Budin, J.

Kung, A.

Robert, P. A.

Thévenaz, Luc

Infoscience - École polytechnique fédérale de Lausanne

90 OPTICS LETTERS / Vol. 22, No. 2 / January 15, 1997Optical fiber ring resonator characterizationby optical time-domain reflectometryA. Ku¨ng, J. Budin, L. The´venaz, and Ph. A. RobertMetrology Laboratory, Swiss Federal Institute of Technology (E´cole Polytechnique Fe´de´ral de Lausanne), CH1015 Lausanne, SwitzerlandReceived September 4, 1996A novel method for characterization of optical fiber resonators by an optical time-domain ref lectometry (OTDR)technique is reported. This easy-to-use technique yields accurate results for cavity lengths ranging from afew meters to several kilometers. A simple relationship is established between the round-trip cavity loss andthe position where the OTDR signal is maximum. The value obtained for the round-trip cavity loss turns outto be quite insensitive to uncertainties in the determination of the OTDR maximum position.  1997 OpticalSociety of AmericaOptical fiber ring resonators have been widely usedin passive and active gyroscopes,1,2 narrow-linewidthBrillouin lasers,3 optical frequency-selective f ilters,4and a wide range of optical f iber sensors.5 Mostof these applications require a high-finesse cavity,so it is of prime importance to know the quality ofthe closed-loop fiber resonator. The quality and thefinesse depend on only two ring parameters6: theintensity transmission coeff icient k of the coupler(coupling coefficient 1 2 k) and the cavity feedbackcoeff icient kr (cavity round-trip loss 1 2 kr). Thebasic experimental problem results from the im-possibility of measuring the light circulating in thecavity without increasing the intracavity loss and per-turbing the resonator operation. One usually char-acterizes a f iber ring resonator by measuring itsintensity transfer function, using a coherent lightsource. The two parameters k and kr can be deter-mined from this transfer function by measurementof the f inesse F of the resonator and the residualintensity transmission Tmin at resonance.6,7 If thecoupler coeff icient k is known, measuring either For Tmin is sufficient for determining kr. However,this method suffers from several drawbacks: (i)the polarization into the loop must be controlledso that light propagates in a polarization eigenstate,(ii) either the length of the cavity or the wavelengthof the light source must be varied to permit scanningof the entire coherent transfer function, and (iii) thelinewidth of the light source must be at least 1 orderof magnitude smaller than the resonance width dnto resolve this resonance properly. The last-namedcondition can be a seriously limiting factor for longcavity length.A novel nondestructive technique is proposed thatuses an optical time-domain ref lectometry (OTDR) in-strument to characterize optical fiber ring resonators.The ring structure has the unique feature of lettingthe OTDR pulse circulate in the ring while generatingRayleigh backscattering. The Rayleigh backscatteredlight also circulates in the ring but in the opposite di-rection. One part of the scattered light keeps circu-lating into the ring, whereas the other part is directedthrough the coupler onto the detection stage. This re-0146-9592/97/020090-03$10.00/0circulation of the OTDR pulse combined with the re-circulation of the Rayleigh backscattered light allowsdifferent Rayleigh contributions to be summed and de-tected simultaneously. Each contribution correspondsto a definite number of turns for the OTDR pulse and adefinite scattering point and a definite number of turnsfor the Rayleigh backscattered light. A typical OTDRtrace of a ring resonator is shown in Fig. 1.The trace is made of equal-length steps correspond-ing to one round trip in the ring and resulting from theaddition of contributions circulating in the ring for agiven propagation time. The first steps are given bya few contributions of great intensity. As the step or-der gets higher the number of contributions grows andtheir intensity decays, resulting in a maximum whoseposition depends on the ring parameters.The aim of the following demonstration is to showthat the relevant ring parameters can be determinedonly from the position of this maximum. For thispurpose a model describing the Rayleigh backscatteredintensity at the ring output is developed. Problems ofthe source polarization and the ring birefringence areaddressed and lead to a simple equation characterizingthe ring. Finally measurements are compared withthe model, showing excellent agreement with theory.According to the schematic description in Fig. 2,the electric f ield that results from the OTDR probeFig. 