Development of a comprehensive PMT optical model for the JUNO experiment

TL;DR

This work develops a comprehensive PMT optical model for JUNO by jointly fitting PDE and reflectance data to extract per-PMT photocathode and anti-reflective coating thickness maps, CE, and wavelength-dependent optical constants across $300$--$700$ nm. By decomposing the PDE into absorption, escape factor, and collection efficiency ($PDE(\lambda,\alpha,\vec{r})=\sum_j a_j\beta_j\rho_j\,CE_j=\sum_j a_j\beta_jF_j$), the authors decouple quantum efficiency from CE, enabling per-PMT non-uniformities to be captured through thickness maps $d_{PC}(\theta)$ and $d_{ARC}(\theta)$ with $d_{PC,ARC}=c_2\theta^2+c_1\theta+c_0$. The model uses $n$, $k$ for the PC and ARC across 300–700 nm, leveraging a dispersion-based extension for the ARC and a permittivity-based approach for the PC, with an escape factor derived from measured PDE. Results include thickness distributions for all 17,612 PMTs, per-PMT CE curves, and extensive optical-property spectra, revealing significant reflectance variations between HPK and NNVT PMTs and only modest PDE changes at small incidence angles. The comprehensive model, once integrated into JUNO simulations, is expected to sharpen energy-response predictions and can serve as a reference for other PMT-based experiments.

Abstract

There are 17,612 20-inch photomultiplier tubes (PMTs) installed at the Jiangmen Underground Neutrino Observatory (JUNO). Developing a precise optical model for the PMTs is crucial for enhancing the accuracy of detector simulations and refining the energy response model at JUNO. In this study, we established a comprehensive PMT optical model based on prior studies, taking into account the non-uniformity of photon detection efficiency (PDE) across the PMT surface and the variances in PDE as well as reflections among different PMTs. By collecting reflectance data from 669 PMTs and utilizing PDE data from mass testing systems, we estimated the thickness maps of the photocathode (PC) and the anti-reflective coating (ARC) for each PMT. We also determined the collection efficiency (CE) by decomposing PDE with consideration of the optical processes occurring within the PMTs. The refractive index and extinction coefficient of both the PC and ARC, along with the escape factor, were evaluated over a broad wavelength range of 300~nm to 700~nm, covering the entire spectrum of interest for JUNO. Compared to the prediction from a simplified PMT optical model, which assumes uniform PC and ARC across all PMTs of the same type, the further developed PMT optical model yields much more reflectance for HPK PMTs and less for NNVT PMTs, and the change in PDE is at the level of a few percent. This comprehensive PMT optical model also provides a valuable reference for other PMT-based applications.

Figures (10)

• Figure 1: Contours of reflectance (top) and absorptance (bottom) at 415 nm and 420 nm, respectively, as a function of thicknesses of the ARC (x-axis) and PC (y-axis) for the HPK PMT (left), NNVT normal-QE PMT (middle) and NNVT high-QE PMT (right).
• Figure 2: The zenith angle distribution contributing to the total absorption for HPK PMTs shown in red, NNVT normal-QE PMTs in green, and NNVT high-QE PMTs in blue, and the ratio of the contributions from transmitted photons is shown in the last panel.
• Figure 3: The schematic diagram of the reflectance setup.
• Figure 4: An example of the measured spectra: the background (blue), the PMT (green), and the reference sample (orange).
• Figure 5: The measured reflectance of the HPK PMTs (left), NNVT normal-QE PMTs (middle), and NNVT high-QE PMTs (right). The solid blue lines shown in the figure represent the average reflectance for each type of PMT.