Material Discontinuity
The Material Discontinuity node is the default feature on all boundaries.
The Geometrical Optics interface always applies reflection and refraction at boundaries between different media using a deterministic ray splitting approach. The direction of the refracted ray is computed using Snell’s law, based on the refractive index on either side. If extra degrees of freedom have been allocated for secondary rays, a reflected ray is also released. If the incident ray undergoes total internal reflection, no refracted ray is produced and no secondary rays are needed to release the reflected ray.
You can use the Rays to Release section (see below) to decide whether to split the incident ray into reflected and refracted rays, or to ignore the reflected ray.
If the ray intensity or power is solved for in the model, the Material Discontinuity feature computes the new values of these variables for the reflected and refracted rays. This reinitialization uses the Fresnel Equations while accounting for the incident ray polarization and the influence of any dielectric films on the surface reflectance.
The maximum number of reflected rays can be controlled via the Maximum number of secondary rays text field, which is found under the Ray Release and Propagation section for the physics interface.
If a reflected ray should be produced, but all of the preallocated secondary rays have already been released, the study will produce a Warning node.
The Accumulator (Boundary) subnode is available from the context menu (right-click the parent node) or from the Physics toolbar, Attributes menu. The Thin Dielectric Film subnode is also available if the following conditions are met:
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The ray intensity or power is being computed, and
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One of the following options is selected from the Thin dielectric films on boundary list in the Coatings section: Add layers to surface or Add layers to surface, repeating.
Coatings
This section is available if ray intensity or power is being computed in the model. Use the options in this section to add thin dielectric layers to the boundary between the media. These thin dielectric layers are used, together with the refractive indices on either side, to modify the Fresnel equations for the reflection and transmission coefficients at the boundary.
The thicknesses of the thin dielectric layers must be small relative to the coherence length of the radiation. They are usually comparable in length scale to the free-space wavelength.
Select an option from the Thin dielectric films on boundary list. The default is None. The following options are available.
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None: no dielectric films are on the boundary. The intensity of the reflected and refracted light is computed solely using the Fresnel equations with the refractive indices of the two adjacent domains.
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Add layers to surface: you can add any number of thin dielectric films to the boundary by adding one or more Thin Dielectric Film subnodes; right click the Material Discontinuity node or select Thin Dielectric Film from the Physics toolbar, Attributes menu. If multiple thin films are added to a single surface, they are arranged in the same order as the corresponding Thin Dielectric Film subnodes in the Model Builder, from the upside of the boundary toward the downside.
Anti-Reflective Coating with Multiple Layers: Application Library path Ray_Optics_Module/Prisms_and_Coatings/antireflective_coating_multilayer
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Add layers to surface, repeating: this option functions like the Add layers to surface option described above. Add individual dielectric coatings to the boundary using the Thin Dielectric Film subnode. In addition, enter a value or expression for the Number of repeating unit cells N (dimensionless). The default value is 3. In the settings windows for the Thin Dielectric Film subnodes, you can decide which layers constitute a unit cell that will be repeated the specified number of times. Use this option to specify periodic arrangements with a large number of repeating dielectric layers, without having to add each layer manually.
Distributed Bragg Reflector: Application Library path Ray_Optics_Module/Prisms_and_Coatings/distributed_bragg_reflector
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Anti-reflective coating: the incident ray is refracted with unit transmittance and zero reflectance.
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Single-layer coating, specified thickness: this is a simplified version of the Add layers to surface option that only allows a single dielectric layer. Enter a value or expression for the Film refractive index n (dimensionless). The default value is 1. Then enter a value or expression for the Film thickness t (SI unit: m). The default value is 1 μm.
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Specify reflectance: enter a value or expression for the reflectance at the boundary directly. Enter a value or expression for the Reflectance R (dimensionless). The default is 0.1. If the Specify different values for s- and p-polarization check box is selected, you can instead enter separate values for the reflectance of p- and s-polarized light, called Rp and Rs, respectively. The layers are considered nonabsorbing so that the sum of the reflectance and transmittance is unity.
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Specify transmittance: enter a value or expression for the transmittance at the boundary directly. Enter a value or expression for the Transmittance T (dimensionless). The default is 0.9. If the Specify different values for s- and p-polarization check box is selected, you can instead enter separate values for the transmittance of p- and s-polarized light, called Tp and Ts, respectively. The layers are considered nonabsorbing so that the sum of the reflectance and transmittance is unity.
