arX

iv:1

001.

0694

v2 [

quan

t-ph

] 7

Jan

2010

JOURNAL OF LIGHTWAVE TECHNOLOGY , VOL. X, NO. Y, JANUARY 200Z 1

Photon Counting OTDR :Advantages and Limitations

Patrick Eraerds, Matthieu Legre, Jun Zhang, Hugo Zbinden,Nicolas Gisin

c© 20xx IEEE. Personal use of this material is permitted.However, permission to reprint/republish this material foradvertising or promotional purposes or for creating newcollective works for resale or redistribution to servers orlists,or to reuse any copyrighted component of this work in otherworks must be obtained from the IEEE.

Abstract—We give detailed insight into photon counting OTDR(ν−OTDR) operation, ranging from Geiger mode operation ofavalanche photodiodes (APD), analysis of different APD biasschemes, to the discussion of OTDR perspectives. Our resultsdemonstrate that an InGaAs/InP APD basedν−OTDR has thepotential of outperforming the dynamic range of a conventionalstate-of-the-art OTDR by 10 dB as well as the 2-point resolutionby a factor of 20. Considering the trace acquisition speed ofν−OTDRs, we find that a combination of rapid gating for highphoton flux and free running mode for low photon flux is themost efficient solution. Concerning dead zones, our resultsare lesspromising. Without additional measures, e.g. an optical shutter,the photon counting approach is not competitive.

Index Terms—Distributed detection, fiber metrology, opticaltime-domain reflectometry, photon counting

I. I NTRODUCTION

OPTICAL Time Domain Reflectometry [1] is a wellknown technique for fiber link characterization. Most

of today’s commercially available optical time domain reflec-tometers (OTDRs) are based on linear photon detectors, suchas p-i-n or avalanche photodiodes (APDs). Although singlephoton detection features unmatched sensitivity, OTDRs basedon this technique (ν−OTDR) [2] have reached the market onlyin niches [3].Several single photon detection techniques are possible [4]-[9], but only few of them are suitable for in-field measure-ments. Geiger-mode operated InGaAs/InP APDs (for telecomwavelengths) [5] [10] [11] are the most promising candidates,due to their robustness and manageable cooling.In this paper we discuss the advantages and limitations of thesedevices, when used in anν−OTDR. We concentrate in par-ticular on the dynamic range, 2-point resolution, measurementtime and dead zone. Allν−OTDR measurements are supple-mented by measurements using a conventional state-of-the-art OTDR (Exfo, FTB7600). This makes it easier to evaluate

P. Eraerds, J. Zhang, H. Zbinden, N. Gisin are with the Group of Ap-plied Physics, University of Geneva, 1211 Geneva 4 Switzerland, e-mail:Patrick.Eraerds@unige.ch

M. Legre is with idQuantique SA, 1227 Carouge/Geneva, SwitzerlandManuscript received April x, 200y; revised January x, 200y.Financial

supports from the Swiss Federal Department for Education and Science(OFES), in the framework of the European COST299 project, from the SwissNCCR ”Quantum photonics” are acknowledged.

the ν−OTDR performance. Our discussion also contains thepossible yield of newly emerged gating techniques likerapidgating [12] [13] [14].We note that some years agoν-OTDRs based on silicon APDs,suitable for C-band operation, were demonstrated [15] [16].Although silicon APDs show superior behavior, concerningafterpulsing and timing jitter, the upconversion of telecomphotons to the visible regime demands more expensive opticsand more sophisticated alignment. Therefore we believe thatthey are less suitable when robustness is required.Paper organization : In Sect.II we provide information aboutGeiger-mode operation of InGaAs/InP APDs and discuss itsmajor impairment, the afterpulsing effect. Sect.III focusses onν−OTDR operation and performance (dynamic range, 2-pointresolution, measurement time, dead zone) and compares it withthe performance of a conventional state-of-the-art long haulOTDR (Exfo FTB7600). Sect.IV considers time efficient biasschemes (rapid gating, free running) and finally we summarizeour results in Sect.V.

II. GEIGER-MODE APD

A. Basic operation

In Geiger-mode, the APD is biased beyond its breakdownvoltage, typically by a few percent. This provides a sufficientlylarge gain (order of106) to detect a single incident photon(with detection efficiencyη). In contrast to a linear modeAPD, the output signal is no longer proportional to thenumber of primary charges. Whenever an avalanche occursand the current reaches a certain discrimination level, adetection is counted, independent of how many primarycharges caused or were created during the avalanche.To reset the APD for the next detection, the avalanche needsto be quenched. This is typically done by lowering the biasvoltage, either actively or passively [17].An APD based on InGaAs/InP is particularly well suited foruse with the principal telecom wavelength bands. Althoughthe dark count1 rate is higher than in silicon based APDs,high sensitivity can be regained by cooling, typically around−50◦C (see also Sect.II-B).There are different ways of applying the overbias (Vbias > Vbd

(breakdown voltage)) to the diode. The most common onesare thegated modeand thefree running mode[18]. In gatedmodethe overbias is applied only during a short time∆tgate(called gate), in a repetitive manner with frequencyfgate(respectingfgate < 1

∆tgate). Typically ∆tgate ∈ [2ns, 20µs]

1A detection which was not initiated by a signal photon but thermalexcitation or tunneling.

JOURNAL OF LIGHTWAVE TECHNOLOGY , VOL. X, NO. Y, JANUARY 200Z 2

and fgate ∈ [100Hz, 10MHz]. In free running mode, theoverbias is applied until a photon or noise initiates anavalanche.While the gated modeachieves high signal to noise ratioswhen a synchronized signal is being detected, thefree runningmode is most suited when the photon arrival time is notknown (e.g. in OTDR).More recent developments, summarized by the namerapidgating [12] [13] [14], apply very short gates (≈ 200 ps)in order to severely limit avalanche evolution and reduceafterpulsing (see Sect.II-C). The technical challenge consistsin discriminating the rather small avalanche signal fromthe capacitive response to overbias of the diode itself. In”classical gating”, described in the previous paragraph, oneusually waits until the avalanche signal is easy to discriminate.Typical gating frequencies inrapid gatingare of the order of1 GHz.In Sect.IV we will discuss pros and cons of these differentapproaches, in particular concerning their applicabilityforν−OTDRs.

B. Detection sensitivity

A figure of merit for the sensitivity of a detector is itsnoise equivalent power (NEP ). For example, the bandwidthnormalizedNEPnorm of a linear photo detector is given by[21] [22]

NEPnorm =∆InoiseS ·G [

W√Hz

] (1)

where∆Inoise [A/√

Hz] is the standard deviation of the totalnoise current (thermal-, dark-, signal shot- and in case of gainalso gain noise), normalized with respect to the bandwidth ofthe detector,S [A/W] is the detector photosensitivity andG is the gain of the diode (p-i-n diode :G = 1, linear APD(typically) : G = 10− 100).APDs are superior to p-i-n diodes in the circuit noise limitedregime2 [23], but lose their advantage when the gain noisebecomes important, i.e. at stronger signal powers. Theminimal detectable powerNEPnorm,0 [W/

√Hz] is obtained

by setting the signal power and thus the signal shot-noiseequal to zero.NEPnorm,0 can usually be found in the datasheet of the diode, typically10−15 − 10−13 [W/

√Hz] for

InGaAs APDs at25◦C.A similar expression can be derived for Geiger-mode APDs(see App.B, Eq.20):

NEPnorm =hν

η·√

2 · pnoise [W√Hz

] (2)

where η is the detection efficiency andpnoise is the noisedetection probability per gate (including signal and dark countshot noise), normalized with respect to the gate width∆tgate

2Circuit noise results for example from thermal motion of charges inresistors or charge fluctuation in transistors in the receiver amplifier.

