Can an "impulse response" really be defined for a photoreceiver?

TL;DR

This paper critically examines the concept of impulse response for photoreceivers, arguing that it is ill-defined when applied to single-photon detection due to fundamental theoretical limitations.

Contribution

It challenges the applicability of traditional impulse response formalism to single-photon photodetectors, highlighting conceptual and theoretical issues.

Findings

Impulse response is ill-defined for single-photon detection.

Traditional analog linear system formalism does not extend straightforwardly to quantum-level detection.

The concept of a predictable output pulse for a photon impulse is problematic.

Abstract

In this paper we examine the validity of the concept of impulse response employed to characterize the time response and the signal-to-noise ratio of p-i-n and similar photodetecting devices. We analyze critically the way in which the formalism of analog linear systems has been extrapolated, by employing results from macroscopic electromagnetic theory such as the Shockley--Ramo theorem or any equivalent approach, to the extreme case of a single-photon detection. We argue that the concept of "response to an optical impulse" is ill-defined in the customary terms it is envisioned in the literature, this is, as an output current pulse having a certain predictable, calculated temporal shape, in response to the detection of an optical "Dirac delta" impulse, conceived in turn as the absorption of a single photon.