1. OTDR trace of a 765-m-long fiber ring resonatorwith coupler coeff icient k ­ 95% together with the numeri-cal fit of Eq. (4) below, giving a calculated cavity feedbackcoeff icient kr ­ 89.5%. 1997 Optical Society of AmericaJanuary 15, 1997 / Vol. 22, No. 2 / OPTICS LETTERS 91Fig. 2. Schematic description of the measurement tech-nique. The optical paths corresponding to the Jones ma-trices My and Ty are represented.pulse propagating n counterclockwise turns in the ring,which is scattered at a distance y from the coupler andthen propagates m clockwise turns, is given byEnms yd ­ E00s yd skjdsn1m/2dexpf2asn 1 mdLy2g3 expfibsn 1 mdLgTy T My TmMynTyeˆ , (1)where E00s yd corresponds to the electric f ield ampli-tude for n ­ m ­ 0:E00s yd ­qIinRs yd j exps2aydexpsi2byd , (2)where Iin is the input intensity, b is the propagationconstant, k is the coupler intensity coefficient, j is theintensity transmission coeff icient of the ring excludingthe fiber linear loss, Rs yd is the intensity Rayleighbackscattering coefficient, a is the intensity linearattenuation of the fiber, L is the ring length, andy s0 # y # Ld is the distance along the fiber from thecoupler to the scattering point. eˆ is the Jones vectorof the incident light, and My and MyT are the Jonesmatrices in the probe (counterclockwise) direction andthe backscattered direction (clockwise), respectively,for a full round trip in the ring starting from point y :My ­"cos uy expsiwy y2d sin uy expsiwyy2d2sin uy exps2iwyy2d cos uy exps2iwy y2d#,(3)where wy and uy are the phase delays for a full roundtrip that are due to linear and circular birefringence,respectively. Ty and Ty T are the Jones matrices fromthe coupler to scattering point y for the probe pulse andthe Rayleigh backscattered signal, respectively.The cavity feedback coeff icient kr is given by kr ­j exps2aLd. We obtain the resulting OTDR trace bysumming over m and n each contribution of Eq. (1)that experiences equal propagation times. As thesecontributions are generated simultaneously by thesame source and are also detected simultaneously,they experience the same propagation delay and mustbe added coherently. A simple intensity summationresults in a low-accuracy model.8 However, the contri-butions scattered from different centers are not corre-lated9 and must be added incoherently as a result of therandom character of Rayleigh scattering. For a givenpropagation time each contribution may be scatteredby two different centers spaced by a distance Ly2, asshown in Fig. 3 for step 1.These considerations result in the following discon-tinuous steplike backscattered intensity function:Ius yd ­ I0s yd skjdu21exps2auLd3"kjuXp­0sMyT du2psMydpeˆ21u21Xp­0sMTy1L/2du2p21sMy1L/2dpeˆ2#, (4)where I0s yd ­ jE00s ydj2 correspond to the intensityfunction for step zero, the integer u ­ intszyLd is thestep order, and z is the total propagation distance.Position ys0 # y # Ly2d of the scattering center issimply related to the other quantities by z ­ uL 1 2y.The matrices Ty and Ty T cancel, as they are identicalfor each contribution of each coherent summation.Let us show now that the polarization of the incidentlight and the ring birefringence have only an amplitudescaling effect on the OTDR signal waveform; theintensity ratio between distinct steps remains constant.Using the unimodularity property detsMy d ­ 1 and asimple but tedious calculation giveuXp­0sMyT du2psMy dpeˆ2­ lsuy , wy , ud , (5)where lsuy , wy , ud is a scalar function of the birefrin-gence parameters uy and wy and the step order u and isindependent of the incident polarization eˆ. Substitut-ing Eq. (5) into the intensity function [Eq. (4)] for bothsummations results in a backscattered intensity Ius yd,independently of the input light polarization.To analyze the effect of birefrigence on the signalwaveform one must address short and long rings sep-arately. For short rings let us assume that over oneround trip the birefrigence is independent of the wave-length and that the circular birefringence results in aphase delay much smaller than p. This condition lim-its the cavity length to ,10 times the birefringence beatlength. In this case low birefringence delay makespossible the following first-order approximation:lsuy , wy , ud > F suy , wydls0, 0, ud ­ F suy , wyd su 1 1d2,(6)which results from summation (5) with no birefrin-gence and where F suy , wyd is a scalar function of thebirefringence parameters. For a f ixed ref lection atpoint y the birefringence dependence of the