Method for characterizing single photon detectors in saturation regime by cw laser

Transcription

1 Method for haraterizing single oton detetors in saturation regime by w laser Jungmi Oh, Cristian Antonelli, 2 Moshe Tur, 3 and Misha Brodsky,* AT&T Labs, 2 S. Laurel Ave., Middletown, New Jersey 7748, USA 2 Department of Eletrial and Information Engineering and CNISM, University of L Aquila, L Aquila 674, Italy 3 Shool of Eletrial Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel * brodsky@researh.att.om Abstrat: We derive an analytial expression for the ount probability of a single oton detetor for a wide range of input optial power that inludes afterpulsing effets. We onfirm the validity of the expression by fitting it to the data obtained from a saturated ommerial Single Photon Detetor by illuminating it with a w laser. Detetor effiieny and afterpulsing probability extrated from the fits agree with the manufature spes for low repetition frequenies. 29 Optial Soiety of Ameria OCIS odes: (27.557) Quantum detetors; (27.529) Photon statistis; (6.238) Fiber optis soures and detetors. Referenes and links. B. F. Levine, D. G. Bethea and J. C. Campbell, Near room temperature.3 um single oton ounting with a InGaAs avalanhe otodiode, Eletron. Lett. 2, (984). 2. D. Stuki, G. Ribordy, A. Stefanov, H. Zbinden, J. G.Rarity and T. Wall, Photon ounting for quantum key distribution with Peltier ooled InGaAs/InP APD s, J. Mod. Opt. 48, (2). 3. M. Wegmuller, F. Sholder and N. Gisin, Photon ounting OTDR for Loal Birefringene and Fault Analysis in the Metro Environment, J. Lightwave Tehnol. 22, 39-4 (24). 4. D. S. Bethune, W. P. Risk and G. W. Pabst, A high performane integrated single oton detetor for teleom wavelengths, J. Mod. Opt. 5, (24). 5. A. Yoshizawa, R. Kaji and H. Tsuhida, Quantum effiieny evaluation method for gated-mode single oton detetor, Eletron. Lett. 38, (22). 6. PGA-6, 7. M. A. Itzler, R. Ben-Mihael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zpa and R. Ispasoiu, Single oton avalanhe diodes (SPADs) for.5 um oton ounting pliations, J. Mod. Opt. 54, (27). 8. X. Jiang, A. A. Itzler, R. B. Mihael and K. Slomkowski, InGaAsP-InP avalanhe otodiodes for single oton detetion, IEEE J. Sel. Top. Quant. Eletron. 3, (27). 9. Y. Kang, H. X. Lu, Y.-H. Lo, D. S. Bethune and W. P. Risk, Dark ount probability and quantum effiieny of avalanhe otodiodes for single-oton detetion, Appl. Phys. Lett. 83, 2955 (23).. J. Zhang, R. Thew, J. D. Gautier, N. Gisin and H. Zbinden, Comprehensive haraterization of InGaAs/InP avalanhe otodiodes at 55 nm with an ative quenhing ASIC, IEEE J. Quantum Eletron. 45, (29).. S. V. Polyakov and A. L. Migdall, High auray verifiation of a orrelated oton-based method for determining Photon ounting detetion effiieny, Opt. Express 5, (27), Introdution Photon ounting by InGaAsP/InP diodes at 55 nm wavelength was reported a quarter of entury ago []. Sine then Single Photon Detetors (SPD) have found a range of pliations from quantum information experiments [2] to fiber haraterization tehniques [3]. To ensure proper operation of SPDs, various proahes for testing SPD have been developed. Modern advaned methods suh as the interleaved bias method [4] and the time-interval analysis

