Polarimetric parameters associated to commercial optical fibers

Transcription

1 RESEARCH Revta Mexcana de Fíca NOVEMBER-DECEMBER 14 Polarmetrc parameter aocated to commercal optcal fber O. J. Velae-Ecobar a, K. M. Sala-Alcántara b, R. Epnoa-Luna b,, G. Atondo-Rubo a, and I. Torre-Gómez c a GIPYS, Pogrado en Fíca, Facultad de Cenca Fíco-Matemátca, Unverdad Autónoma de Snaloa, Cudad Unvertara /n, 81 Culacán, Snaloa, Méxco, e-mal: [email protected]; [email protected] b GIPYS, Centro de Invetgacone en Óptca, A. C., Loma del Boque 115, Colona Loma del Campetre, 3715 León, Guanajuato, Méxco, e-mal: [email protected]; [email protected] c Centro de Invetgacone en Óptca, A. C., Loma del Boque 115, Colona Loma del Campetre, 3715 León, Guanajuato, Méxco, e-mal: [email protected] Receved May 14; accepted 11 September 14 The mot mportant polarmetrc parameter are determned for x dfferent type of commercally avalable optcal fber, at 155 nm of tranmon wavelength. The dattenuaton, polarzance, retaance, polarzaton dependent lo PDL, among other conventonal polarmetrc parameter, are determned from the Mueller matrx aocated to 1m length of each fber tuded here. An mprovement to the data analy method, reported recently by our group, preented. Reult obtaned how the fber can be ued not only a tatc element, but alo a veratle optcal devce, dependng on the ncdent polarzaton tate employed. Keywo: Polarzaton n optcal fber; brefrngence n optcal fber; analy of polarzed lght. Se determnan lo parámetro polarmétrco má mportante para e dtnto tpo de fbra óptca acceble comercalmente, a una longtud de onda de tranmón de 155 nm. La datenuacón, polarzanca, retaanca, péda dependente de la polarzacón PDL, entre otro parámetro polarmétrco convenconale, e obtenen medante la matrce de Mueller aocada a 1 m de longtud de cada fbra etudada aquí. Una mejora al método de anál de dato, reportado recentemente por nuetro grupo, e preentada. Lo reultado obtendo muetran que la fbra no olo pueden utlzare como elemento óptco etátco, no como dpotvo verátle, dependendo del etado de polarzacón ncdente. Decrptore: Polarzacón en fbra óptca; brrefrngenca en fbra óptca; anál de luz polarzada. PACS: 4.81.G; 78..Fm 1. Introducton The ue of optcal fber n communcaton a the tranmon medum or n applcaton a enor n medcal, engneerng, and centfc feld a common theme nowaday [1-4]. It well known an optcal fber can be ued a a ngle- or a a mult-mode tranmon medum, dependng on the operaton wavelength employed, core-claddng dameter rato, and t numercal aperture [5]. The ngle- or mono-mode operaton n optcal fber SMF partcularly mportant due to the ue n long dtance tranmon range becaue there a need to tranmt gnal whch, by ther nature, cannot be tranmtted multaneouly wthout elaborate mean to ad gnal recovery. A oluton to th problem to tranmt the gnal at dfferent wavelength whch requre wavelength multplexng and demultplexng arrangement at the tranmttng and recevng end of the lnk, repectvely. Wth the trend towa ever ncreang bt rate, there a requrement for wavelength multplexng and demultplexng method whch are compatble wth ngle-mode optcal fber lnk. Method of wavelength demultplexng, whch are currently avalable n ngle-mode ytem, employ ether nterference flter or gratng or drectonal coupler or a combnaton of thee, where they exhbt low gnal dperon low lo n tranmtted ntenty. Multmode fber MMF are preferred for home and bune, becaue they are eay to connect, need low-precon component, and permt wavelength-multplexng. Sngle-mode fber wth typcal core rad le than 1 µm permt tranfer rate of 1 Gb/ec. One of the man potental applcaton of ngle-mode optcal fber ther ue n encrypted optcal and quantum communcaton, where the polarmetrc properte are eental element to determne ther applcaton n th emergng area [6]. Properte uch a the polarzaton dependent lo, the brefrngence, the anotropc depolarzaton degree, among other, repreent valuable nformaton for a lot of poble applcaton lke the tranmon of entangled par of photon to long dtance ung ngle-mode fber [6]. In th ene, the Mueller-Stoke matrcal formalm, provde an eay and drect way to get the polarmetrc properte when the depolarzaton calar metrc are appled to the Mueller matrx [7-1]. In th work, the Mueller matrce aocated to x dfferent commercal optcal fber are obtaned and everal depolarzaton calar metrc are employed to analyze each one of them.

