstead of an optcal power meter because t can measure the bend loss at the peak output wavelength of the tunable laser rather then over a range of wavelengths. The fber used n the eperment s SMF8 whch s a very common fber and wdely used n optcal communcaton systems. It has core claddng nner and outer prmary coatng layers. Correspondng parameters are presented n Table. Tunable laser Varable ameter Mandrel Optcal Spectrum nalyzer Fg.. Epermental setup for measurng fber bend loss Table. Parameters of SMF8 at wavelength 55nm n.454 a 8.3μm n.4447 b 5±.7μm n c 9μm n4.594 d 5±5μm Usng a bendng fber of length ~ m we measured the bend loss n the bend radus range of 8.5 mm to mm nclusve n ncrements of.5 mm and n the wavelength range from 5 nm to 6 nm. For bend radus smaller than 8.5 mm the bend fber s easly broken whle for a bendng radus larger than mm the bend loss s too low for relable and repeatable measurement. Fgure 3 presents typcal measured bend losses for SMF8 wth or wthout an absorbng layer appled to the outsde of the fber. The curves for bend losses for a fber wthout an absorbng layer outsde have random varatons that are small relatve to the absolute bend loss at a gven wavelength. The mamal varaton n Fg. 3 s 3d when the bend loss s 8d. Further the measured results are not eactly repeatable and dffer each tme Fg. 3 gves bend losses for ten measurements. fter we coated the fber wth an absorbng layer #7 - $5. US Receved 8 prl 5; revsed 9 May 5; accepted 3 May 5 C 5 OS 3 June 5 / Vol. 3 o. / OPTICS EPRESS 4479

5 these random varatons dsappear and the measured bend losses also become nvarant. Ths ndcates that these random varatons are caused by the reflecton that occurs at the nterface between the outer prmary coatng layer and ar. It also shows that most of the radated feld s absorbed n the coatng layers. Only a small amount of radated feld reaches the fber surface and s reflected back resultng n nterference wth the propagaton mode. Otherwse accordng to the measured results and analyss method presented n Ref. [9] the curve for bend losses as a functon of wavelength should have a perodcal oscllatory nature comparable n ampltude to the bend losses themselves due to the reflecton of the nterface between the outer prmary coatng layer and ar rather than these small random varatons n our eperments. 4 Wthout absorbng layer outsde Wth absorbng layer outsde 6 end loss d wavelength nm Fg. 3. Measured bend losses for bendng radus R=.5 mm and bent length of.66 m. 4. Comparsons between theoretcal and epermental results etaled comparsons between theoretcal and epermental results have been carred out n ths secton to nvestgate the accuracy of dfferent models; the mpact of the coatng layers on bend losses and the so-called elastooptcal correctons for modelng n the prevously publshed nvestgatons. Intally for the purpose of comparson wth prevous works we treat the nner prmary coatng layer to be nfnte whch s also euvalent to the case that the nner prmary coatng layer absorbs most of radated feld. Typcal measured bend losses for dfferent bendng rad under two dfferent wavelengths.e. 5 nm and 6 nm are gven n Fg. 4a and 4b wth suares and crcles respectvely. Theoretcal calculaton results based on the smplest model core-nfnte claddng layer structure the formulas proposed n Ref. [6] and [7] and the formula presented n the above secton all treat the fber as a core-claddng-nfnte coatng layer structure n ths calculaton are presented n Fg. 4a and Fg. 4b. From Fg. 4a and 4b frstly one can see the coherent couplng between the fundamental propagaton feld and the reflected radated feld by the coatng layer.e. socalled whsperng-gallery mode has an apparent effect on bend loss characterstcs so that the calculated results wth the smplest model.e. treatng the fber as the core and nfnte claddng structure are obvously dfferent from the measured bend losses. Smulaton results wth the formula proposed n Ref. [6] predcts the mpact of the whsperng-gallery as compared to the smplest model but t stll cannot agree wth the measured results well due to the appromatons made n dervng ths formula. Calculated results wth the formula developed n Ref. [7] and formulas presented n Secton have a good agreement wth the #7 - $5. US Receved 8 prl 5; revsed 9 May 5; accepted 3 May 5 C 5 OS 3 June 5 / Vol. 3 o. / OPTICS EPRESS 448

6 epermental results and therefore calculated results based on the presented formulas n Secton are used n the followng comparsons. end loss d/m 6 4 Usng the formulas n Secton Usng the formula n Ref.[7] Usng the formula n Ref.[6] Usng the smplest model endng radus mm a end loss d/m 6 8 Usng the formulas n Secton Usng the formula n Ref.[7] Usng the formula n Ref.[6] Usng the smplest model endng radus mm b Fg. 4. Measured and calculated bend loss for dfferent bendng rad at wavelength a 5 nm and b 6 nm. The agreements between epermental measured bend losses and calculated results n Fg. 4 also suggest that the nner prmary coatng layer absorbs most of the radated feld and the outer prmary coatng layer has lttle mpact on the bend loss characterstcs. In order to verfy t we carry out the calculaton of bend losses consderng the outer prmary coatng layer wth the formula presented n Secton whch has the advantage that t can calculate bend losses for more than one coatng layer. The calculaton treats that the nner prmary coatng layer as deally transparent and the outer prmary coatng layer to be nfnte. Fgures 5a and 5b present the correspondng bend losses n wavelength range from 5 nm to 6 nm for #7 - $5. US Receved 8 prl 5; revsed 9 May 5; accepted 3 May 5 C 5 OS 3 June 5 / Vol. 3 o. / OPTICS EPRESS 448

