Problem Description

Solution

COMSOL Multiphysics uses the time-harmonic relation

u(t,x,y,z) = Re(e^jωt)*U_c(x,y,z),

where U_c is the complex-valued solution variable, ω is the angular frequency, t is time, and j is the imaginary unit. In order to maintain the compatibility between the application modes, this same convention is used in all time-harmonic application modes, in COMSOL Multiphysics and the add-on modules. While this definition is generally the rule in electrical and structural engineering, there are fields, such as optics, where most literature adds a minus sign inside the exponential. The convention in use decides which sign the imaginary part of a complex permittivity should have in order to represent a lossy material. The following is what holds throughout COMSOL Multiphysics and the modules, for quasi-statics as well as electromagnetic waves:

Im(ε) < 0 means a lossy material.

Im(ε) > 0 means a material with gain.

For electromagnetic waves, you can also opt to specify the losses in terms of a complex refractive index. Since the refractive index is defined as the relative permittivity squared, the same rule applies:

Im(n) < 0 means a lossy material.

Im(n) > 0 means a material with gain.

Note that you can model dispersive (frequency-dependent) materials by entering the permittivity or the refractive index as a function of the frequency. Also, if you prefer, you can model losses using a real-valued permittivity and a non-zero conductivity.

Electromagnetic losses are associated with a skin depth, which needs to be resolved by the mesh or modeled as a boundary condition. See Knowledge base 1004 for more information.

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