Photon-Number Discrimination from Increasing Time-of-Arrival Separation in Wide Superconducting Microstrip Single-Photon Detectors

Measurements of photon-number-dependent time-of-arrival (TOA) distributions in wide NbN superconducting microstrip single-photon detectors (SMSPDs) are presented. Two \SI{10}{\um}-long devices with widths of \SI{3.2}{\um} and \SI{6.4}{\um} are characterized under pulsed \SI{515}{nm} excitation. The TOA histograms are described by sums of exponentially modified Gaussian (EMG) components, with the wider device exhibiting components assigned to photon numbers up to $n=8$. Adjacent TOA peaks become more distinguishable relative to their widths at higher photon number, in contrast to the compression of neighboring photon-number timing shifts observed in conventional narrow-wire SNSPDs. For the components assigned to $n=7$ and $n=8$, the FWHM-normalized peak separation is $2.15$, and the fitted EMG distributions yield an equal-prior pairwise TOA-assignment fidelity of $99.6\%$. The EMG exponential-tail parameter $τ_n$ decreases strongly with photon number, while the Gaussian-location parameter $μ_n$ continues to shift between neighboring components. A phenomenological model motivated by absorption-site-dependent vortex processes and collective current redistribution captures these timing trends. These results support wide SMSPDs as a platform for TOA-based photon-number discrimination at high photon number, relevant to multiphoton-state characterization and photonic quantum information processing. The same geometry also provides a setting to examine how the spatial distribution of photon absorption affects vortex-assisted detection.