7 bendng rad R=9 mm and R= mm respectvely. The measured bend losses and the calculated results consderng only the nner coatng layer are also presented n Fg. 5 for comparson. From Fg. 5a and 5b one can see that the calculated bend losses consderng only the nner coatng layer are much closer to the epermentally measured results. The estence for a two coatng layer structure of a wave-lke varaton n the bend loss of the fber wth wavelength s manly caused by the reflectons at the nterface between the nner and outer coatng layers. The fact that the measured results do not dsplay ths wave-lke varaton support a concluson that the nner coatng layer absorbs most of the radated feld from the claddng. 5 end loss d/m 5 Wth two-coatng-layer structure Wth one-coatng-layer structure wavelength nm a end loss d/m 5 Wth two-coatng-layer structure Wth one-coatng-layer structure wavelength nm b Fg. 5. Calculated wth one-coatng layer and wth two-coatng layers respectvely and measured bend losses n wavelength range from 5 nm to 6 nm for a for R= mm and b R=9 mm. #7 - $5. US Receved 8 prl 5; revsed 9 May 5; accepted 3 May 5 C 5 OS 3 June 5 / Vol. 3 o. / OPTICS EPRESS 448

8 In the prevous publshed nvestgatons the elastooptcal correcton or a so-called effectve bendng radus was reured n order to make the calculated bend losses agree wth epermental results [5-7] due to the refractve nde change caused by the bendng stress. Generally the relatonshp between effectve bend radus R eff n modelng and actual bend radus R n eperments s R eff = ~. 7R and ths correcton s appled n modelng bend losses under whatever bendng rad and wavelengths. We calculated the eamples presented n prevously publshed nvestgatons wth the formula developed n Ref. [7] and formulas presented n Secton respectvely. It shows that numercal results usng effectve bendng radus agree better wth the measured bend losses than those obtaned usng actual bendng radus drectly. owever n the above calculatons the agreement between theoretcal and measured results for SMF8 suggests that ths elastooptcal correcton s not reured.e. R eff = R. Theoretcal bend losses for SMF8 wth the so-called effectve bendng radus R eff = ~. 7R are presented n Fg. 6a and Fg. 6b wth sold lnes for wavelength range from 5 nm to 6 nm and bendng rad 9 mm and mm respectvely. Correspondng measured results and calculated results based on the same bendng rad as those n eperments are also shown n Fg. 6a and 6b. From ths comparson one can see that t wll lead to ncorrect results f the effectve bendng radus s used n modelng bend loss for SMF8 as compared to the measured results. Ths suggests that n the present eperment the bendng stress has lttle effect on the refractve nde so that the so-called effectve bendng radus for SMF8 almost euals to the actual bendng radus. Ths could be caused by two reasons. One reason could be the fber materal tself and the other could be the fber parameter V. Compared to the fbers used n the prevously publshed nvestgatons about macrobend losses a sgnfcant dfference s that n the present paper the fber parameter V of SMF8 s bgger than those of the fbers used n prevous papers. For eample fber parameter V of the fber L employed n Ref. [7] s.68 The consdered bendng radus s from 3.5 mm to 4 mm.. owever for the SMF8 used n the present paper the correspondng fber parameter V s about.3 The consdered bendng radus s from 8.5 mm to mm. Further epermental and theoretcal nvestgatons about elastooptcal correcton for fber bend loss are ongong. #7 - $5. US Receved 8 prl 5; revsed 9 May 5; accepted 3 May 5 C 5 OS 3 June 5 / Vol. 3 o. / OPTICS EPRESS 4483

9 Wth effectve bendng rad end loss d/m 5 Wth actual bendng radus 5.5R.7R.35R Wavelength nm a end loss d/m 5 Wth effectve bendng rad Wth actual bendng radus 5.5R.7R.35R wavelength nm b Fg. 6. Calculated wth and wthout elastooptcal correcton and measured bend losses n wavelength range from 5 nm to 6 nm for a for R= mm and b R=9 mm. 5. Concluson Modelng of bend losses for a sngle mode fber wth multple claddng layers has been presented. end loss characterstcs of the SMF8 have been nvestgated theoretcally and epermentally. oth epermental and theoretcal results have shown that reflecton at the nterface between the claddng layer and the coatng layer has apparent effect on the bend loss characterstcs. Comparsons between the epermental and theoretcal results have ndcated that: most of the radated feld s absorbed n the nner coatng layer and a theoretcal model wth only one coatng layer structure agrees well wth the epermental results. The agreement between theoretcal results and measured results suggests that so-called elastooptcal correcton used n prevous publshed nvestgatons s not reured for SMF8. #7 - $5. US Receved 8 prl 5; revsed 9 May 5; accepted 3 May 5 C 5 OS 3 June 5 / Vol. 3 o. / OPTICS EPRESS 4484