2 444 O. J. VELARDE-ESCOBAR, K. M. SALAS-ALCÁNTARA, R. ESPINOSA-LUNA, G. ATONDO-RUBIO, AND I. TORRES-GÓMEZ TABLE I. Polarzaton-dependent parameter derved from the Mueller matrx. Depolarzaton ndex, DIM. DIM = { 3 Degree of polarzaton, DoP M, S. DoP M, S = = j,k= m jk m } 1// 3 m [ 3 ] 1/ j=1 m j +m j1 1 +m j +m j3 3 m +m 1 1 +m +m Anotropc degree of depolarzaton, Add. Add = DoP Max DoP mn 1 DoP Max +DoP mn Total dattenuaton, DM. DM = m 1 + m + m 3 /m 1 Lnear dattenuaton, LD. LDM = m 1 + m /m 1 Crcular dattenuaton, CD. CDM = m 3 /m 1 Total polarzance, P M. P M = m 1 + m + m 3 /m 1 Lnear polarzance, LP. LP M = m 1 + m /m 1 Crcular polarzance, CP. CP M = m 3 /m 1 QM metrc, QM. QM = 3j=1,k= m jk 3k= m k = 3[DIM] [DM] 1+[DM] Gl-Bernabeu theorem, T GB. T rm t M = 4m Polarzaton dependent lo, P DL. = { 3 j,k=1 m jk}/m +[P M] 3 1+[DM] [ ] m +m P DL = 1 logt max /T mn = 1 log 1 +m +m 3 1/ m m 1 +m +m 3 1/ Gan, g. g = o = m +m 1 1 +m +m Total retaance, R. R = co 1 1 T rm 1 R [MR1, Lnear retaance, δ. δ = co M R, ] + [M R, 1 M R1, ] 1 { } Crcular retaance, Cr. Cr = 1 MR tan 1,1 M R 1, M R 1,1+M R, The polarzance and the dattenuance parameter lnear, crcular, and total, the degree of polarzaton, the depolarzaton ndex, the QM metrc, the Gl-Bernabeu theorem, the polarzaton dependent lo, the anotropc depolarzaton degree, and the retaance lnear, crcular, and total are calculated from the Mueller matrx [7-15]. An mprovement to a reported method by our group [8] preented for the data analy. Reult how the optcal fber can alo be ued a devce, whoe optcal repone are clearly dependent on the ncdent polarzaton tate.. Mathematcal Mueller-Stoke formalm The lnear repone of a medum to the polarzaton ntenty, characterzed by a Mueller matrx M, gven by [11] o =MS S S1 S S3 S o S1 o S o S3 o = m m 1 m m 3 m 1 m 11 m 1 m 13 m m 1 m m 3 m 3 m 31 m 3 m 33 m S + m 1 S1 + m S + m 3 S3 m = 1 S + m 11 S1 + m 1 S + m 13 S 3 m S + m 1 S1 + m S + m 3 S3 1 m 3 S + m 31 S1 + m 3 S + m 33 S3 where S named the Stoke vector. S,o repreent the polarzaton tate of the ncdent and the output lght beam, repectvely, defned n term of the orthogonal component of the electrc feld vector E p, E and ther phae dfference. Rev. Mex. F

3 POLARIMETRIC PARAMETERS ASSOCIATED TO COMMERCIAL OPTICAL FIBERS 445 The normalzed polarzed Stoke parameter can be dplayed n a real three dmenonal pace a a functon of the azmuth ψ π/ and the ellptcty π/ ε π/ angle of the Poncaré phere, repectvely [11]. S = DoP 1 coε coψ coεnψ nε, where repreent the average lght ntenty aocated to the Stoke parameter and DoP the degree of polarzaton. By applyng the depolarzaton calar metrc ee Table I to the Mueller matrx M, t poble to analyze the polarmetrc properte aocated to a ecton of the optcal fber and ther capablty to depolarze lght [7-15]. One can oberve that all of them are obtaned from the Mueller matrx drectly m = 1 Where M R the Mueller matrx aocated to the retaance contrbuton, obtaned from the polar decompoton method [1]. 