Layered Transition Boundary Condition
The Layered Transition Boundary Condition is an extension of the Transition Boundary Condition that allows to model a sequence of geometrically thin layers using a Layered Material. It represents a discontinuity in the tangential electric field. For each layer in the Layered Material, the transfer and surface impedances are obtained from the layer thickness and material properties. The impedances are then used to relate the discontinuity in the tangential electric field to the current flowing on the surface of either side (up/down) of the corresponding layer. Mathematically this reads:
where the index i = 1, 2,..., n refers to the layer number. The system of equations above is solved for each layer in the Layered Material. The index i has been omitted from the expressions of the impedances and the wave vector k in order to improve their readability.
Figure 3-6: The layered material is composed of n layers. The surface currents on the up and downside of each layer are determined from the transfer and surface impedances and are functions of the tangential electric fields.
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See Layered Material, Layered Material Link, Layered Material Stack, Layered Material Link (Subnode), and Single Layer Materials in the COMSOL Multiphysics Reference Manual for details on the definition of layered materials.
The Layered Transition Boundary Condition is based on the assumption that the wave propagates in the normal direction in the thin layer. Thus, the wave could be incident in the normal direction or the wave could be refracted to propagate in a direction close to the normal direction. The latter condition is fulfilled for a good conductor.
The thickness of the layer should be less than the radius of curvature for the boundary.
A consequence of the normal direction propagation assumption is that the Layered Transition Boundary Condition is not compatible with mode analysis, as for mode analysis it is assumed that the wave predominantly propagates in the out-of-plane direction whereas the normal to the boundary is in an in-plane direction.
For the Electromagnetic Waves, Beam Envelopes interface, the propagation in the layer can be specified to be given from the wave vectors specified for the physics and Snell’s law of refraction. For this option, the assumption of normal propagation in the layer is not required. Thus, this option is useful also when the layer is a dielectric material.
When adding a Layered Transition Boundary Condition node, the phase specified for the Electromagnetic Waves, Beam Envelopes interface can be discontinuous.
Shell properties
The Shell Properties section displays which Layered Material the Layered Transition Boundary Condition is coupled to.
Clear the Use all layers check box in order to select a specific Layered Material from the list. The Layered Transition Boundary Condition feature is then applicable only on the boundaries where the chosen material is defined.
You can visualize the selected Layered Material and the layers that constitute it by clicking the Layer Cross Section Preview and Layer 3D Preview buttons.
The thickness of the Layered Material should be set as follows, depending on the type of material:
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In a Material node, the layer Thickness is set in the Material Contents section by adding a Shell property group from the Material Properties section in the material Settings window. This automatically adds a Shell subnode under the Material node, transforming it into a Layered Material.
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When the Layered Material is a Single Layer Material, the Thickness is set in the Material Contents section in the Settings window. Alternatively it can be set in the Layer Definition section of the Shell property group Settings window.
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For a general Layered Material, added through a Layered Material Link or a Layered Material Stack, the Thickness is set in the Layer Definition section of the Settings window. Several layers may be defined in the table, and the Thickness should be defined for each of them. The total thickness of the Layered Material is the sum of all the layers thicknesses.
Propagation Direction
This section is only available for the Electromagnetic Waves, Beam Envelopes interface. Select a Propagation direction — Normal direction (the default) or From wave vector. The Normal direction option assumes that the waves in the layer propagate essentially in the normal direction, whereas the From wave vector option assumes that the tangential wave vector component is continuous at the layer boundaries, as specified by the wave vectors k1 and k2 for the Electromagnetic Waves, Beam Envelopes interface. The normal component for the wave vector in the layer is obtained from the wave number, given the specified material parameters. Thus, this option implements Snell’s law of refraction for the layer, which makes this option useful also for dielectric layers.
Layered Transition Boundary Condition
Select an Electric displacement field model — Relative permittivity, Refractive index (the default), Loss tangent, loss angle, Loss tangent, dissipation factor, Dielectric loss, Drude-Lorentz dispersion model, Debye dispersion model, or Sellmeier dispersion model. See the Wave Equation, Electric node, Electric Displacement Field section, for all settings.
The defaults use the values From material, taking the properties from the Layered Material specified for the boundary. Otherwise, choose User defined and enter different values or expressions. In the latter case all layers constituting the chosen Layered Material will take on the same value for the selected property.
See Skin Depth Calculator to evaluate the skin depth of a homogeneous material.