Layered Transition Boundary Condition

The is an extension of the that allows to model a sequence of geometrically thin layers using a . It represents a discontinuity in the tangential electric field. For each layer in the , 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 . The index i has been omitted from the expressions of the impedances and the wave vector k in order to improve their readability.

Figure 4-5: 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.

Shell properties

The section displays which layered material the is coupled to.

Clear the check box in order to select a specific layered material from the list. The 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 and buttons.

The thickness of the layered material should be set as follows, depending on the type of material:

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In a node, the layer is set in the section by adding a property group from the section in the material window. This automatically adds a subnode under the node, transforming it into a layered material.

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When the layered material is a , the is set in the section in the window. Alternatively it can be set in the section of the property group window.

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For a general , added through a or a , the is set in the section of the window. Several layers may be defined in the table, and the should be defined for each of them. The total thickness of the layered material is the sum of all the layers thicknesses.

Layered Transition Boundary Condition

The section lists the material properties of the thin layered material that this boundary condition approximates:

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, εr (dimensionless)

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, μr (dimensionless)

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, σ (SI unit: S/m)

The defaults use the values , taking the properties from the layered material specified for the boundary. Otherwise, choose 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.