-50 -40 -30 -20 -10 0 10 20

1x10-16

10-15

Hz]

Ö

AAAA

NE

Pnorm

,0[W

/

T [°C]

Fig. 1. Bandwidth normalized noise equivalent power (NEPnorm,0, seeEq.3) as function of Geiger-mode APD temperature. The detection efficiencyηis kept constant at 10%. At ambient temperatures the noise equivalent poweris increased by almost a factor of 10 with respect to the usualoperatingtemperature of−50◦C.

in seconds. Again, setting the input optical power equal tozero, we infer the minimal detectable power (App.B, Eq.21)

NEPnorm,0 =hν

η·√

2 · pdc [W√Hz

] (3)

where pdc denotes the dark count probability per gate, nor-malized with respect to the gate width∆tgate in seconds.Inserting the parameters of the Geiger mode APD used inour experiments (pdc = 2000 s−1, η = 10%, T = −50◦C,Sect.III-A), we estimateNEPnorm,0 ≈ 10−16 [W/

√Hz].

In Fig.1 we see the evolution ofNEPnorm,0 as functionof temperature. We observe that when approaching ambienttemperatures, we almost reach the regime of the best linearmode diodes. Conversely, one might be tempted to cool lineardiodes to−50◦C to reach theNEP of Geiger mode APDs.Even if this might be in general achievable, one should notforget, that the output signal still needs to be amplified. Evenat ambient temperatures the small pulse amplifier noise usuallyconstitutes the dominating noise source leading to much highereffective NEPs.By analyzing the performance of a conventional OTDR inSect.III, we will gain more insight into the sensitivity limitsof linear mode APD detection systems.

C. Afterpulsing

One of the major impairments of InGaAs/InP APDs isthe afterpulsing effect. Imperfections and impurities in thesemiconductor material are responsible for intermediate energylevels (also called trap levels), located between the valenceband and the conduction band. During an avalanche, theselevels get overpopulated with respect to the thermal equi-librium population. If the APD gets reactivated right afterthe quenching of an avalanche, the probability of thermalexcitation or tunneling of one of these charges into theconduction band and the subsequent initiation of an afterpulse

JOURNAL OF LIGHTWAVE TECHNOLOGY , VOL. X, NO. Y, JANUARY 200Z 3

0 10 20 30 40 50

1E-4

1E-3

0.01

0.1

1 ∆t

gate=10 ns

τ

pA

P,g

ate

dead time [µs]

Fig. 2. Afterpulse probability as function of dead timeτ . The detectionefficiency η is equal to 10% and the temperature T=−50◦C. An activequenching application specific integrated circuit (ASIC) [19] was used.

avalanche, is high. Although fundamentally the improvementof semiconductor purity and thus the reduction of the numberof trap levels is preferable, different mitigation measures canbe carried out :a) dead time: A purely passive measure is the introductionof a dead time. The trap population decreases exponentiallywith time, due to thermal diffusion. Finally the thermal equi-librium configuration is restored. The impact of afterpulsingcan therefore be mitigated by maintaining the bias voltagebelow breakdown, i.e. the application of a dead timeτ , after adetection takes place. Dead times severely limit the maximumachievable detection rate.b) heating: An increased temperature accelerates the diffusionof trapped charges. However, at the same time charge excita-tion from the valence into the conduction band increases, lead-ing to globally increased noise, which eventually reduces thedetector sensitivity. Thus one cannot achieve low afterpulsingand high sensitivity at the same time. It is necessary to find atrade-off depending on the particular application.c) quenching technique: As soon as the avalanche has gainedenough strength such that the current pulse can be detected,itneeds to be quenched. The quenching speed is crucial to limit-ing the number of secondary charges which can populate traplevels. Here, fully integrated active quenching circuits yieldmuch better results than non-integrated ones [19]. Anotherapproach israpid gating (Sect.II-A). Avalanche evolution isterminated by short gate durations (200 ps) and the numberof secondary charges is kept low.

In Fig.2 we plot an example of afterpulse probability asfunction of dead timeτ , using a fully integrated ASIC basedactive quenching circuit [19]. Whenever a detection takesplace, we activate a second gate of width∆tgate = 10 nswith a temporal delay ofτ . In this second gate, no incidentphotons are present. If there is a detection it is either a darkcount or an afterpulse. Since for largeτ only the actualdark counts remain, we can subtract it from the total count

rate and obtain the pure afterpulsing probability (→ Fig.2).During larger gates, the afterpulse probability sums up andafterpulsing increases. One can easily calculate the afterpulseprobability of a gate of width∆tgate (≤ 10µs) by

pAP,∆tgate(τ) = 1− (1− pAP,10ns(τ))

m (4)

wherepAP,10ns(τ) is the afterpulse probability in a gate of 10ns width andm =

∆tgate

10ns .We note that if no afterpulse occurs in the first activatedgate after a detection, it can also happen in any succeedinggate. However, the probability decreases due to trap chargediffusion. To get the total afterpulse probability, or ratherthe signal to afterpulse ratio, one needs to account for thissumming effect as well. The lower the signal detection rate,themore summing-up takes place. Thus a higher signal detectionrate improves the signal to afterpulse ratio.In Fig.3 we illustrate the impact afterpulsing can have in aν−OTDR measurement. Firstly and most importantly we mustconsider dead zones (see Sect.III-D for definition, not to beconfused with dead time). Whenever an important loss (at 25km) or a reflection (at 36 km) occurs, it is followed by atail which prevents the detection of the Rayleigh backscatterdirectly behind it. Secondly, the backscatter trace is shifted tohigher values, since more detections than in the pure signalcase occur (pile-up effect). Thirdly, the slope of the traceisflatter than it should be.

0 5 10 15 20 25 30 35 40 45 50

−30

−25

−20

−15

−10

−5

0

distance [km]

dB

afterpulsing no afterpulsing

reflection

Fig. 3. Illustration of the afterpulsing effect onν−OTDR trace. Most severeare the dead zones after large loss events (at 25 km) and reflections (at 35km). More subtle is the change of the slope of the trace which is usuallysmaller than what is measured when afterpulsing can be neglected.

How much afterpulsing can be tolerated, generally dependson the particular measurement. For instance in a coarsemeasurement on a long span of fiber, where only peakpositions or large loss events are of interest, one can toleratea fairly high afterpulsing contribution. On the other hand,in the case of short links, where high precision for fiberattenuation measurement and dead zone minimization isdesired, afterpulsing must be kept to a few percent or evenlower, depending on required precision of the measurement.Numerical afterpulse correction methods were also analyzed[20], but it was found that for high precision measurementsthe algorithm lacks robustness due to possible variations in

JOURNAL OF LIGHTWAVE TECHNOLOGY , VOL. X, NO. Y, JANUARY 200Z 4

the afterpulse probability. It should therefore be used onlywhen the requirements on precision are not stringent.

III. PHOTON COUNTING VS. CONVENTIONAL OTDR

Although this section is mainly concerned with theν-OTDRtechnique, we also perform measurements using a state-of-the-art conventional3 OTDR (FTB-7600, EXFO), a productespecially designed for long-haul applications (up to 50 dBdynamic range). This makes it easier for us to highlight theadvantages and drawbacks of the photon counting approach.The experimental setup and a detailed explanation is given inFig.4.

