KAHIBARO
37.1. Optical Physics
Table of Contents
Scintillation light
In GATE, optical physics becomes important whenever you simulate how scintillation detectors convert deposited energy into visible or UV photons. Scintillation light is produced when charged particles or high energy photons deposit energy in a scintillating material, for example LYSO, BGO, NaI(Tl), or plastic scintillators. The deposited energy excites the atoms or molecules in the material, which then de-excite and emit photons in the optical range.
From the point of view of a GATE simulation, scintillation is a statistical conversion between energy deposition and optical photons. You do not simulate every atomic excitation explicitly. Instead, you configure a set of material properties and optical processes, and Geant4 handles the stochastic production and transport of optical photons.
To enable scintillation in GATE, you must use an optical physics configuration and define appropriate optical properties for the scintillating material. The material definition must include, at minimum, a scintillation yield and emission spectrum, and usually additional time and quenching properties. These properties are attached to the material, not to the geometry volume.
A central quantity is the scintillation yield, often specified in photons per unit deposited energy. If the material has a yield $Y$ in photons/MeV and a step deposits an energy $E$ in MeV, then the mean number of scintillation photons $N$ produced in that step is
$$
N = Y \, E.
$$
The actual number of photons is sampled from a statistical distribution. In Geant4 based optical physics, this is often modeled with a Poisson or Gaussian fluctuation depending on configuration. The stochastic nature of $N$ is what ultimately contributes to the detector energy resolution.
Important rule: For a scintillator material, you must define a scintillation yield (photons per MeV) and an emission spectrum. Without these properties, no scintillation photons will be generated even if energy is deposited.
Key relation: The mean number of scintillation photons is
$$
N = Y \, E,
$$
where $Y$ is the scintillation yield and $E$ is the deposited energy.
Beyond the yield, the emission spectrum describes the probability of emitting photons at different wavelengths. This spectrum is usually given as an array of photon energies or wavelengths with corresponding relative intensities. It strongly influences how many photons are detected because it must be compatible with the photodetector quantum efficiency.
Scintillation is not instantaneous. Real scintillators exhibit one or more decay components characterized by time constants. In GATE you can configure decay times, for example a fast and a slow component with relative weights. When a particle deposits energy, the emission times of the resulting photons are sampled from these decay distributions. This timing distribution is essential for simulating detector timing response or time of flight measurements.
Another effect that may be represented is non proportionality of light yield and quenching. For high linear energy transfer particles, the light output per unit energy can be reduced. A common description is Birks law, where the light yield per unit path length $dL/dx$ depends on the energy loss per unit length $dE/dx$ as
$$
\frac{dL}{dx} = \frac{S \, \frac{dE}{dx}}{1 + k_B \, \frac{dE}{dx}},
$$
with $S$ a scaling factor and $k_B$ Birks constant. In GATE, if you enable Birks law for a scintillator, this modifies the effective light yield for heavily ionizing particles.
Once scintillation photons are created, they are propagated as optical photons. Their transport is governed by optical material properties such as refractive index, absorption length, scattering length, and boundary properties at interfaces. Although these transport aspects belong to other sections, it is important to understand that scintillation in GATE is only the first step: creation of optical photons with specific wavelengths and times. The later detection probability depends on how you define the optical properties for the scintillator and for any coupling media, reflectors, and photodetectors.
A typical workflow for scintillation in a detector simulation in GATE is as follows. You define a detector crystal as a volume with a scintillating material. You assign to that material a scintillation yield, emission spectrum, and decay times. You enable optical physics in the physics list so that scintillation is an active process. When a gamma or charged particle interacts and deposits energy in the crystal, GATE creates optical photons according to these properties. The photons then travel through the geometry and may eventually reach a photodetector volume where they can be counted or time stamped using appropriate optical actors and digitizers.