2 method [5] permit extration of both the afterpulsing probability and the detetor effiieny. However, these methods rely on ompliated timing ontrol shemes and extremely low input power levels. Thus, they require expensive equipment suh as eletroni time delays, pulsed lasers, high dynami range attenuators and sensitive power meters, and might not be suitable for field pliations. An end-user of reent generation portable table-top instruments ould benefit from a simple method that works at relatively high power levels and requires only a onventional w laser. In this letter, we demonstrate a new haraterization method for Single Photon Detetors that utilizes a w laser at modestly high power ranging from 6dBm to 53dBm (for our detetors this orresponds to the average number of oton per gate,, of 3 2). First, we measure probability of a ount over a range of power and trigger rates for both pulsed and w lasers. The data suggest higher afterpulsing probability at higher rates, whih, unexpetedly, is aompanied by a slight derease in detetor effiieny. These tendenies are more pronouned with w lasers than with pulsed lasers. Then, we fit the experimental results by a newly derived analytial expression using the detetor effiieny and afterpulsing probability as fitting parameters. Our fits perfetly math the data within rms deviation of <.3%. Extrated effiienies of 2%, and onditional afterpulsing probability in the range of. -.3 for 25 khz trigger rate (devie dependent) are similar to the values reported in manufaturer tests performed at the onventional low power regime of =. [4]. We found that in the w regime the afterpulsing is somewhat stronger and deays faster with the harateristi time of 2.5-3s, whih is shorter than the 4-5s measured for pulsed laser. This observation suggests that different proesses dominate in the w and pulsed regime. But when the trigger rates are below 2 khz the results obtained by w and pulsed methods are nearly idential. 2. Experimental setup Figure shows our experimental setup. Light from a standard teleom nm w laser is fed via a 3dB oupler to a variable attenuator and into a detetor under test. For our experiments we used several ommerial SPDs, operating in a gated mode [6-8]. To determine the effetive detetor gate and to ompare our results with those obtained by the onventional pulsed laser method [4] we onneted a 55nm pulsed laser soure (idquantique, id3) to the other input of the 3dB oupler. The laser optial pulse width is about 3ps. We used a double stage variable attenuator with a range of 85dB. Eah stage was alibrated independently at relatively high power levels of -5dBm by using a power meter. The alibration enabled us to ontrol the power preisely at levels below the sensitivity of our power meter. Thus, the average number of otons per detetor gate,, was adjusted down to.2 for both w and pulsed soures. The detetor produes an eletrial NIM pulse (Nulear Instrumentation Module Standard) for eah detetion event. These NIM pulses were then integrated by an eletroni ounter. w.55 m laser soure short-pulse laser soure =.55 m 5 : 5 oupler Variable attenuator Fig.. The experimental setup. Single oton detetor Power meter In order to determine the average number of otons per detetor gate in the w regime, we measure the effetive gate window of the detetor, g. Eah ounting yle, a short ns-wide eletrial bias pulse brings the diode above the breakdown voltage. Conventionally, the maximum effiieny ahieved at the peak of the bias pulse is measured with a properly aligned narrow optial pulse [4] and serves as the major spe for SPDs. On the other hand, w light experiene effiieny that hanges during the bias pulse in a nonlinear fashion. To

3 simplify alulations, we model the SPD in the w regime as operating at its maximal effiieny value for an effetive gate window g. To assess g experimentally, we first measure the probability of a ount P over a wide power range of eah w and pulsed laser. The repetition rate of the detetor is R=kHz in both ases, and the pulsed laser is synhronized with the detetor. Then we pik the values of the w laser power P w and the average pulsed laser power P p that equates the orresponding ount probabilities P Pw P Pp Pp Pw log R. Finally the gate window an be alulated as: g, where the power values P p and P w are in dbm. When averaged over the entire power range this proedure results in g in a range of.49ns.59ns for different detetors. P pulsed laser w laser Fig. 2. Measured ount probability P as a funtion of the average number of otons per gate for pulsed ( ) and w ( ) laser. Here g.49ns. Figure 2 plots measured ount probabilities P as a funtion of the average number of otons per gate P w P w g h and p p, where h is the Plank h R onstant and is optial frequeny. Here the value g.49ns equates the measured ount probabilities in the w and the pulsed. Although here we determined the effetive gate window g by ourselves, it ould preferably be provided by the manufaturer as one of the instrument s spes. 3. Derivation of the detetor ount probability The dependene shown in Fig. 2 saturates beause avalanhe SPDs are not sensitive to the number of registered otons. For the Poissonian oton statistis, this saturation was first desribed by a simple expression in [], P ( P ) exp( ) () Here P is the probability of a dark ount, μ is the average number of otons per SPD gate and is the detetor effiieny. However, we find that our data deviates from suh dependene in two ways. First, we find that the measured probability is somewhat higher at lower μ values, whih suggests the presene of afterpulses [7-8]. Seond, the entire urve seems to be tilted toward higher μ indiating a slight derease in effiieny. These two effets beome more pronouned with higher repetition rates. To aount for these deviations we modify the expression for the ount probability to inlude the afterpulsing effet.