Fig. 4. Basicν-OTDR setup. The laser (we use the laser of the FTB-7600,Ppeak = 400 mW) emits pulses with a frequencyfpulse adapted to thelength of the fiber under testLfiber (→ fpulse = c

2·Lfiber). The signal

is split at a 99/1-coupler. The 99% part is launched into the fiber under test(FUT) via a circulator. Backscattered light from the fiber exits the lower portof the circulator and illuminates the InGaAs/InP-APD. The 1% part is usedto measure the time of departuret0 of the laser pulse (for synchronizationreasons) using a conventional photodiode (Newport, 1GHz).The output signalis sent to a delay generator. A delayed signal att0+tdelay is sent to the APDto apply a detection gate of length∆tgate and the backscattered intensitycorresponding to the applied delay is measured. The APD reverse bias is equal48.7 V, yielding a detection efficiencyη = 10% at−57◦C (minimal value).We measure a dark count probability per gate equal topdc = 2000 s−1

(normalized with respect to the gate width, Eq.3). This corresponds to a darkcount probability of2 · 10−5 for a gate width of 10 ns and2 · 10−2 for a10 µs gate.

For a fixed delay, a number of laser pulsesNpulse (repeti-tion frequencyfpulse) are sent andNgate(= Npulse) gatesare activated. A counter records the number of detections.The incident signal power can be inferred from the ratio ofdetections to activated gates (for details, see App.A).To get information on the backscatter of the entire fiber, thedelay needs to be scanned, repeating the procedure explainedbefore for each single delay position. The sampling resolution,i.e. the delay step∆tdelay (tdelay = i ·∆tdelay, i = 1, 2, 3...),needs to be adapted to the requirements of the particularmeasurement (e.g. zooming or coarse full trace measurement).The detection bandwidth is given byB = 1

2∆tgate.

We note that this is only the most basic version of a photoncounting OTDR. One of the advantages of this system isthat due to the low gating frequency, we can totally exclude

3Based on linear-mode APD detection.

afterpulse effects (dead time 2 ms). Therefore we can deter-mine the unadulterated dynamic range and 2-point resolution.Nevertheless, data acquisition is very time consuming. Forexample the measurement of the entire 200 km fiber, discussedin the next section (Fig.5), took about 6 hours. In Sect.IV wewill see, how it can be performed more efficiently.

A. Dynamic range

To measure the dynamic range of both devices for differentlaser pulse widths, we take a 200 km fiber, composed of a50 km spool and an installed fiber link of 150 km (Swisscom,Geneva-Neuchatel), which itself consists of several fibers. Thelength of the fiber allows a maximal laser pulse repetition rateof flaser = c

2·Lfiber= 500 Hz, wherec is the speed of light

in standard optical fiber.We start measuring the trace with the FTB-7600 for 3 min-utes4 with a laser pulse width of 1µs. The device acquires180 s·500 Hz = 9·104 different traces. The final output trace isthe numerical average of these single traces (Fig.5, light greycurve). For a fair comparison the detection bandwidth shouldbe equal for the two devices. For the conventional OTDR itis automatically chosen by the device and not available to us.We infer its value by looking at the noise period at the end ofthe measurement range. For a pulse width of1µs we obtain 4MHz. Under these conditions the dynamic range is found tobe 34.5 dB.We then perform theν-OTDR measurement, ensuring thatwe do not saturate the detector with the backscatter fromthe beginning of the fiber. Therefore we insert an additionalattenuator in front of the APD to reach the unsaturated regime.We adjust the attenuation to yield a detection rate of about90% of the gate rate for the first delay position. At each delayposition we count the number of detections within 3 minutes,which yields the same statistics per sampling point as in theprevious case (180 s ·500 Hz = 9 ·104 samplings). We choose∆tdelay equal to 3µs (=300 m sampling point separationin fiber) and∆tgate = ∆tpulse. With increasing delay thebackscatter power and thus the detection rate decreases. Whenwe start to approach the noise level of the detector, wepause the measurement and remove a part of the attenuation(to regain 90% detection rate), reduce the delay for a fewkilometers (to get an overlap with the previous part) andresume the measurement. In this way we obtain several singletraces of adjacent parts of the fiber. In the following wewill refer to this as partial trace measurement. By meansof the overlaps, the entire trace can be reconstructed. Eachpartial trace measurement contributes approximately 20 dBtothe overallν-OTDR dynamic range. For example, to cover50 dB of fiber loss, we need to perform three partial tracemeasurements5.The result of theν-OTDR measurements is also shown in

Fig.5 (blue curve). It is important to note that we adapt the

4We choose 3 min because this is the time specified in the definition ofOTDR dynamic range for conventional OTDRs [24].

5The first measurement covers 0-20 dB, the second 15-35 dB and the third30-50 dB respecting the necessary overlap between different partial tracemeasurements.

JOURNAL OF LIGHTWAVE TECHNOLOGY , VOL. X, NO. Y, JANUARY 200Z 5

0 20 40 60 80 100 120 140 160 180 200

-50

-40

-30

-20

-10

0

10

-46 dB

-34.5 dB

dB

distance [km]

conventional OTDR

photon counting OTDR

Fig. 5. OTDR traces of 200 km fiber link using a laser pulse width of1µs. The light gray curve represents the result of the conventional OTDR(Exfo FTB-7600) after 3 minutes of measurement in standard configuration.In this configuration it uses a detection band width of 4 MHz atthe end of themeasurement range. Theν−OTDR result is represented by the blue curve.The measurement bandwidth is 500 kHz using the same number ofsamplingsfor each point as the conventional device. The bandwidth adapted results fordifferent pulse widths can be found in Fig.6.

gate width to the laser pulse width to obtain the minimalNEP0 (App.B, Eq.19) without affecting the 2-point resolution(limited by the laser pulse width). This means that in the caseof Fig.5, the detection bandwidth of theν−OTDR is B =

12·∆tgate

= 500 kHz6. To be able to compare the measuredresults in a representative manner, we average the conventionalOTDR trace in order to obtain the same bandwidth as wasused in theν−OTDR measurement. We gain 2.5 dB, yieldinga corrected dynamic range of 37 dB. Theν−OTDR advantageis found to be roughly 9 dB in this case.We repeat the measurement for different pulse widths keepingall other parameters unchanged. The final results are shownin Fig.6. The detection bandwidths were adapted as before. Itholds thatB = 1

2∆tpulsefor both devices.

For pulse widths between 30 ns and 1µs the dynamic rangedifference is about 9-10 dB. This is a direct consequence ofthe smallerNEPnorm,0 (see Sect.II-B) of the Geiger-modeAPD, since bandwidth and integration time per sampling pointwere equally chosen. This means that theNEPnorm,0 ofthe ν−OTDR is roughly a factor 63-100 smaller7 than theNEPnorm,0 of the conventional OTDR (noise dominated bythe small pulse amplifier). However, going to larger laserpulses, we observe increased noise for theν-OTDR and theadvantage gets smaller. We suppose that this happens due tothe increased backscatter power from the beginning of thefiber. Although the diode is not active, the charge persistenceeffect (also sometimes called charge subsistence) can haveanon negligible impact on the noise counts in a subsequentlyactivated gate (for more details see also Sect.III-D).In summary, by adapting sampling statistics and detection

6The conventional device uses a higher bandwidth since higher samplingresolution is useful when the position of an event needs to bedetermined withhigher precision.