Cherenkov light
Cherenkov light is another important optical process that GATE can simulate. It occurs when a charged particle moves through a medium faster than the phase velocity of light in that medium. In a material with refractive index $n$, the phase velocity of light is $c/n$, where $c$ is the speed of light in vacuum. If the particle speed $v$ satisfies $v > c/n$, Cherenkov radiation is emitted.
The condition for Cherenkov emission can be written in terms of the particle speed $\beta = v/c$ as
$$
\beta n > 1.
$$
Only when this inequality holds does Cherenkov light occur. For a given refractive index $n$, this sets a minimum $\beta$ and corresponding energy threshold for different particle types. Heavier particles require more kinetic energy to exceed this threshold.
Cherenkov condition: Cherenkov photons are emitted only if
$$
\beta n > 1,
$$
where $\beta = v / c$ is the particle speed relative to light in vacuum and $n$ is the refractive index of the medium.
Cherenkov angle: The characteristic emission angle $\theta_C$ relative to the particle direction satisfies
$$
\cos \theta_C = \frac{1}{\beta n}.
$$
When Cherenkov radiation is produced, photons are emitted at a characteristic angle $\theta_C$ with respect to the direction of motion of the particle, given by
$$
\cos \theta_C = \frac{1}{\beta n}.
$$
This leads to a cone of light around the particle track. In a GATE simulation, Geant4 samples the emission directions according to this Cherenkov cone, taking into account the material refractive index as a function of photon energy.
The number of Cherenkov photons produced per unit path length and per unit wavelength interval can be expressed by the Frank Tamm formula. In differential form, the number of photons $dN$ emitted in a wavelength interval $d\lambda$ along a track segment of length $dx$ is proportional to
$$
\frac{d^2 N}{dx \, d\lambda} \propto \left(1 - \frac{1}{\beta^2 n^2(\lambda)}\right) \frac{1}{\lambda^2},
$$
for wavelengths where $\beta n(\lambda) > 1$. In practice, in GATE you do not implement this formula directly. Instead, you provide the wavelength dependent refractive index of the material. The Cherenkov process in Geant4 uses these optical properties to generate photons with a spectral distribution that is more intense at shorter wavelengths.
To simulate Cherenkov light in GATE, you must again enable optical physics in the physics list and define a refractive index for the material through which the charged particles travel. The refractive index must be defined as a function of photon energy or wavelength. If no refractive index is provided, the Cherenkov process is effectively disabled because the condition $\beta n > 1$ cannot be evaluated correctly.
Cherenkov light is especially relevant in water and certain crystals. In water, Cherenkov photons can be used directly as a detection signal in large detectors, while in medical physics it can contribute to optical signals in water phantoms or tissue. Some fast Cherenkov based detectors also rely on this process for excellent timing performance, since Cherenkov emission is essentially prompt. Unlike scintillation, which often has decay times of tens or hundreds of nanoseconds, Cherenkov emission occurs nearly instantaneously as the particle travels.
In a medical physics context with GATE, Cherenkov simulations may be used to study optical signals in water or tissue for beam monitoring, to investigate Cherenkov light in optical dosimetry, or to quantify Cherenkov contributions to detector signals. Cherenkov photons will then be transported through the medium according to the same optical material properties used for scintillation photons, including absorption and scattering lengths and boundary interactions.
The practical implementation in a GATE simulation follows a similar pattern to scintillation. You ensure that the material through which fast charged particles will pass has an appropriate refractive index spectrum. You enable Cherenkov as part of the optical physics. When the simulation runs, any charged particle step that satisfies the Cherenkov condition produces optical photons with wavelengths and directions sampled from the Cherenkov distributions. These photons then propagate through the geometry and can be collected and analyzed, for example to form time profiles, spatial distributions, or photon counts at a photodetector surface.
By combining scintillation and Cherenkov processes, GATE can model complex optical responses in advanced detectors where both mechanisms may be present. Proper control of the material optical properties and of the optical physics configuration is crucial to obtain realistic predictions of light yield, timing, and detection efficiency.
Views: 10