Non-Markovian Property of Afterpulsing Effect in Single-Photon Avalanche Detector

Abstract

The single-photon avalanche photodiode(SPAD) has been widely used in research on quantum optics. The afterpulsing effect, which is an intrinsic character of SPAD, affects the system performance in most experiments and needs to be carefully handled. For a long time, afterpulsing has been presumed to be determined by the pre-ignition avalanche. We studied the afterpulsing effect of a commercial InGaAs/InP SPAD (The avalanche photodiode model is: Princeton Lightwave PGA-300) and demonstrated that its afterpulsing is non-Markovian, with a memory effect in the avalanching history. Theoretical analysis and experimental results clearly indicate that the embodiment of this memory effect is the afterpulsing probability, which increases as the number of ignition-avalanche pulses increase. This conclusion makes the principle of the afterpulsing effect clearer and is instructive to the manufacturing processes and afterpulsing evaluation of high-count-rate SPADs. It can also be regarded as a fundamental premise to handle the afterpulsing signals in many applications, such as quantum communication and quantum random number generation.

Comparative study of afterpulsing behavior and models in single photon counting avalanche photo diode detectors

“… 19 provides evidence for the hyperbolic sinc model. Recently 26 showed that the afterpulse probability is dependent on past events–a property not considered in the exponential, power, or hyperbolic sinc models. By comparing previously reported results to our own, we realize that there is a large variation between the different commonly used manufactures/makes of detectors and between individual detectors.…”

Reducing Afterpulsing in InGaAs(P) Single-Photon Detectors with Hybrid Quenching

“…These afterpulses will trigger more afterpulses later, and eventually contribute to a large number of afterpulses. This phenomenon is usually called the higher-order afterpulsing effect [18]. When active quenching is added with high-frequency gated-passive quenching, it can maintain the excess bias at a value below break down voltage for a short period of time, e.g., the first tens of nanoseconds, which physically closes the following tens of gates after an avalanche event and prevents the release of afterpulses within these gates.…”

Counting Statistics of Actively Quenched SPADs Under Continuous Illumination

“…For more information, see https://creativecommons.org/licenses/by/4.0/ The proposed counting model generalizes known approaches that only consider dead time [23], [24] by incorporating afterpulsing and twilight pulsing. Afterpulsing is also generalized [25], [26], being treated as a translated point process [27]. A Monte Carlo simulation algorithm is provided [22] that accurately reproduces desired counting statistics under stated assumptions [28], [29].…”

“…Each type of trap has its own exponential decay rate γ, its occurrence density in the material and a certain probability of being populated (we assume a constant avalanche charge). These traps work independently [26], which means that after each detection, the set of n AP populated traps {γ k } n AP k=1 is a realization of an inhomogeneous Poisson point process with intensity ρ(γ). This allows for both discrete and continuous spectra of γ (see the Suppl.…”

“…Subsequently, the occurrence of afterpulses in time t becomes a translated point process with intensity ρ (t) = γ exp(−γt)ρ(γ)dγ. This process is considered unaffected by later detection avalanches [26] and is therefore superimposed on the counting process of the detector. Because of recovery time, we only consider the offset intensity ν(t) := ρ (t + τ R ).…”