3. Expermental determnaton of the Mueller matrx In oer to expermentally determne the Mueller matrx element of the optcal fber, we propoe to ue the method of x meaurement reported recently by our group, where a et of x ncdent Stoke vector are ued and analyzed [8]. The ncdent and the analyzed Stoke vector correpond to lnear polarzaton tate parallel p, perpendcular, to +45 degree +, and to -45 degree -, and to crcular rght- r and left-hand l polarzaton tate, repectvely. In a recent work, our group ha reported the Mueller matrx parameter can be obtaned by applyng the followng equaton ee Ref. 8, named there a Eq. 6: pd + d, m 1 = 1 pd d, m = 1 d, m3 = 1 ld, pd 1 pd 1 d m 1 = 1, m 11 = 1 m = 1 pd d, m 1 = 1 m 3 = 1 pd 3 3 d, m 31 = 1 pd 1 pd d 1 d pd pd d d pd 3 pd d 3 d, m 1 = 1, m = 1, m 3 = 1 1 d 1 d, m13 = 1 1 ld 1 ld, d d, m3 = 1 ld ld, 3 d 3 d, m33 = 1 3 ld 3 ld, We have mproved thee relatonhp, by conderng a multplcatve factor aocated wth the degree of polarzaton, whch now ha been ncorporated to each detected Stoke parameter, wth excepton to element of the frt row, whch are detected drectly a aocated to the normalzed power regtered by the commercal equpment th factor reduced to the untary value when the ytem under tudy doe not depolarze. By followng a mlar development than the decrbed n Ref. 8, but now takng nto account that the equpment provde the Stoke vector of the polarzed part of the detected lght, the followng mproved equaton are obtaned m = 1 m 1 = 1 m 1 = 1 m = 1 m = 1 m 3 = 1 m 3 = 1 pd + d, m 1 = 1 pd d, m = 1 d, m3 = 1 ld, pd 1 pd ρpd + d 1 d ρ d, m 11 = 1 1 ρ d 1 d ρ d, m 13 = 1 pd pd ρpd + d d ρ d, m 1 = 1 ρ d d ρ d, m 3 = 1 pd 3 pd ρpd + d 3 d ρ d, m 31 = 1 pd 1 pd ρpd d 1 d ρ d, 1 ρ ld 1 ld ρ ld, pd pd ρpd d d ρ d, ρ ld ld ρ ld, pd 3 pd ρpd d 3 d ρ d, 3 ρ d 3 d ρ d, m 33 = 1 3 ρ ld 3 ld ρ ld, 3 Where ρ kd the degree of polarzaton aocated to the detected Stoke vector S kd, k tand for the polarzaton tate k = p,, ±45, r, and l and d ndcate detected. Equaton 3 can be undertood ealy by takng nto account the commercal oftware regter the total energy detected a the power, n normalzed unt, whch the orgn of the ncomplete term aocated to th Stokemeter ytem. However, t can be a complete Stokemeter f the uer multple the power detected Rev. Mex. F

4 446 O. J. VELARDE-ESCOBAR, K. M. SALAS-ALCÁNTARA, R. ESPINOSA-LUNA, G. ATONDO-RUBIO, AND I. TORRES-GÓMEZ for each polarzaton, S p,,+,,r,l,d, by the normalzed value detected for the remanng three Stoke parameter and for ther correpondng degree of polarzaton factor, S p,,+,,r,l,d 1,,3 S p,,+,,r,l,d ρ, p,,+,,r,l,d th mut be done for each polarzaton. Th procedure ure wll be eay to ue once the manual of the ytem be conulted t can be downloaded freely from the Thorlab web te. Experence ha hown u, ndeed, t true. The x optcal fber tuded here are commercally avalable ther techncal charactertc are ealy obtaned by ung any nternet earch engne. They have been elected jut becaue are broadly employed n everal laboratore and n the communcaton ndutry; n th way, our reult could be of ome nteret for ther uer. Here are decrbed only ome bac charactertc, a reporter by ther manufacturng company. The optcal fber ESM-1-1 fber a, an endlely ngle-mode photonc crytal fber SM-PCF ued n enor and modal nterferometrc applcaton manly, t ha an attenuaton a low a <.8 db/km for λ = 155 nm. The fber b a Nufern 98 nm 98 HP, whch decrbed a hgh performance elected