Material Properties
Until now, there has only been a formal introduction of the constitutive relations. These seemingly simple relations can be quite complicated at times. There are four main groups of materials where they require some considerations. A given material can belong to one or more of these groups. The groups are:
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Inhomogeneous materials
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Anisotropic materials
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Nonlinear materials
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Dispersive materials
The least complicated of the groups above is that of the inhomogeneous materials. An inhomogeneous medium is one where the constitutive parameters vary with the space coordinates, so that different field properties prevail at different parts of the material structure.
For anisotropic materials, the field relations at any point are different for different directions of propagation. This means that a 3-by-3 tensor is required to properly define the constitutive relations. If this tensor is symmetric, the material is often referred to as reciprocal. In these cases, the coordinate system can be rotated in such a way that a diagonal matrix is obtained. If two of the diagonal entries are equal, the material is uniaxially anisotropic. If none of the elements have the same value, the material is biaxially anisotropic (Ref. 2). An example where anisotropic parameters are used is for the permittivity in crystals (Ref. 2).
Nonlinearity is the effect of variations in permittivity or permeability with the intensity of the electromagnetic field. This also includes hysteresis effects, where not only the current field intensities influence the physical properties of the material, but also the history of the field distribution.
Finally, dispersion describes changes in the velocity of the wave with wavelength. In the frequency domain, dispersion is expressed by a frequency dependence in the constitutive laws.
Material Properties and the Material Browser
All interfaces in the Wave OpticsModule support the use of the COMSOL Multiphysics material database libraries. The electromagnetic material properties that can be stored in the materials database are:
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The electrical conductivity
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The relative permittivity
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The relative permeability
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The refractive index
The physics-specific domain material properties are by default taken from the material specification. The material properties are inputs to material laws or constitutive relations that are defined on the feature level below the physics interface node in the model tree. There is one editable default domain feature (wave equation) that initially represents a linear isotropic material. Domains with different material laws are specified by adding additional features. Some of the domain parameters can either be a scalar or a matrix (tensor) depending on whether the material is isotropic or anisotropic.
In a similar way, boundary, edge, and point settings are specified by adding the corresponding features. A certain feature might require one or several fields to be specified, while others generate the conditions without user-specified fields.