4 We haraterize the afterpulsing effet by the onditional probability Q( t ) of having an avalanhe for the detetor gate being open after a time interval t sine the suessful detetion event. We further assume that this onditional probability deays exponentially with a time onstant : Q( t ) Q exp t [9]. Then Q n is the onditional probability of the avalanhe ourrene after exatly n lok yles in the detetor that is gated with the trigger rate R: Q Q exp n n (2) R Within this model the overall probability of a registered event P an be found to be 2 e P 2 R 2 e P P Q R 2 2 R P P Q 4 e P P (3) Here P would be probability of deteting otons generated by the soure under srutiny in the absene of both dark ounts and afterpulses. For a Poissonian soure of single otons, suh as attenuated oherent laser light, P exp. As an aside, we would like to mention that if a low-power Poissonian soure of oton pairs is available instead of attenuated laser light, then Eq. (3) still an be used, but with P exp 2. The derivation of Eq. (3) is aomplished in two steps. The first step onsists of evaluating the marginal probability of an afterpulse P : ( n2 ) ( n2 ) ( n3 ) P P Q P P P Q... P P Q 2 3 (4) where the supersript n denotes that the orresponding probability is evaluated at the n-th time interval. Note that Q k is a onditional probability of an afterpulse given that no ounts our during the time t k R. Substitution of Eq. (2) into Eq. (4) yields: P P Q Q P Q P (5) After a some large number of trigger yles the probabilities P and P reah their stationary values and an be replaed by P and P, respetively, in Eq. (5), whih hene an be solved for P, yielding P P Q (6) P Q Q Finally, the seond step of our derivation onsists of extrating P from P P P P, where P is given by Eq. (6). Note that for Q or (that is Q ) Eq. (6) yields P, hene P, as evaluated from P P P, redues to the simple form given by Eq. ().

5 5 2 P Fig. 3. Count probability P versus average number of otons per gate w. 2 for w laser at different trigger rates of khz ( ) and MHz( ). Inset: a zoom in with more trigger rates. Data is shown by symbols, lines are fits. 4. Experimental results Figure 3 shows the measured ount probability for w laser for the average inoming oton P number w w g h f ranging from. to 2. The data taken at eah of the four different trigger rates is plotted in different symbols. Our alulation presented above shows that for eah trigger rate R the experimental dependene of P on w an be desribed by the expression in Eq. (3), omputed with the orresponding values of R. This allows us to extrat the effiieny for eah trigger rate ( R ), the afterpulsing onstant Q o, and the detr time by fitting Eq. (3) to the data. We first measure the rate dependent dark ount probability P. Then we perform a simultaneous fit to all four experimentally obtained dependenies of the ount probability on the average oton number. By inserting the resulting parameters bak into Eq. (3) we plot lines in Fig. 3. The high quality of the fits an be learly seen. In fat, by using only a limited range of w 3 2 (orresponding to easily measurable interval of 6dBm Pw 53 dbm ) we obtained a nearly perfet math to our data within rms 4 deviation of 3. Thus we onlude that the basi detetor parameters an be extrated from measured oton ounts at a relatively high number of inoming otons. Additionally, we ply our high power haraterization method for both pulsed and w lasers. The extrated effiieny is shown on the top panel of Fig. 4 as squares (w soure) and triangles (pulsed soure). For low repetition rates R khz and R 25kHz the two methods produe nearly idential results. At R 25kHz the measured effiieny is 2%, whih is suffiiently lose to the spe value of 2% at that frequeny. Our data indiate that the effiieny drops somewhat with repetition rate. However, this drop is rather dramati for the w regime and results in 2% deviation from the value of 9.7 %, measured in the pulsed regime at R MHz. The observed trends in the effiieny are also refleted in the afterpulsing probabilities. The latter is illustrated in the bottom panel as Q( t ) Q exp t, with the onstant Q and detr time extrated by the fits. Again we obtain for the two regimes very similar results for times longer than 4 5s, orresponding to rates less than 2 25kHz. For small time values afterpulsing for the w regime grows signifiantly. In fat, the w detr time 2.5 3s pears to be somewhat smaller than the values w.8.7 khz 25 khz 5 khz MHz

6 obtained for the pulsed regime pulsed 4 5s, whih are more onsistent with those reported by the manufaturer [7-8]. We speulate that the relaxation in the w regime might be a ombination of several proesses beyond afterpulsing, with the other proesses suh as the harge persistene or twilight effet being dominant for small time values in the w regime [-]. (%) Q(t) 24 2 w pulsed trigger rate R (khz) time (s) Fig. 4. Top: extrated detetor effiieny at different trigger rates R for w ( ) and pulsed ( ) lasers. Bottom: onditional afterpulsing probability for w (red thin line) and pulsed (blue thik line) measurements. 5. Conlusion We presented a new method of extrating the SPD effiieny and the afterpulsing probability. The method onsists of measuring oton ounts at relatively high w power at several repetition rates and fitting the data with a newly derived analytial expression. We show that the method produes good results for repetition rates below 25 khz. Suh a simple and reliable method ould potentially help a servie provider with maintenane and onfiguration of QKD systems. w pulsed