KAHIBARO
37.3. Optical Properties
Table of Contents
Refractive index
In optical photon simulations, the refractive index is the central property that controls how light propagates in each material. In GATE, as in Geant4, every material that participates in optical transport must have its refractive index defined as a function of photon energy or wavelength. If the refractive index is missing for a material where optical photons travel, the simulation will either stop with an error or propagate photons incorrectly.
Conceptually, the refractive index $n$ relates the speed of light in vacuum, $c$, to the speed of light in the material, $v$:
$$
n = \frac{c}{v}.
$$
A refractive index larger than 1 means photons travel more slowly than in vacuum. For example, air is close to $n \approx 1.0$, water is around $n \approx 1.33$ in the visible range, and typical scintillation crystals like LYSO have $n \approx 1.8$ to $1.85$ for visible light.
In a Monte Carlo simulation, the refractive index does not only set the speed. It also determines what happens at boundaries between materials. At an interface between two media with different refractive indices, the relative values of $n_1$ and $n_2$ control reflection and refraction through Snell’s law. In GATE you do not implement these equations manually, but you must supply consistent refractive indices so that boundary processes (reflection, refraction, total internal reflection) are modeled correctly.
A key feature of realistic optical modeling is that the refractive index depends on wavelength. This energy dependence is called dispersion. Scintillation light is not monochromatic, so if your light spectrum spans a wide range of wavelengths, you should provide the refractive index as a list of photon energies together with the corresponding index values. For each material you typically define a table like:
| Photon energy (eV) | Wavelength (nm) | Refractive index $n$ |
|---|---|---|
| 2.0 | 620 | 1.80 |
| 2.5 | 496 | 1.81 |
| 3.0 | 413 | 1.82 |
Internally, GATE interpolates between these points. The same photon energy grid must be used consistently for all optical properties of a given material, such as emission spectrum, refractive index, and absorption length. Inconsistent energy grids can lead to confusing behavior, because different processes will use different interpolations.
When configuring a scintillation detector, you usually define a higher refractive index for the crystal and a lower index for the surrounding medium, such as air or optical grease. This difference directly affects light extraction. A large mismatch in refractive index increases internal reflection at the crystal boundary and can trap light inside. Coupling layers like optical grease have intermediate indices to reduce this mismatch and improve light collection.
The refractive index also affects Cherenkov light production. If a charged particle moves through a medium faster than the phase velocity of light in that medium, Cherenkov photons may be produced. The threshold for Cherenkov emission depends explicitly on the refractive index, so realistic Cherenkov simulations require a properly defined index as a function of energy.
In practice, you will often take refractive index data from measurements or from manufacturer data sheets. For simple teaching or prototyping you may approximate the refractive index as constant across the relevant wavelength range. This is acceptable for narrow-band scintillation spectra, but it becomes less accurate for broad spectra or for optical systems where chromatic effects are important.
For correct optical photon transport in GATE, every material that contains or borders optical photons must have a refractive index defined, preferably as a function of photon energy using a consistent energy grid shared with all other optical properties of that material.
Absorption length
Absorption length describes how far an optical photon can travel in a material before it is absorbed. In GATE this is specified as the bulk absorption length, sometimes also called the attenuation length for true absorption, and it is provided as a function of photon energy.
The absorption length $L_{\text{abs}}$ is related to the probability that a photon survives after traveling a distance $x$ in the material. The survival probability follows an exponential law:
$$
P_{\text{survive}}(x) = \exp\!\left(-\frac{x}{L_{\text{abs}}}\right).
$$
A larger absorption length means photons tend to travel farther before being absorbed, which increases the probability that they reach a photodetector. Short absorption lengths indicate strong absorption and can strongly reduce light collection efficiency, especially for photons that must traverse long paths inside crystals, light guides, or coupling layers.
As with refractive index, absorption length in GATE is defined as a set of photon energies and corresponding length values. A typical table might look like:
| Photon energy (eV) | Wavelength (nm) | Absorption length (mm) |
|---|---|---|
| 2.0 | 620 | 200 |
| 2.5 | 496 | 150 |
| 3.0 | 413 | 100 |
The length can be given in any supported unit, commonly millimeters or centimeters, and GATE will convert using its unit system. Shorter wavelengths are often absorbed more strongly, giving shorter absorption lengths, but the exact behavior depends on the material. As with all optical properties, the photon energy grid used for absorption length should be identical to that used for refractive index and emission spectra for that material.
Absorption length is a bulk property of the volume, not a surface property. When a photon propagates through the interior of a medium, the simulation samples a random free path based on the exponential law above. If the sampled path is shorter than the distance to the next boundary, the photon is absorbed in the bulk. If the sampled path is longer, the photon reaches the boundary where surface processes are applied.
It is important to distinguish bulk absorption from scattering. Bulk absorption permanently removes the photon from the simulation, usually converting its energy into heat. Scattering, by contrast, redirects the photon while keeping it alive. Scattering in optical media is controlled by separate scattering lengths or Mie/Rayleigh scattering parameters, which are distinct from the absorption length. In many detector simulations, bulk absorption in the scintillator is relatively small compared to scattering and surface losses, but in other materials such as optical glue or protective coatings, absorption can be a major loss mechanism.
Inhomogeneous absorption properties can significantly influence detector uniformity. For example, if the absorption length is too short relative to the crystal dimensions, photons produced far from the photodetector end will have a smaller chance of reaching the sensor, which can create position-dependent light yield. By adjusting the absorption length in simulations, you can study such nonuniformities and compare them with measurements.
Realistic values for absorption length are typically taken from experimental measurements or manufacturer specifications. For simple studies, you may choose a very long absorption length to approximate a nearly transparent medium. This is common for air, optical grease, and some light guides, where you want to minimize bulk absorption and focus on reflection and refraction behavior.
Finally, you should make sure that absorption lengths are compatible with your geometry scale. If your detector crystal has a length of a few centimeters, using an absorption length of only a few millimeters will cause most photons to be absorbed before reaching any surface, which may not be realistic. Conversely, if you use absorption lengths much longer than any dimension in your geometry, bulk absorption will be almost negligible.
In GATE, the bulk absorption length must be defined for each optically active material as a function of photon energy, using the same energy grid as other optical properties. The exponential survival law $P_{\text{survive}}(x) = \exp(-x / L_{\text{abs}})$ governs photon loss in the bulk and strongly influences light collection efficiency and detector response.
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