KAHIBARO
33.1. Introduction to Optical Physics
Table of Contents
Scintillation
Scintillation is the process where a material converts deposited particle energy into visible or ultraviolet light. In Geant4 you do not simulate the microscopic atomic physics in detail. Instead, you tell Geant4 how many optical photons to create per unit of deposited energy, how fast they are emitted, and with what spectrum and angular distribution.
A scintillating material absorbs energy from charged particles or high energy photons. This energy excites atoms or molecules into higher energy states. When they de excite, part of the energy can be released as light. In a detector, this light is collected by photodetectors such as photomultiplier tubes or silicon photomultipliers, and is turned into an electrical signal.
The total number of scintillation photons follows approximately a linear law in many materials. If a particle deposits an energy $E_{\text{dep}}$ and the scintillation light yield of the material is $Y$ photons per MeV, the mean number of generated photons is
$$
\langle N_{\gamma} \rangle = Y \cdot E_{\text{dep}}.
$$
Key rule: In Geant4, the total scintillation light is controlled mainly by the material light yield and the energy deposited, not by the primary particle type.
Real scintillators also show non linearities, described for example by Birks law. Geant4 supports Birks quenching, where the light yield is reduced for heavily ionizing particles. The basic idea is that high stopping power $dE/dx$ leads to more recombination losses and therefore fewer emitted photons per MeV.
Scintillation light is not emitted instantaneously. Many materials have characteristic decay times, often a fast and a slow component. In Geant4, these are represented by exponential time constants that affect when optical photons are generated relative to the interaction time. Fast components are important for timing measurements and coincidence detection, slow components contribute to afterglow or pile up.
The spectrum of scintillation light is typically broad. It is described by the emission spectrum of the material, usually specified as photon energy dependent intensity. Geant4 uses this to assign wavelengths or photon energies to individual optical photons. This spectrum matters because it must match the sensitivity of the photodetector and the transmission properties of optical components.
Scintillation light is usually emitted isotropically at the microscopic scale. In a simulation you normally assume isotropic emission, so optical photons are created with random directions in $4\pi$ solid angle. The transport of these photons is then influenced by refraction, reflection, absorption, and scattering in materials and at surfaces. This means that the pattern of detected light is determined mainly by geometry, material optical properties, and surface definitions, not by the initial emission direction.
Scintillation plays a central role in many detector types that you will simulate with Geant4. Examples include gamma spectroscopy detectors made of NaI(Tl) or LaBr$_3$, calorimeters in particle physics experiments, and plastic scintillators for timing and triggering. In all of these cases, Geant4 models the conversion from particle energy deposition to optical photons, and then the subsequent transport of those photons to your photodetector model.
Cherenkov radiation
Cherenkov radiation appears when a charged particle travels through a medium faster than light can travel in that medium. The speed of light in a material is $c/n$, where $n$ is the refractive index. If a particle has speed $v$ with $\beta = v/c$, Cherenkov light is produced if
$$
\beta n > 1.
$$
Cherenkov condition: Cherenkov photons are emitted only when the particle speed satisfies $\beta n > 1$, that is, when the particle is faster than $c/n$ in the material.
The emitted photons form a coherent wavefront that appears as a cone around the particle trajectory. The Cherenkov angle $\theta_c$ relative to the particle direction is given by
$$
\cos \theta_c = \frac{1}{\beta n}.
$$
As the particle slows down due to energy loss, it may fall below the Cherenkov threshold and emission stops. This threshold depends on the particle mass, its kinetic energy, and the refractive index of the material. In a medium with larger refractive index, the threshold momentum for Cherenkov emission is lower.
The number of Cherenkov photons produced per unit path length and per unit wavelength interval follows the Frank Tamm formula. The important qualitative features are that the yield is proportional to the path length, increases with the square of the particle charge, and is stronger at shorter wavelengths. This explains why Cherenkov light often appears blue.
In Geant4, Cherenkov photons are created according to the refractive index spectrum of the material. You specify $n(E)$ as a function of photon energy. Geant4 uses this to determine both the Cherenkov threshold and the spectral distribution of emitted photons. Without a defined refractive index, Cherenkov emission cannot occur in that material.
The direction of Cherenkov photons is strongly correlated with the particle direction through the Cherenkov angle. This directional nature is very different from the usually isotropic emission of scintillation light. Many detector designs exploit this by reconstructing ring patterns in imaging Cherenkov detectors or by measuring directional information in neutrino telescopes and water Cherenkov detectors.
Cherenkov photons are also optical photons in Geant4 and are transported with the same optical processes as scintillation light. They are subject to refraction, reflection, absorption, and scattering. This means the observable pattern at a photodetector is a combination of the initial Cherenkov cone geometry and the material and surface properties of the detector.
Cherenkov radiation is essential for a variety of applications that you may later simulate. Examples include water and ice Cherenkov detectors for neutrinos or cosmic rays, ring imaging Cherenkov counters used for particle identification, and fiber based timing detectors that rely on fast Cherenkov signals. In all of these, Geant4 uses the particle speed and the refractive index to decide when to produce Cherenkov photons, and then follows their paths through your optical system.
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