signal isidentical for any steps except step zero, which has aFig. 3. Addition of the three contributions of Step 1.The contributions scattered at the same point are addedcoherently.92 OPTICS LETTERS / Vol. 22, No. 2 / January 15, 1997Table 1. OTDR Measurements of Several Fiber Ring Resonators of Increasing Length Compared withMeasurements with a Coherent Light SourceaOTDR Measurements Coherent MeasurementsRing Characteristics Zmax smd kr s%d Tmin s%d kr s%dk ­ 94.8%, L ­ 5.568 m 136 6 1.5 97.19 6 0.09 9 6 1 97.21 6 0.1k ­ 96.9%, L ­ 10 m 445 6 3 98.66 6 0.04 13 6 1 98.55 6 0.05k ­ 90.3%, L ­ 10 m 165 6 2 98.10 6 0.13 45 6 1 98.06 6 0.05k ­ 97.1%, L ­ 26.5 m 490 6 5 92.42 6 0.1 19 6 1 92.58 6 0.15k ­ 95.0%, L ­ 765 m 9440 6 150 89.5 6 0.23 – –aExperimental conditions could not be achieved for a coherent measurement on the long fiber ring.Fig. 4. OTDR trace of a 5.568-m-long fiber ring resonatorwith coupler coeff icient k ­ 94.8% together with thenumerical f it of Eq. (7), giving a calculated cavity feedbackcoeff icient kr ­ 97.2%.single scattering contribution and thus shows no inter-ference. When step zero is discarded the normalizedOTDR waveform does not therefore depend on bire-fringence. In the ideal case in which the birefringenceis purely linear the whole signal becomes independentof the birefringence as My ­ My T . For long rings thebirefringence contains large linear and circular compo-nents, so the birefringence delay depends on the wave-length, and because OTDR sources have wide spectrathis results in an ensemble average on polarization de-lays. The signal is averaged and becomes independentof the birefringence.This analysis demonstrates that the polarizationchanges only the level of the global signal withoutaltering its shape, provided that either the short- or thelong-cavity assumption is satisfied. So one can use themodel without considering polarization by discardingstep zero.The summations contained in the steplike backscat-tered intensity function [Eq. (5)] can be replaced by thecorresponding integrals, resulting in a continuous func-tion:I sud ­ IinRsudj2 exp"2aLµu 112¶#3 skjdu21fkjsu 1 1d2 1 u2g , (7)where u is now a continuous parameter:u ­ szyL 2 1y2d . (8)Differentiation of Eq. (7) over z followed by a first-order approximation yields a simple approximate re-lation between the position zmax of the maximumbackscattered intensity and the resonator parameters:kkr ­ expˆ22Lzmax!. (9)Thus, if k and L are known, we determine kr sim-ply by measuring the position zmax where the Rayleighbackscattered signal is maximum. The particular re-lationship between zmax and kr results in a high accu-racy of kr, even if the relative accuracy of zmax is poorer.Table 1 compares kr determined by this method with krderived by the conventional measurement that uses acoherent source for different fiber ring resonators.Figure 1 shows an OTDR trace obtained from a longring resonator and the numerical fit of relation (4).Each round trip is clearly resolved. Ref lection peaksat the output f iber end are measured, but they arediscarded before f itting.Figure 4 shows the OTDR trace of a short ringresonator and its corresponding fit obtained by useof the continuous function [Eq. (7)]. In this case theOTDR resolution is not sufficient to resolve each step,but the information can still be obtained, which is aremarkable feature of the method.This simple method demonstrates that long andshort optical f iber ring resonators can be successfullycharacterized by use of an OTDR, even for a cavityshorter than the OTDR spatial resolution. The accu-racy of standard OTDR instruments is suff icient forreliable measurements of the intracavity loss of a f iberring resonator.References1. K. Takiguchi and K. Hotate, IEEE Photon. Technol.Lett. 4, 7 (1992).2. F. Zarinetchi, S. P. Smith, and S. Ezekiel, Opt. Lett. 16,6 (1991).3. L. Thevenaz, J. Boschung, and P.-A. Robert, Electron.Lett. 30, 18 (1994).4. K. Kalli and D. A. Jackson, Opt. Lett. 17, 17 (1992).5. Y. Ohtsuka and Y. Imai, Appl. Opt. 24, 4199 (1985).6. L. F. Stokes, M. Chodorow, and H. J. Shaw, Opt. Lett. 7,6 (1982).7. F. Zhang and J. W. Y. Lit, J. Opt. Soc. Am. A 5, 8 (1988).8. D. J. Ives, R. L. Palmer, and B. Walker, Electron. Lett.27, 4 (1991).9. P. Gysel and R. K. Staubli, J. Lightwave Technol. 8, 4(1990).

Optical fiber ring resonator characterization by optical time-domain reflectometry

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Optical fiber ring resonator characterization by optical time-domain reflectometry

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