Real and Ideal Optical Coatings
The options Anti-reflective coating, Specify reflectance, and Specify transmittance all include a check box called Treat as single layer dielectric film, which is cleared by default. While this check box is cleared, the specified reflectance or transmittance applies to all rays, regardless of wavelength or angle of incidence, and the remaining inputs in this section are not shown. This makes complicated multilayer films easier to set up because you can enter the reflectance or transmittance explicitly without having to know the properties of each layer in the coating. If the coating properties depend on the wavelength or angle of incidence, you can usually build this dependence into the model by defining the film reflectance or transmittance as an Interpolation function of the ray properties. The tradeoff is that accurate information about the discontinuities in ray phase is lost, even if the Compute phase check box is selected in the physics interface Intensity Computation section, because this information depends on the complex-valued Fresnel coefficients.
If the Treat as single layer dielectric film check box is selected, then instead the Material Discontinuity automatically computes the thickness of a single layer needed to produce the given reflectance or transmittance. The drawback is that the specified value will only be attained for rays at a specific wavelength and angle of incidence.
The following inputs are only shown when Treat as single layer dielectric film is selected.
For Specify reflectance and Specify transmittance enter the Film refractive index n (dimensionless). The default is 1. If it is impossible to construct a single layer of this refractive index and obtain the specified reflectance or transmittance, then the boundary is treated as having no dielectric films. For Anti-reflective coating, the refractive index of the coating is not an input because it is always the geometric mean of the refractive indices in the two adjacent domains.
For Anti-reflective coating, Specify reflectance, and Specify transmittance enter the following:
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Vacuum wavelength for specified film properties λ0 (SI unit: m). The default is 660 nm.
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Angle of incidence for specified film properties θi (SI unit: m). The default is 0.
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Select an option from the Angle of incidence specification list: With respect to upside (the default) or With respect to downside. You can see which side is the upside by selecting the Show boundary normal check box (see Advanced Settings below); the normal vector rendered in the Graphics window points from the upside to the downside.
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Select an option from the Specified film behavior applies to list: S-polarized radiation (the default) or P-polarized radiation.
Rays to Release
Use the inputs in this section to control whether the incident ray is split into a reflected and refracted ray at the material discontinuity. Select an option from the Release reflected rays list: Always (the default), Never, or Based on logical expression.
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If Always is selected, whenever a ray hits the material discontinuity, the incident ray is refracted across the boundary, and a reflected ray is produces using some of the preallocated degrees of freedom for secondary rays.
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If Never is selected, the incident ray is refracted, but no reflected ray is produced. This does not prevent a ray from undergoing total internal reflection at the boundary.
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If Based on logical expression is selected, enter a value or expression for the Evaluation expression e (dimensionless). The default is 1. A reflected ray is produced only if the value of this expression is nonzero for the incident ray.
If the ray intensity is solved for in the model, enter a Threshold intensity Ith (SI unit: W/m2). The default is 1 mW/m2. If the interaction of a ray with a material discontinuity would create a reflected ray of intensity less than the threshold intensity, the release of this reflected ray is suppressed.
If the ray power is solved for in the model, enter a Threshold power Qth (SI unit: W). The default is 10-3 mW. If the interaction of a ray with a material discontinuity would create a reflected ray of power less than the threshold power, the release of this reflected ray is suppressed. Suppressing the release of reflected rays of extremely low intensity or power is a convenient way to avoid wasting computational resources.
If both the Evaluation expression and the Threshold intensity are specified, a reflected ray is only released if the value of the expression is nonzero and the intensity of the reflected ray exceeds the threshold. In other words, a ray must satisfy all of the criteria in the Rays to Release section in order to be released, not just one of them.
Auxiliary Dependent Variables, Refracted Ray
This section includes a check box (cleared by default) and a text field (default 0) for every Auxiliary Dependent Variable in the model. Select the check box to activate the text field, which controls the new value of this auxiliary dependent variable for the refracted ray. If the check box is cleared, the new value equals that of the incident ray.
The value can be a function of any combinations of ray variables and variables defined on the boundary. For example, to increment the value of psi by 1 when a ray touches or crosses a boundary, enter psi+1 in the text field for psinew.
Auxiliary Dependent Variables, Reflected Ray
This section is the same as Auxiliary Dependent Variables, Refracted Ray, except that the expressions are used to auxiliary dependent variables for the reflected ray.
Advanced Settings
Select the Show boundary normal check box to view the boundary normal in the Graphics window.
Visualization of the boundary normal is important when adding multiple Thin Dielectric Film subnodes, since the thin films are oriented from the upside of the boundary to the downside in the same order as their corresponding nodes in the Model Builder.
If the Compute optical path length check box is selected in the physics interface Additional Variables section, select the Reset optical path length check box to set the optical path length of reflected and refracted rays to 0. Otherwise both the reflected and refracted ray inherit the optical path length of the incident ray.
Material Discontinuity Theory