7Respecting the functional dependence between NEP and dynamic rangegiven in Eq.25, usingNEP0 ∝ NEPnorm,0

10n 100n 1µ 10µ20

25

30

35

40

45

50

55

photon counting OTDRconventional OTDR

dyn

am

icR

ange

[dB

]

D tpulse

[s]

Fig. 6. Dynamic ranges of FTB-7600 andν−OTDR for different laser pulsewidths. The length of the used fiber was 200 km. The detection bandwidthsB were adapted in each case, it holds thatB = 1

2∆tpulse.

bandwidth of both devices we find an advantage of about 9-10 dB in dynamic range for theν-OTDR. By increasing thelaser pulse width we observe increased detector noise and theeffective advantage gets smaller. We uncouple the questionofmeasurement time since it is highly dependent on the gatingtechnique used in theν−OTDR. This discussion is postponedto section IV.

B. 2-point resolution

When considering the 2-point resolution8, one can divideOTDR operation into two regimes a) the receiver limited andb) the laser peak power limited regime. In case a) the ultimatetiming resolution is either given by the amplifier bandwidthorthe detector jitter (using fine laser pulses), whereas in case b)the limited laser peak power makes it necessary to use largerpulse widths (larger than the limit given in case a)) in orderto reach high dynamic ranges. In the receiver limited regime,the advantages of photon counting were already discussed in[20], yielding a maximal 2-point resolution of 10 cm for theν-OTDR and 1 m for the conventional device. In long haulOTDR applications, we operate in the laser peak power limitedregime.It is easy to see that in this regime the sensitivity advantage(NEPnorm,0) of photon counting translates directly into anadvantage in 2-point resolution.Example : we consider a reflective event at the end of thedynamic range (with a certain pulse width and measurementtime) of the FTB-7600, see Fig.7.The ν−OTDR can achieve the same dynamic range with amuch smaller pulse width, see Fig.6. According to App.D,an advantage of 10 dB in dynamic range9 corresponds to anadvantage in 2-point resolution by a factor of 20. In Fig.8 wesee the results of threeν−OTDR measurements focusing on

8By 2-point resolution we mean the minimal distance, necessary betweentwo reflective events, in order to be able to recognize them asdistinct peakson the OTDR trace output (e.g. dip between peaks at least 1 dB lower thanthe peaks themselves)

9Bandwidth normalized.

JOURNAL OF LIGHTWAVE TECHNOLOGY , VOL. X, NO. Y, JANUARY 200Z 6

0 20 40 60 80 100 120 140

-40

-30

-20

-10

0

10

102.70 102.75 102.80 102.85 102.90

-30

-28

-26

-24

dB

distance [km]

dB

distance [km]

Fig. 7. OTDR trace measured using the FTB-7600 with a laser pulse widthof 300 ns, acquisition time = 3min. The achieved dynamic range is about30 dB. At the transition to the noise level (at about 102.8 km), we can seea reflection peak (maybe two, see inset). The FTB-7600 cannotachieve abetter resolution of the peak without decreasing the laser pulse width. As thedynamic range would drop (keeping the acquisition time unchanged) and thepeak would not be seen anymore.

102.55 102.60 102.65 102.70 102.75 102.80

-10

-9

-8

-7

-6

-5

-4

-3

-2

∆

102.70 102.75 102.80 102.85 102.90

-9

-8

-7

-6

-5

-4

-3

∆tpulse

=100 ns

dB

distance [km]

102.76 102.78 102.80 102.82 102.84

-11

-10

-9

-8

-7

-6

-5

∆tpulse

=30 ns

dB

distance [km]

102.800 102.805 102.810 102.815 102.820-15

-14

-13

-12

-11∆t

pulse=10 ns

dB

distance [km]

Fig. 8. Step by step reduction of laser pulse width inν−OTDR measurement,when zooming on the reflective event seen by the FTB-7600 (Fig.7). The lowergraph is again a zoom on the two reflective events which were revealed bythe second graph (peak 2 and 3). Due to its larger sensitivitythe ν−OTDRcan afford smaller laser pulses at distances where the FTB-7600 reaches itslimits.

the reflective event at about 102.8 km. With each reductionin pulse width more and more structure is revealed and weactually find 3 reflections. The ratio of the peak widths agreeswell with the calculated one.In summary, when the OTDRs are operated in the laser

peak power limited regime, the sensitivity advantage of theν−OTDR translates directly into an advantage in 2-pointresolution. Its amount is described by Eq.27 in App.D.

C. Measurement time

We start discussing the measurement time by taking a lookat the time necessary to obtain a sufficient signal to noise ratio

(SNR) for a specific delay position in the fiber, from whichwe receive a backscatter powerPopt (see App.E):

t =1

fpulse·(

SNR ·NEPnorm ·√B

Popt

)2

(5)

whereNEPnorm (see Eq.20) is the noise equivalent powernormalized with respect to detector bandwidth in [W/

√Hz],

B the detector bandwidth in [Hz] andfpulse the laser pulserepetition rate in [Hz]. This formula applies to both the Geigerand linear mode operation as long as linearity between inputand output signal is guaranteed10.While the Geiger mode exhibits linearity only in a relativelyrestricted domain ofPopt, the linear mode is able to coverseveral orders of magnitude of input power. Therefore Eq.5is applicable for a much wider range of optical powers andshows the significant advantage of the linear mode when largerpowers need to be measured (∝ P−2

opt ).More interesting from theν−OTDR perspective is the casewhen Eq.5 applies as well for Geiger-mode, i.e. for sufficientlysmall powers (order -100 dBm). We can then easily calculatethe ratio of measurement times (assumingfpulse, B andPopt

to be equal):

t(conv)

t(pc)=

(

NEP(conv)norm

NEP(pc)norm

)2

(6)

where the superscriptpc signifies photon counting (i.e. Geigermode), andconv represents the conventional detection mode(i.e. linear mode).NEPnorm can be split into a signal initiated noise contributionNEPnorm,sig (e.g. due to signal shot noise) and a contributionfrom signal independent sources (dark current, dark counts)represented here byNEPnorm,0 :

NEP 2norm = NEP 2

norm,sig +NEP 2norm,0 (7)

For sufficiently small input power,NEPnorm becomesNEPnorm,0. In Sect.III-A we estimated the ratio of theNEPnorm,0 of conventional andν−OTDR to lie within 63and 100. Thus the ratio given in Eq.6 approaches a valuebetween 4000 and 10000. This means that we continuouslypass from a huge linear mode advantage (Popt large) to ahuge Geiger mode advantage (Popt small).We stress at this point that this result applies forthe measurement of a specific delay position. OTDRmeasurements consist of scanning a range of differentpowers, i.e. the exponentially decreasing backscatter power.In case of the conventional OTDR the achievement of asufficient SNR for a certain delay position, e.g. far down thefiber, means that all delays closer to the beginning of thefiber have been scanned at least with the same SNR. Thus wealready obtain the full trace up to that point. How large theactually scanned interval is in the case of photon countingdepends on the gating technique. For example, using the basicapproach, explained earlier (Fig.4), one would scan exactly

10Linearity in Geiger mode applies if the signal detection probability pergatepsig,gate depends linearly on the input powerPopt, see App.A Eq.9 &10. For sufficiently smallPopt it holds that :psig,gate = η ·

Popt·∆tgate

hν

JOURNAL OF LIGHTWAVE TECHNOLOGY , VOL. X, NO. Y, JANUARY 200Z 7

one position. In Sect.IV we discuss how the NEP advantageof photon counting can be used more efficiently.

