Polarization-encoded photon statistics for counting dipole emitters
Abstract
Counting the emitters within a diffraction-limited region is a prerequisite for localizing overlapping molecules. Under pulsed excitation, each molecule emits at most one photon per pulse, so photon-number-resolved detection can count emitters without resolving them. But the required number of pulses grows steeply with the emitter number. Here we show that polarization, conventionally used to measure the orientations of dipole emitters, also carries information on their number. Because mean polarization-resolved signals are unchanged when every emitter is replaced by multiple dimmer copies, this information resides in the photon statistics within each pulse, which polarization reshapes in two ways. Linearly polarized excitation at three angles increases the sub-Poissonian deficit of the photon count by a factor of 1.5 for any emitter orientation, and detection in four polarization channels reveals the emitter number through how the photons of multiphoton pulses are distributed among the channels. Maximum-likelihood simulations for two to five emitters of unknown orientations and brightnesses show that three-angle excitation reduces the required number of pulses by about 2.3-fold, close to the predicted 1.52=2.25, and that adding four-channel detection raises the reduction to as much as 4.8-fold. These gains require only polarization optics added to photon-number-resolved detection.
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BibTeX
@misc{zhang2026polarizationencoded,
title = {{Polarization-encoded photon statistics for counting dipole emitters}},
author = {Oumeng Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32885},
eprint = {2610.32885},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32885},
}
RIS
TY - UNPB
TI - Polarization-encoded photon statistics for counting dipole emitters
AU - Oumeng Zhang
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32885
UR - https://arxiv.org/abs/2610.32885
AB - Counting the emitters within a diffraction-limited region is a prerequisite for localizing overlapping molecules. Under pulsed excitation, each molecule emits at most one photon per pulse, so photon-number-resolved detection can count emitters without resolving them. But the required number of pulses grows steeply with the emitter number. Here we show that polarization, conventionally used to measure the orientations of dipole emitters, also carries information on their number. Because mean polarization-resolved signals are unchanged when every emitter is replaced by multiple dimmer copies, this information resides in the photon statistics within each pulse, which polarization reshapes in two ways. Linearly polarized excitation at three angles increases the sub-Poissonian deficit of the photon count by a factor of 1.5 for any emitter orientation, and detection in four polarization channels reveals the emitter number through how the photons of multiphoton pulses are distributed among the channels. Maximum-likelihood simulations for two to five emitters of unknown orientations and brightnesses show that three-angle excitation reduces the required number of pulses by about 2.3-fold, close to the predicted 1.5^2=2.25, and that adding four-channel detection raises the reduction to as much as 4.8-fold. These gains require only polarization optics added to photon-number-resolved detection.
ER -