cut-off ngle-mode fber SMF, optmzed for ue by component manufacturer n the telecommuncaton ndutry. Fber b offer exceptonal unformty and core/clad concentrcty pecfcaton, very tght econd mode cut-off tolerance, and tghter bend radu applcaton n mnaturzed fber optc package. The optcal fber FS- PM-661 fber c decrbed a a polarzaton mantanng ngle mode fber SM-PMF, ha a tre-nduced brefrngence whch allow low lo tranmon of polarzed lght wth lttle cro talk between fber polarzaton mode, and ha an attenuaton of db/km; thee data were determned at 13 nm. The SMF-8 fber d a Cornng ngle mode fber SMF and t ha been wdepread ued n a long haul and regonal network, wth a maxmum attenuaton of.17 db/km. The LB 13 fber e a low-brefrngence fber that preerve both lnear and crcular polarzaton and can relay wth mnmum error over large dtance, wth an attenuaton of 4 db/km. The optcal fber LB13 preent tre-nduced brefrngence and allow low lo tranmon of polarzed lght wth lttle cro talk between fber polarzaton mode. It how a SMF behavor at 155 nm. The UV photoentve fber fber f ued for gratng fabrcaton and tranmt lght a a SMF at 155 nm. Fgure 1 how the tranveral ecton of the optcal fber tuded here, a oberved by an optcal mcrocope wth amplfcaton of 4X. Each one of the fber tuded here had approxmately one meter length and PC/FC connector were employed to connect them wth the equpment. FIGURE 1. Tranveral optcal-mcrocopy ecton of the commercal fber a ESM 1-1, b 98 HP, c FS-PM-661, d SMF-8, e LB-3, and f UV photoentve fber. Rev. Mex. F

5 POLARIMETRIC PARAMETERS ASSOCIATED TO COMMERCIAL OPTICAL FIBERS 447 FIGURE. Dagram of the expermental etup employed for the determnaton of the Mueller matrx of the fber. 4. Expermental reult and dcuon The objectve n th work the analy of the polarmetrc properte aocated to the former x commercal optcal fber, once the full determnaton of the Mueller matrx obtaned. The expermental etup ketched n Fg. ued for the bac meaurement of polarzaton properte of the optcal fber [8]. The lght ource a tunable laer wthn nm range Anrtu, Tunc Plu SC, tuned to 155 nm n th work. Th laer connected to a Determntc Polarzaton Controller nput, DPC, Thorlab, model DPC55. The optcal gnal wth arbtrary nput polarzaton tate enter on the DPC, whle at t output we obtan a gnal wth a fxed and predetermned polarzaton tate. The output gnal from the DPC ued a a polarzaton tate generator, PSG, for the fber beng tuded, whch connected drectly to the polarzer tate analyzer, PSA, Thorlab, model PAX571/IR3 and the meaurement are taken for the x ncdent polarzaton tate p,, +45, -45, r, and l, repectvely. A computer control the PSG and the PSA, and a computer program provde the calculu of the Mueller matrx, ung the Stoke vector meaured. For each polarzaton tate generated, the polarmeter analyze the Stoke vector of the lght beam leavng the ytem under tudy. Then, x meaurement provde the 16 Mueller parameter requred, accong to the mproved Eq. 3. Once the Mueller matrce are determned for each fber, ther polarmetrc parameter are calculated, accong to the relatonhp hown n Table I. The reult obtaned are hown n Table II. The data hown n Table II repreent the average lnear repone of the optcal fber to any lnear, crcular