D. Dead zone

Dead zones are parts of a fiber link where the OTDR tracedoes not display the actual Rayleigh backscatter, but a signalinduced by another source. One example that we have alreadyencountered is the afterpulsing effect. If not accounted for itleads to tails after large loss events or reflections (see Fig.3).Unfortunately this is not the only origin of dead zones. Ifwe mitigate the afterpulsing effect by using an appropriatedead time, another effect, very similar to afterpulsing getsdominant : charge persistence. Even though the APD is notbiased beyond breakdown between adjacent gates, there is stilla bias which can weakly multiply primary charges createdby photons incident during that time. These weak avalanchesmight however lead to increased trap population and increasednoise avalanche probability in the next gate (Vbias > Vbdown).This effect, although less severe than afterpulsing, becomesvisible under the same circumstances, namely after large lossevents and reflections.To estimate the impact of this effect on the OTDR output,

we perform a measurement on a fiber link containing a largeloss event (17 dB), with a reflection (-45 dB) just before it.This link simulates a typical situation encountered in passiveoptical networks, where a splitter of high multiplicity induces asignificant loss. Weak reflections right in front can be inducedby bad connectors.We perform a measurement of this particular fiber link situa-tion, using ourν−OTDR in basic mode, which ensures thatno afterpulsing effect is present and the charge persistenceeffect becomes visible. Our results, including the measurementusing the conventional OTDR, are shown in Fig.9. We observe

2 4 6 8 10 12

-16

-12

-8

-4

0

4

8

RBS level 2

RBS level 1

dB

distance [km]

conventional OTDR

photon counting OTDR-45dB Refl.

17 dB loss

Fig. 9. Behavior of conventional and photon counting OTDR when subjectedto significant change in backscatter power level (here : 17 dB). We introduceda reflection of -45dB in front of the loss, simulating for example a badconnector. The black line represents a fit of the backscatterbehind 8 kmand can be used as a reference to assess the magnitude of the dead zone.

the emergence of a tail approximately 10 dB below the lossedge, which decays by approximately 3.5 dB/km. The lowerRayleigh backscatter level gets visible again after about 2km(20µs).The result obtained with the conventional OTDR is muchbetter. The emergence of the tail starts on a significantly lowerlevel. Full sensitivity is regained after 1 km. The results foundfor the ν−OTDR, confirm the observations made in [20] and[25]. One possibility to mitigate dead zones, induced by chargepersistence, is the use of an optical shutter as performed in[25]. If the initial backscatter is blocked by the shutter andthe gate gets activated, as well as the shutter deactivated rightafter the loss event, much better results can be obtained.In summary, concerning dead zones, the conventional OTDRshows superior behavior, when no additional measures aretaken in the case of theν−OTDR, e.g. using an optical shutter.

IV. T IME EFFICIENT BIAS SCHEMES

The way we implemented theν-OTDR in Sect.III is oneof the simplest and trace acquisition is time consuming. Itis well suited to study general characteristics, but not forother applications. Its apparent drawback is the wasting ofbackscattered signal, due to the fact thatfgate = fpulse, i.e.only one gate per laser pulse is activated.A more efficient approach is thetrain of gatesscheme [20].Unlike to the basic mode, the gating frequency is higher thanthe laser pulse repetition rate and more than one gate getsactivated per laser pulse, see Fig.10. In the ideal case wecould choose a gating frequencyfgate in the way that thedesignated sampling resolution is obtained. Unfortunately wehave to account for the afterpulsing effect and thus need toapply a dead timeτ (whose length depends on the tolerableafterpulsing)11. In App.F we discuss the impact of dead timeon the detection statistics in detail. To follow the generaldiscussion here it can be skipped though.A measure for the acquisition speed is the achievable detectionrate fdet. We state a linearized formula forfdet, whichillustrates the most important relations very well :

fdet =1

1η·µ·Γ + τ

(8)

whereη is the detection efficiency, µ is the incident photonflux [photons/sec],Γ = fgate · ∆tgate is the detection dutycycle andτ is the dead time.a) high flux : If the photon flux is large, the detection rateis limited by the dead time, i.e.fdet,max = 1

τ. In order

to increase the detection rate, the dead time needs to bedecreased. In Sect.II-C we have already started to discuss thepossibilities of afterpulse mitigation. The quenching technique,that yields to date the lowest afterpulsing, israpid gating[12][13] [14]. Dead times of the order of 10 ns can be consideredrealistic. This is approximately a factor 1000 better than thebest actively quenched circuits can deliver. To maintain a

11Like depicted in Fig.10, we can number each gate in the train of gates,1...n. In the ideal case (no dead time) each of these gates gets activated foreach laser pulse sent into the fiber. In reality, when a dead time needs to beapplied, it is not certain that gate i gets activated. It is possible that it fallsinto the dead time application range (gate 4-7 in Fig.10).

JOURNAL OF LIGHTWAVE TECHNOLOGY , VOL. X, NO. Y, JANUARY 200Z 8

reasonable duty cycle, gating frequencies of the order of 1GHz are used (∆tpulse ≈ 200 ps).b) low flux : If the flux is small, the dead time is insignificant

Fig. 10. Different bias schemes for backscatter measurement : basic, trainof gates and free running mode.τ represents the dead time.

and fdet = η · µ · Γ. Here the most important parameter isthe duty cycleΓ which should be preferably high. Increasingthe duty cycle will finally lead to a situation that is calledfree running mode[18], Fig.10. The overbias is applied untila signal photon or a noise effect initiates an avalanche. Thephoton flux µ below which the free running modeyieldshigher detection rates is roughly1

η·τ, see also App.F. We

see that in this case improved afterpulsing and thus smallerdead times, would extend the application range to higherphoton fluxes. To date the best low afterpulsing solution forthe free running modeis the earlier discussed integrated activequenching approach [19]. Fig.11 illustrates our discussion.At this point we want to demonstrate, that using thefreerunning modein its application regime (low flux), the acqui-sition speed of the conventional OTDR can be considerablyoutperformed.Example : We want to scan a 10 km interval of a 200 kmfiber (⇒ fpulse = 500 Hz). We assumeτ = 10µs, η = 0.1⇒ the maximal flux isµ = 106 photons/s, which correspondsto a power ofPstart = −99 dBm12. At the end of the 10km interval the power drops to aboutPstop = −103 dBm(assuming regular fiber behavior, attenuation =0.2 dB/km).From Pstop one can inferpsig (Eq.22) and usingpdc= 2000s−1 we obtainNEP

(pc)norm = 3.6 · 10−16 W/

√Hz (see Eq.20),

which enters into Eq.5 for measurement time calculation. ThebandwidthB of the measurement is managed by appropriateaveraging of adjacent points after the full data is acquired.

12It depends on the laser power, pulse width and the fiber link quality, towhich distance this corresponds. ChoosingPpeak = 400 mW and assumingthat this is also the effective power that reaches the fiber (no internal loss),∆tpulse = 100 ns and a regular fiber behavior (loss = 0.2 dB/km), then -99dBm correspond to backscatter power coming from a distance of 158 km.

Fig. 11. According to Eq.8 we can determine the flux regimes where eachof the techniques at disposal deliver their best performance. In the low fluxregimeµ < 1

η·τthe detection duty cycle is most important, therefore the

free running modeis the optimal solution. As soon as the dead time becomesthe limiting factor for the detection rate,rapid gating can take advantage ofits significantly lower afterpulsing, resulting in much smaller required deadtimes.

