Material Discontinuity

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.

If the ray intensity or power is solved for in the model, the feature computes the new values of these variables for the reflected and refracted rays.

	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.

The Accumulator (Boundary) subnode is available from the context menu (right-click the parent node) or from the toolbar, menu. The Thin Dielectric Film subnode is also available if the following conditions are met:

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 list. The default is . The following options are available.

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: you can add any number of thin dielectric films to the boundary by adding one or more Thin Dielectric Film subnodes; right click the node or select from the toolbar, menu. If multiple thin films are added to a single surface, they are arranged in the same order as the corresponding 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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: this option functions like the option described above. Add individual dielectric coatings to the boundary using the subnode. In addition, enter a value or expression for the N (dimensionless). The default value is 3. In the settings windows for the 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 repeatind 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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: this is a simplified version of the option that only allows a single dielectric layer. Enter a value or expression for the n (dimensionless). The default value is 1. Then enter a value or expression for the t (SI unit: m). The default value is 1 μm.

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: enter a value or expression for the reflectance at the boundary directly. Enter a value or expression for the R (dimensionless). The default is 0.1. If the 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 non-absorbing so that the sum of the reflectance and transmittance is unity.

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: enter a value or expression for the transmittance at the boundary directly. Enter a value or expression for the T (dimensionless). The default is 0.9. If the 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 non-absorbing so that the sum of the reflectance and transmittance is unity.

The options , , and all include a check box called , 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 of the ray properties. The tradeoff is that accurate information about the discontinuities in ray phase is lost, even if the check box is selected in the physics interface section, because this information depends on the complex-valued Fresnel coefficients.

If the check box is selected, then instead the automatically computes the thickness of a single layer needed to produce the given reflectance or transmittance. The drawback is that the specified reflectance or transmittance will only be attained for rays at a specific wavelength and angle of incidence.

For and enter the 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 , 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 , , and enter the following:

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Select an option from the list: (the default) or . You can see which side is the upside by selecting the check box (see below); the normal vector rendered in the Graphics window points from the upside to the downside.

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 list: (the default), , or .

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If 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 is selected, enter a value or expression for the 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 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 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.

If both the and the 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 section in order to be released, not just one of them.

The release of reflected rays at a material discontinuity can be suppressed to prevent an arbitrarily large number of degrees of freedom from being used to model rays of extremely low intensity. Keep in mind that this can lead to a reduction in the total energy of the system.

If an Auxiliary Dependent Variable has been added to the model then there is an option to reinitialize the values of auxiliary dependent variables for the refracted ray. These settings are the same as in the New Value of Auxiliary Dependent Variables section for the Wall feature.

If an Auxiliary Dependent Variable has been added to the model then there is an option to reinitialize the values of auxiliary dependent variables for the reflected ray. These settings are the same as in the New Value of Auxiliary Dependent Variables section for the Wall feature.

Select the check box to view the boundary normal in the 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 check box is selected in the physics interface section, select the 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.