KAHIBARO
37.4 Optical Surfaces
Table of Contents
Reflection
In optical photon simulations you do not directly create mirrors or rough interfaces. Instead you describe how light behaves when it reaches the boundary between two volumes. An optical surface is the object that holds this description. Once defined and attached between two volumes, it controls reflection, refraction and absorption at that boundary.
At a basic level, reflection at an optical surface depends on three things: the refractive indices of the two materials, the surface model and type that you choose, and the microstructure of the surface that you describe with parameters such as polish or sigma alpha. GATE uses Geant4’s optical models under the hood, so all surface behavior is inherited from those models but configured in a way that fits GATE.
For a perfectly smooth interface between two dielectrics you can obtain pure Fresnel reflection without any explicit reflectivity parameter. The reflection probability is then fully determined by the refractive indices of the incident and transmitted media and by the angle of incidence. At normal incidence, the Fresnel reflectivity between two media with indices $n_1$ and $n_2$ is
$$
R = \left(\frac{n_1 - n_2}{n_1 + n_2}\right)^2.
$$
In practice this means that even if you do not assign any reflectivity to a water–air interface, photons arriving from water into air will be partially reflected, especially at grazing angles. For many scintillator to air or scintillator to coupling gel interfaces this default Fresnel treatment is physically correct and is usually the first thing to try.
For more realistic detector modeling you often need to describe surfaces that are not perfectly smooth. A rough surface increases the probability that reflection is not purely specular, so photons leave the interface with a wide distribution of reflection angles. In the Geant4 optical models this is controlled by roughness parameters and the chosen surface model, such as unified, which lets you specify contributions from specular lobe, specular spike, diffuse reflection, and backscatter. In GATE you configure these properties through the optical surface definition, and they will determine whether the reflection is mirror-like, blurred, or almost Lambertian.
Some surfaces need a user-defined reflectivity that does not simply follow Fresnel’s law. This occurs for painted surfaces, reflective foils, or absorber coatings where the microstructure and absorption are complicated. In that case you provide a reflectivity property, often as a function of photon energy or wavelength. The simulation then randomly decides, for each optical photon that hits the boundary, whether it is reflected, transmitted, or absorbed, based on the provided probabilities. The fraction that is reflected does not necessarily satisfy the Fresnel formula anymore, it follows your input.
It is important to distinguish between dielectric and metallic surfaces. A metal surface is usually modeled as a boundary between a dielectric and a metal material, but in optical photon simulation you often represent it using a specific surface type with an associated reflectivity spectrum and complex refractive index. A metallic reflector can have high reflectivity over a given wavelength range, but may also introduce absorption and phase effects. For most detector applications in GATE you will specify a wavelength-dependent reflectivity and then treat any non-reflected fraction as absorption.
At grazing incidence, even modest refractive index differences can produce nearly total reflection through Fresnel effects. This is useful to remember when you see photons appearing to be trapped inside crystals or light guides. The trapping is not a bug, it is total internal reflection at angles larger than the critical angle, which is given by
$$
\theta_c = \arcsin\left(\frac{n_2}{n_1}\right)
$$
for light moving from a medium with index $n_1$ into one with index $n_2$ where $n_1 > n_2$. Above this angle all photons are reflected back into the denser medium.
The final outcome at a surface is usually a mixture of Fresnel-driven reflection, user-defined reflectivity, and surface roughness. When you design an optical geometry in GATE, it is important to define consistent refractive indices for all optical volumes, assign appropriate optical surfaces between volumes that need special treatment, and verify with simple test simulations that reflection probabilities and angular distributions behave as expected.
Important: At a smooth interface between two dielectrics with refractive indices $n_1$ and $n_2$, the Fresnel reflectivity at normal incidence is
$$R = \left(\frac{n_1 - n_2}{n_1 + n_2}\right)^2,$$
and total internal reflection occurs for incidence angles larger than the critical angle
$$\theta_c = \arcsin\left(\frac{n_2}{n_1}\right) \quad (n_1 > n_2).$$
Refraction
Refraction describes how an optical photon changes direction when it crosses the boundary between two materials with different refractive indices. In GATE, once you assign refractive indices to your materials and define the surface between them, refraction is automatically handled according to Snell’s law, unless reflection or absorption occurs first.
Snell’s law connects the angle of incidence and the angle of refraction. If $n_1$ and $n_2$ are the refractive indices of the incident and transmitted media, and $\theta_1$ and $\theta_2$ are the corresponding angles with respect to the normal, then
$$
n_1 \sin \theta_1 = n_2 \sin \theta_2.
$$
This relation determines whether a photon is transmitted into the second medium and what direction it will take. When photons move from a high index medium into a lower index medium, Snell’s law has no real solution beyond the critical angle, so the simulation will then treat the interaction as total internal reflection and no refraction occurs. When moving from a low index into a higher index medium, refraction always has a solution, and part of the light goes through with a bent path.
In many detectors you use refractive index engineering to guide light efficiently toward photosensors. Typical examples are scintillator crystals coupled to light guides or optical gels that have refractive indices chosen to minimize reflection losses and to control refraction angles. In a GATE simulation, this is modeled simply by giving each material the correct refractive index at the optical photon energies of interest. The refraction that you see in the simulation is therefore a direct consequence of these material properties.
Real optical materials have refractive indices that depend on wavelength. If you define an energy dependent refractive index in GATE, each photon will experience a slightly different refraction angle according to its energy. This chromatic effect can influence timing and spatial distributions of detected photons, particularly in systems with long light paths or broad scintillation spectra.
Some optical surface models can interfere with simple refraction. For example, a highly rough surface can randomize the local surface normal, so that the effective angle used in Snell’s law is modified. In this case, transmitted photons are still refracted, but their directions are smeared due to the distribution of microscopic normals. In detector design this represents ground or etched surfaces that diffuse transmitted light instead of preserving a sharp beam.
It is also possible to suppress refraction to mimic opaque boundaries. If you define a surface with zero transmission probability, photons reaching that boundary are either reflected or absorbed, but never refracted into the other volume. This is how you can model black paint or perfectly opaque reflectors. Conversely, for transparent windows and coupling layers you ensure that transmission is allowed and that refractive indices are chosen to minimize reflection.
The combination of reflection and refraction at every boundary results in complex photon paths through multi-layer systems. In GATE, you do not manually calculate these paths. You control them by defining correct material optical properties and surface descriptions and then let the Monte Carlo engine apply Snell’s law and Fresnel equations at every interaction.
Key refraction rule: For a photon crossing from medium 1 with index $n_1$ to medium 2 with index $n_2$, the refraction angle $\theta_2$ is determined by Snell’s law
$$n_1 \sin \theta_1 = n_2 \sin \theta_2.$$
If $n_1 > n_2$ and $\theta_1 > \theta_c = \arcsin(n_2 / n_1)$, no refraction occurs and the photon is totally internally reflected.
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