Here we suppose a bandwidthB of 10 MHz (averaging on50 ns intervals) and a signal to noise ratio (SNR) of 4. Alltogether we compute a measurement time of approximately20 s.To obtain the time of the conventional OTDR we calculate

the NEP(conv)norm and the ratio of Eq.6. In the beginning of

Sec.III-C, we stated that theNEP(conv)norm,0 was about 63-100

times larger than theNEP(pc)norm,0 = 10−16 W/

√Hz. The

signal power is low enough to neglect the signal inducednoise contribution and we obtain simplyNEP

(conv)norm ≈ 63 ·

NEP(pc)norm,0 = 6.3 · 10−15 W/

√Hz

⇒ t(conv)

t(pc)=

(

6.3 · 10−15

3.6 · 10−16

)2

≈ 300

yielding a total measurement time for the conventional deviceof about 1.5 h, assuming the same detection bandwidthB.We stress that during this time, the conventional device obtainsinformation not only on our 10 km measurement range, butalso about the entire range before. Theν−OTDR only scansthe designated 10 km, but finishes doing this in around 20 s.

V. CONCLUSION

The huge advantage of Geiger-mode APDs with respect toits linear mode counterparts is the small core noise equivalentpowerNEPnorm,0. Our comparison of a state-of-the-art con-ventional OTDR (based on linear mode APD) and a photoncounting OTDR (based on Geiger-mode APD) reveals a differ-ence of roughly two orders of magnitude. We demonstrate thatthis resource has the potential to improve the dynamic rangeby10 dB as well as the 2-point resolution by a factor of 20 (in thelaser peak power limited regime). The important question is,how efficient can it be used in OTDR applications (concerningthe measurement time)? To sample the backscatter of a fiberwe have different possibilities at hand, i.e.train of gates(with classical gating),free running modeor rapid gating.For sufficiently low backscatter power (order of -100 dBm;long fibers) we show that thefree running modeis capable ofefficiently using the NEP advantage. For example, measuringa 10 km interval far down the fiber, yielded a measurement

JOURNAL OF LIGHTWAVE TECHNOLOGY , VOL. X, NO. Y, JANUARY 200Z 9

time of around 20 s, while the conventional device needs tointegrate for about 1.5 h to average out the noise sufficiently.At higher backscatter power, i.e. closer to the beginning ofthe fiber, we show thatrapid gatingcan largely profit from itsreduced afterpulsing, which makes dead times of the order of10 ns realistic.We see a combination ofrapid gatingfor the beginning of thefiber andfree running modefor its end part as the currentlybest ν−OTDR solution. Alternatively one can also imaginea hybrid of conventional OTDR for high flux and photoncounting for low backscatter power, including high resolutionscans with fine laser pulses on short distances.Concerning dead zones, the conventional OTDR is clearlysuperior. It is more robust to sudden changes in backscatterpower, while theν−OTDR suffers from the charge persistenceeffect. This effect can for example be mitigated by using anadditional optical shutter.

APPENDIX APOWER MEASUREMENT WITH GATEDAPD

We consider coherent light, with a mean photon numberper secondµ, incident on the diode (detection efficiencyη).We apply gates of duration∆tgate, which means that onaverageµ · ∆tgate photons hit the diode during a gate. Dueto the limited detection efficiency not every photon leads toadetection. If our detector would be photon number resolving,the average number of signal detections per gate would begiven byη·µ·∆tgate. Since our APD does not have this ability,all cases where more than one signal detection would occur,results in only one detection output. According to Poissonianstatistics, the probability of having no signal detection is givenby e−η·µ·∆tgate , hence the probability of having an APD signaldetection output is given by :

psig,gate = 1− e−η·µ·∆tgate . (9)

µ can be expressed by the incident optical powerPopt as

µ =Popt

hν(10)

Solving forPopt yields

Popt =−hν

η ·∆tgateln(1− psig,gate) (11)

Measuring the ratio of the number of detectionsNdet (in-cluding signal detectionsNsig and dark countsNdc ) and thenumber of activated gates (Ngate), yields the signal detectionprobability per gate

psig,gate =Ndet −Ndc

Ngate

and finally the incident optical powerPopt.If the signal is weak, then it is apparent that first of allthe signal needs to be separated from noise by applying asufficiently large number of gatesNgate, see also App.B. Oncethis is achieved, one has to consider the precision or statisticalerror of the result, which also is a function ofNgate. Twoexamples : a)Ngates = 10, ∆tgate = 100ns, pdc,gate =2 · 10−4, psig,gate = 0.2, the probability of a dark count to

appear is negligible and we obtain2 ±√2 signal counts=

total counts, from which we can calculate an optical inputpower lying in [0.7 pW, 5.3 pW]. b)Ngates = 10000 andthe other parameters like before, we obtain a number oftotal counts of2002 ±

√2002 from which 2 ±

√2 are dark

counts and2000±√2000 are signal counts. From the signal

counts we infer an optical input power lying within [2.8 pW,2.9 pW]. The statistical error of the second measurement ismuch smaller.

APPENDIX BNOISE EQUIVALENT POWER OFGEIGER-MODE APD

In the treatment of the APD noise we mainly consider twocontributions, i.e. the shot noise of a) the signal counts and b)the dark counts (assuming that afterpulse contributions can beneglected, for example by choosing a sufficiently large deadtime).Let Popt be the incident optical power on the diode. With theenergy per photonhν, the detection efficiencyη and the gatewidth∆tgate, we infer the signal detection probability per gate(linearized version of Eq.9, for sufficiently smallPopt) :

psig,gate = η · Popt ·∆tgatehν

(12)

After applyingNgate gates of the same width the mean numberof signal detectionsNsig is

Nsig = psig,gate ·Ngate (13)

Assuming Poissonian statistics we calculate the fluctuation

∆Nsig =√

psig,gate ·Ngate (14)

The same derivation holds for the dark counts : we introducea dark count probability per gatepdc,gate (which will bemeasured directly) leading to

∆Ndc =√

pdc,gate ·Ngate (15)

thus the total noise fluctuation :

∆Ntot =√

∆N2sig +∆N2

dc (16)

The noise equivalent power (NEP ) is inferred by calculatingthe optical power necessary to produce∆Ntot counts whenapplyingNgate gates. In order to achieve this we replacePopt

by NEP in Eq.12 and multiply byNgate:

∆Ntot = η · NEP ·∆tgatehν

·Ngate (17)

Using Eq.14-16 and solving forNEP yields

NEP =hν

η·√

psig,gate + pdc,gateNgate∆t2gate

[W] (18)

The minimal detectable powerNEP0 is obtained by settingthe signal shot noise contribution equal to zero :

NEP0 =hν

η·√

pdc,gateNgate∆t2gate

[W] (19)

The existence ofNgate in these equations represents theiteration of a measurement and is a function of time

JOURNAL OF LIGHTWAVE TECHNOLOGY , VOL. X, NO. Y, JANUARY 200Z 10

(Ngate = fpulse · t)). The elemental measurement timeis represented by∆tgate, the duration of a single gate,which can be interpreted as the detection bandwidth viaB := 1

2·∆tgate. These formulas are practical when aNEP

for a particular measurement needs to be calculated (see alsoApp.C). In order to obtain a formula which makes it easyto compare different detectors, we normalize with respect toNgate (which represents nothing else than the measurementtime) and bandwidthB :

NEPnorm =hν

η·√

2 · (psig + pdc) [W√Hz

] (20)

and

NEPnorm,0 =hν

η·√

2 · pdc [W√Hz

] (21)

wherepdc :=

pdc,gate∆tgate

, psig :=psig,gate∆tgate

(22)

are the signal and dark count probability per gate, normalizedwith respect to the gate width in seconds13.

