  It is critical to construct an accurate optical model of photomultiplier
tubes (PMTs) in many applications to describe the angular and spectral
responses of the photon detection efficiency (PDE) of the PMTs in their working
media. In this study, we propose a new PMT optical model to describe both light
interactions with the PMT window and optical processes inside PMTs with
reasonable accuracy based on the optics theory and a GEANT4-based simulation
toolkit. The proposed model builds a relationship between the PDE and the
underlying processes that the PDE relies on. This model also provides a tool to
transform the PDE measured in one working medium (like air) to the PDE in other
media (like water, liquid scintillator, etc). Using two 20" MCP-PMTs and one
20" dynode PMT, we demonstrate a complete procedure to obtain the key
parameters used in the model from experimental data, such as the optical
properties of the antireflective coating and photocathode of the three PMTs.
The proposed model can effectively reproduce the angular responses of the
quantum efficiency of PMTs, even though an ideally uniform photocathode is
assumed in the model. Interestingly, the proposed model predicts a similar
level ($20\%\sim30\%$) of light yield excess observed in the experimental data
of many liquid scintillator-based neutrino detectors, compared with that
predicted at the stage of detector design. However, this excess has never been
explained, and the proposed PMT model provides a good explanation for it, which
highlights the imperfections of PMT models used in their detector simulations.