or ellptcal ncdent polarzaton tate, even when only x dfferent polarzaton tate have been ued for the ncdence. Oberve that the data have been oered accong the optcal fber depolarzaton capablty, where the frt two calar metrc theorem of Gl-Bernabeu, TGB, and depolarzaton ndex, DIM ndcate the optcal fber depolarze the tranmtted lght a untary value mean the fber do not depolarze and can be decrbed by the Jone formalm. QM content wth them and how the fber are dattenuatng alo. The Add metrc how all the optcal fber depolarze anotropcally, th mean ome tranmtted polarzaton tate are le affected than other. Fber c how a lower PDL value, whch content wth the total dattenuaton parameter, DM. On the other hand, fber d ha the hgher total polarzance value, whch mean t ha a great capacty to polarze the tranmtted lght. The retaance parameter, R, how all the fber are brefrngent. The reader can ue any of thee fber accong to h/her polarmetrc requrement, or to apply a mlar procedure to determne the pecfc repone of h/her own fber. Th analy doe not provde nformaton about a partcular tranmtted or ncdent polarzaton tate, only how the average optcal repone to any polarzaton tate. However, conderng that the anotropc depolarzaton degree, Add, provde nformaton related wth the anotropc repone of the fber to the polarzaton tate tranmtted, the output degree of polarzaton can provde pecfc nformaton about any partcular tate. Fgure 3 how the graphcal repreentaton of the output degree of polarzaton, DoP, a a functon of the ncdent polarzaton tate for the x optcal fber. Oberve the DoP output dfferent for each optcal fber, whch mean they can be ued not only a tatc element, but alo a dynamc devce, whoe repone can be modulated dependng on the elected ncdent polarzaton tate repreented n the baal plane a the azmuth, ψ, and the ellptcty, ε, angle, ee Eq.. Oberve that ome DoP output value are outde the phycal realzable lmt for ome poble ncdent polarzaton tate for all the ncdent polarzaton tate ued here, alway phycally realzable value were ob- TABLE II. Polarmetrc data obtaned from the Mueller matrce aocated to the optcal fber tuded. Fber TGB DIM QM Add PDL DM LD CD PM LP CP R Cr δ a b c d e f Rev. Mex. F

6 448 O. J. VELARDE-ESCOBAR, K. M. SALAS-ALCÁNTARA, R. ESPINOSA-LUNA, G. ATONDO-RUBIO, AND I. TORRES-GÓMEZ FIGURE 3. Output degree of polarzaton veru the azmuthal ψ and the ellptcty ε angle, for fber a Fg. 3.a, b Fg. 3.b, c Fg. 3.c, d, Fg. 3.d, e Fg. 3.e, and f Fg. 3.f. taned. A poble explanaton for th behavor can be aocated to the calbraton procedure avalable wth the commercal equpment employed here. The calbraton of the expermental arrangement, deally hould be done wth the ue of a truly non-depolarzng, polarzaton-mantanng optcal fber, where each generated polarzaton tate mut be the ame a the detected or analyzed [8]. We have ued a hgh-qualty photonc crytal fber a the calbraton reference; however, t not a good a requred. The Fg. 4 how the Poncaré output phere aocated to each optcal fber. They repreent how the ncdent Stoke vector are mapped after ther tranmon through the optcal fber. Rev. Mex. F