APPENDIX CDYNAMIC RANGE OF OPTICAL TIME DOMAIN

REFLECTOMETER

The strongest backscatter signal is observed right after theemission at timet0 =

∆lpc

, coming from the fiber locationswithin the interval[0; ∆lp

2 ], wherec is the speed of light in thefiber and∆lp is the width of the laser pulse. The correspondingbackscatter power is given by [24]

PBS,0 = S · P0,eff · e−2αsL(1− e−αs∆lp) (23)

whereS is the fibers caption ratio,P0,eff is the effective laserpeak power corrected for internal component (e.g. circulator)and connector loss andαs the scattering coefficient. If weassume thatαs∆lp << 1, which is true in standard fiber (αs ≈0.04km−1) and∆lp < 2 km (∆tp < 10µs) we can expandthe exponential and get

PBS,0 ≈ S · P0,eff · αs ·∆lp (24)

The dynamic range is then given by the ratio ofPBS,0 andthe minimal detectable powerNEP0 [W ] (Eq.19):

dynR= 5 log(PBS,0

NEP0) (25)

where the factor 5 accounts for the roundtrip in the fiber.Finally we obtain :

dynR≈ 5 log(S · P0,eff · αs ·∆lp

NEP0) (26)

We note thatNEP0 like used here, includes the measurementtime and decreases∝

√t (see also Eq.19 in the case of the

13The relation between signal count/dark count probability per gate and gatewidth is almost linear over a large range of practical gate widths (typicallyranging from nanoseconds to microseconds).Knowingpsig and pdc makes iteasy to calculate the signal count and dark count probability of a particulargate of widths∆tgate, just by multiplying it by∆tgate.

ν−OTDR, where the measurement timet is represented bythe number of applied gates,Ngate = fpulse · t).The operational definition of the dynamic range of an OTDR,given for example in [24], contains a measurement time of3 minutes. It is apparent that an extended measurement timeenhances theNEP0 and thus the dynamic range. In general, ifthe measurement time is increased by a factord, the standarddeviation of the noise is lowered by a factor

√d and thus the

NEP0 by the same amount.

APPENDIX D2-POINT RESOLUTION ADVANTAGE OFν-OTDR

We assume anx dB ν-OTDR advantage in dynamic range(with respect to conventional OTDR, using the same laserpulse width∆lp). Now we look for a factorα such thatα·∆lpyields a reduction of theν-OTDR dynamic range byx dB.Using Eq.26,19 and∆tgate =

∆lpc

(adapting laser pulse widthand gate width) we have to fulfill

5log((α ·∆lp)3

2 ) = 5log((∆lp)3

2 )− x

yieldingα = 10−

2

15x (27)

For example :x = 10 dB → α = 0.046. Thus theν-OTDRcan achieve the same dynamic range with a 20 times smallerpulse width.

APPENDIX ESIGNAL TO NOISE RATIO AS FUNCTION OF MEASUREMENT

TIME

We derive a formula for the SNR ratio as a function oftime from the photon counting perspective. However, the finalresult, after linearization will not contain any photon countingspecific quantity and is therefore generally applicable.We define the signal to noise ratio(SNR) as the ratio ofsignal countsNsig to the total fluctuation of the counts∆Ntot

including fluctuation of signal and dark counts (like definedin App.B).

SNR =Nsig

∆Ntot

=psig,gate ·Ngate

√

(psig,gate + pdc,gate) ·Ngate

using Eq.13 and 16. Now we introduce the bandwidth normal-ized NEP (Eq.20) and useNgate = fpulse · t wheret is themeasurement time

⇒ SNR =

√2 · hνη

·psig,gate ·

√

fpulse · tNEPnorm ·

√

∆tgate

then replacingpsig,gate using Eq.9 and 10:

SNR =

√2 · hνη

·(1− e−

ηhν

·Popt·∆tgate) ·√

fpulse · tNEPnorm ·

√

∆tgate(28)

If the optical input power is sufficiently small, the signaldetection probability increases linearly with the opticalpowerand we can expand the exponential to obtain

SNR =Popt ·

√

fpulse · t ·√

2 ·∆tgate

NEPnorm

JOURNAL OF LIGHTWAVE TECHNOLOGY , VOL. X, NO. Y, JANUARY 200Z 11

=Popt ·

√

fpulse · tNEPnorm ·

√B

(29)

where we usedB = 12·∆tgate

, the detection bandwidth.This final formula is independent of any photon countingquantities and does also apply for the general case, includinglinear APD detection. In the linear regime there is even no suchsevere restrictions as in photon counting mode since muchhigherPopt can be processed.On the other hand, if measurement time needs to be calculatedas a function ofSNR, we obtain straight forward

t =1

fpulse·(

SNR ·NEPnorm ·√B

Popt

)2

(30)

APPENDIX FTRAIN OF GATES DISCUSSION

The application of a dead time can have considerable impacton the gate activation statistics. Fig.12 shows what happens ifthe productfgate · τ is chosen too large.If we assume, that the probability of detecting a signal photon

0 2 4 6 8 10 12 14 16 18 20 22 240

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

gate number [1/12] or distance [km]

gate

act

ivat

ion

prob

abili

ty

activation minimum

fgate

= 1.2 MHz, τ= 10µ s, psig,gate1

=0.2

Fig. 12. Dead time application (here :τ = 10µs corresponding to 1 kmin terms of sampling distance) has considerable impact on the gate activationstatistics. If the gating frequencyfgate is chosen too high, then the activationminimum approaches zero, no signal can be acquired there.

in the first gate of the train of gates ispsig,gate1 , then gate 2gets activated with probability(1 − psig,gate1) (otherwise itfalls into the dead time of gate 1). The probability that gateigets activated (i ≤ fgate · τ ) is then given by

pact,gate i = (1− psig,gate1)(i−1) (31)

where we assume, that the signal detection probability isalmost constant at the beginning of the fiber. This expressionapproaches 0 when i is large. In the worst case, ”activationholes” appear in a repetitive manner (see Fig.12, in the casewhere the minima of the periodic structure at the beginningtouch zero probability) and therefore detections around theselocations are impossible or only possible with very low statis-tics.To avoid this, we can define a criteria, which ensures thateach gate has a sufficient number of activations. The first

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

100

101

102

psig,gate1

f gate

,max

⋅ τ

activation min > 0.2activation min > 0.4activation min > 0.6activation min > 0.8

Fig. 13. The maximally allowed gating frequencyfgate,max, in order toavoid activation holes, is a function of the photon detection probability in thefirst gatepph,gate1 and the designated dead time, which itself is set by thedesignated afterpulsing probability. Depending on the choice of the activationminimum value one can infer the productfgate,max · τ , which also signifiesthe number of non activated gates after a detection. An example is given inthe text.

minimum plays the role of a bottleneck. When it is abovesome threshold (to be defined), all the other minima are aswell14. The minimum depends onpsig,gate1 andfgate · τ .Using Eq.31 we can calculate, the maximally suitable gatingfrequencyfgate,max, depending on a designated threshold, seeFig.13.Example : assumingτ = 1 µs, psig,gate1 = 0.25 and anactivation minimum of 0.4. Then we inferfgate,max · τ = 4(see arrows in Fig.13) and thereforefgate,max = 4

τ= 4 MHz.

If the maximally suitable gating frequencyfgate,max is notlarge enough to obtain the designated sampling resolution,it is necessary to shift the start delay of the train of gates.For instance, if we want a sampling resolution of 5 m, butfgate,max = 4 MHz, yielding only 25 m, we need to delaythe train (with respect to the laser pulse departure) four timesby 50 ns. This of course increases the total measurement timeby a factor 5.We note thatfgate,max, is in principle bounded by1/∆tgate.If the suggestedfgate,max, according to Fig.13, is larger than1/∆tgate, we are naturally led to thefree running mode, wherethe diode stays active until a detection is obtained [18], seeFig.10.This happens if

µ <b

η · τ (32)

or equivalently

Popt < hν · b

η · τ (33)

whereµ is the photon flux (number of photons per second,cw) and Popt the corresponding power,η the detectorefficiency, τ the detector dead time andb a constantdepending on the activation minimum criteria, explicitly :

14The reason for this is the fiber loss, which decreases the backscatteredsignal and therefore yields less detections and dead time applications. Thedead time effect gets less severe. When the backscatter power is very lowthere is almost no difference to the ideal case

JOURNAL OF LIGHTWAVE TECHNOLOGY , VOL. X, NO. Y, JANUARY 200Z 12

for an activation minimum of0.2(0.4, 0.6, 0.8), one obtainsb = 1.61(0.92, 0.51, 0.23). Due to its superior duty cycle, thefree running modeis the ideal low power solution.

ACKNOWLEDGMENT

The authors would like to thank EXFO for providing theFTB-7600 OTDR module and support, in particular S. Perron,J. Gagnon and G. Schinn. We also like to thank J.D. Gautierfor providing technical support and Bruno Sanguinetti forthorough cross-reading. We thank Swisscom for providingaccess to the fiber link between Geneva and Neuchatel.

REFERENCES

[1] ”Fiber waveguides: a novel technique for investigatingattenuationcharacteristics”, M. K. Barnoski and S. M. Jensen, Appl. Opt., Vol.15, Issue 9, pp. 2112-2115, (1976)

[2] ”Optical time domain reflectometry by photon counting”,P.Healey, P.Hensel, Electronics Letters Vol.16 Issue 16, p.631-633 (1980)

[3] Luciol instruments (www.sunrisetelecom.ch), Scientex(www.scientex.co.jp/english/index.html)

[4] ”Photomultiplier Tubes: Basics and Applications (3rd Edition)”, Hama-matsu Photonics, Hamamatsu City, Japan, (2006)

[5] ”Performance of InGaAs/InP avalanche photodiodes as gated-modephoton counters”, G.Ribordy, J.D. Gautier, H.Zbinden, N. Gisin, AppliedOptics 37 (12), pp.2272-2277, (1998).

[6] ”Picosecond superconducting single-photon optical detector”, G. N.Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K.Smirnov, B. Voronov, A. Dzardanov, C. Williams, R.Sobolewski, Appl.Phys. Lett. 79, 705 (2001)

[7] ”Detection of single infrared, optical, and ultraviolet photons usingsuperconducting transition edge sensors”, B. Cabrera, R. M. Clarke, P.Colling, A. J. Miller, S. Nam, R. W. Romani, Appl. Phys. Lett., Volume73, Iss. 6, (1998)

[8] ”A single-photon detector in the far-infrared range”, S. Komiyama, O.Astafiev, V. Antonov, T. Kutsuwa, H. Hirai, Nature, Vol. 403,pp. 405-407, (2000)

[9] ”Superconducting Tunnel Junction Photon Detectors: Theory and Ap-plications”, S. Friedrich, J.Low Temp. Phys. 151, pp. 277-286, (2008)

[10] ”Photon counting for quantum key distribution with Peltier cooledInGaAs/InP APDs” D.Stucki, G.Ribordy, A. Stefanov, H. Zbinden, J.G.Rarity, T. Wall, Journal or Modern optics Vol.48 No. 13, 1967-1982,(2001)

[11] ”Single-photon counting for the 1300-1600-nm range byuse of aPeltier-cooled and passively quenched InGaAs avalanche photodiodes”,J.G.Rarity, T.E.Wall, K.D.Ridley, P.C.M. Owens, P.R.Tapster, Appl.Opt.Vol.39, No.36 (2000)

[12] ”High speed single photon detection in the near infrared”, Z.L.Yuan,B.E.Kardynal, A.W. Sharpe, A.J. Shields, Appl.Phys.Lett.91, 041114(2007)

[13] ”800 MHz Single-photon detection at 1550-nm using an InGaAs/InPavalanche photodiode operated with a sine wave gating”, N. Namekata,S. Sasamori, S. Inoue, Opt. Express, Vol. 14, No. 21 (2006)

[14] ”Practical fast gate rate InGaAs/InP single-photon avalanche photodi-odes”, J. Zhang, R. Thew, C. Barreiro, H. Zbinden, Appl. Phys. Lett.95, 091103 (2009)

[15] ”1.5 µm photon counting optical time-domain reflectometry with asingle-photon detector based on upconversion in a periodically poledlithium niobate waveguide”, E. Diamanti, C.Langrock, M.M.Fejer, Y.Yamamoto, Opt.Lett. Vol. 31 No. 6 (2006)

[16] ”High resolution optical time domain reflectometer based on 1.55µmup-conversion photon-counting module”, M. Legre, R.Thew, H.Zbinden,N. Gisin, Opt. Express, Vol. 15 Issue 13, pp.8237-8242 (2007)

[17] ”Avalanche photodiodes and quenching circuits for single-photon detec-tion”, S. Cova, M. Ghioni, A. Lacaita, C. Samori, F. Zappa, Appl. Opt.,Vol. 35, Iss. 12, pp. 1956-1976, (1996)

[18] ”Free-running InGaAs/InP Avalanche Photodiode with Active Quench-ing for Single Photon Counting at Telecom Wavelengths”, R.T. Thew,D. Stucki, J.D. Gautier, A. Rochas, H.Zbinden, Appl. Phys. Lett. 91,201114 (2007)

[19] ”Comprehensive Characterization of InGaAs/InP Avalanche Photodiodesat 1550 nm with an Active Quenching ASIC”, J. Zhang, R. Thew, J.D.Gautier, N. Gisin, H. Zbinden, IEEE J. Quantum Electron., vol. 45, no.7, pp. 792-799, (2009)

[20] ”Photon-Counting OTDR for Local Birefringence and Fault Analysis inthe Metro Environment” M.Wegmuller, F. Scholder, N. Gisin,Journalof Lightwave Technology, Vol. 22, No.2 (2004)

[21] ”Photodiode Technical Guide” Hamamatsu,http://sales.hamamatsu.com/assets/html/ssd/si-photodiode/index.htm

[22] ”Avalanche Photodiode : A User Guide”, Application Note Perkin Elmer[23] ”Fundamentals of Photonics” B.E.A. Saleh, M.C.Teich,John Wiley &

Sons second edition Chapter 17 ”Semiconductor Photon Detectors”[24] Fiber Optic Test and Measurement, Dennis Derickson, Prentice Hall

(1998)[25] ”Long-distance OTDR using photon counting and large detection

gates at telecom wavelength”, F.Scholder, J.D. Gautier, M.Wegmuller,N.Gisin, Optics Communications 213, 5761,(2002)