7 POLARIMETRIC PARAMETERS ASSOCIATED TO COMMERCIAL OPTICAL FIBERS 449 FIGURE 4. Poncaré output phere aocated to fber a Fg. 4.a, b Fg. 4.b, c Fg. 4.c, d, Fg. 4.d, e Fg. 4.e, and f Fg. 4.f. Oberve the phercal hape and ze are lot progrevely accong the depolarzaton repone aocated to each fber ncreaed and that the depolarzaton depend trongly on the ncdent polarzaton tate. Th behavor content wth the reult hown n Table II and n Fg Concluon Fourteen polarmetrc parameter and a graphcal analy have been performed for x dfferent type of commercal optcal fber, for a tranmon wavelength of 155 nm. All of them have been determned from the expermental Mueller matrx aocated to each fber tuded. Reult are content and how the performance of each optcal fber drectly related to t polarzaton properte, uggetng the fber can be ued not only a tatc element, but alo a veratle optcal devce, dependng on the ncdent polarzaton tate employed. Accong to our reult, the optcal fber FS-PM- 661 named here a fber c, preent the lowet value of PDL for th et of commercal fber; n th ene, th fber Rev. Mex. F

8 45 O. J. VELARDE-ESCOBAR, K. M. SALAS-ALCÁNTARA, R. ESPINOSA-LUNA, G. ATONDO-RUBIO, AND I. TORRES-GÓMEZ can be ued n modern fber communcaton ytem for long dtance or n the contructon of devce lke optcal coupler, pump dode pgtal, gratng, among many other applcaton. On the other hand, fber b Nufern 98 nm, 98 HP, preent the hghet value of PDL, whch make t a good canddate a a fber nlne lnear polarzer due to t capablty to polarze the tranmtted lght. Note the ESM-1-1 fber a, ha the lowet depolarzaton and anotropc depolarzaton degree, whch mean t ha a lower and almot unform brefrngence and preent a hgh qualty compoton. We ugget th fber be ued n encrypted telecommuncaton ytem. Even when we have determned thee polarmetrc charactertc at a ngle wavelength 15 nm, our man goal wth th work ha been to preent a methodology able to be appled for any ntereted uer accong ther own need. An mprovement to a reported method by our group ha been preented for the data analy. Acknowledgment O. J. Velae-Ecobar 1681 and K. M. Sala-Alcántara 4163 expre ther grattude to CONACYT Méxco for the cholarhp receved through ther doctoral tude. Th work ha been done wth the fnancal upport of CONACYT- Méxco project A. Ghatak, K. Thyagarajan, An Introducton To Fber Optc, Cambrdge Unverty Pre, New York B. Culhaw and J. Dakn, Ed, Optcal Fber Senor: Sytem and Applcaton, Vol. II, Artech Houe A. Mendez, Specalty Optcal Fber n Bomedcal Applcaton: Need & Applcaton, n Workhop on Specalty Optcal Fber and ther Applcaton, Optcal Socety of Amerca Q. Wang, G. Farrell, T. Frer, G. Rajan, and P. Wang, Opt. Lett E. Collett, Polarzed Lght n fber Optc, The PolaWave Group X. Wang, P. Moraw, D. R. Relly, J. B. Altepeter, and G. S. Kanter, J. Lghtwave Tech K. M. Sala-Alcántara, R. Epnoa-Luna, and I. Torre- Gómez, Opt. Eng K. M. Sala-Alcántara, R. Epnoa-Luna, I. Torre-Gómez, and Y. Barmenkov, Appl. Opt N. Ghoh, M. F. G. Wood, and I. A. Vtkn, J. Bomed. Opt T. A. Eftmov, W. J. Bock, P. Mkulc, and J. Chen, J. Lghtwave Technol D. Godten, Polarzed Lght, nd Ed., Marcel Decker S.Y. Lu and R. A. Chpman, J. Opt. Soc. Am. A J. J. Gl and E. Bernabeu, Opt. Acta R. Epnoa-Luna and E. Bernabeu, Opt. Commun R. Epnoa-Luna, G. Atondo-Rubo, S. Hnojoa-Ruz, Optk Rev. Mex. F