Scattering Boundary Condition
Use the Scattering Boundary Condition to make a boundary transparent for a scattered wave. The boundary condition is also transparent for an incoming plane wave. The scattered (outgoing) wave types for which the boundary condition is perfectly transparent are
The field E0 is the incident plane wave that travels in the direction k. The boundary condition is transparent for incoming (but not outgoing) plane waves with any angle of incidence. In addition, to an incident plane wave, E0 can also be the electric field distribution for a Gaussian beam that propagates in the direction k.
If there is an incident field, a Reference Point subnode can be added by right-clicking the context menu (right-click the parent node) or from the Physics toolbar, Attributes menu. The Reference Point subnode redefines the incident field to be expressed as
,
where rref is a reference point determined by the Reference Point subnode. If no reference point subnode is added, the reference point is calculated as the average position boundary selection.
In 2D axisymmetry, when incident field can be specified, the default subnode Symmetry Axis Reference Point is available. This subnode defines a reference point at the intersection between the symmetry axis and the Scattering boundary condition’s boundary selection.
The boundary is only perfectly transparent for scattered (outgoing) waves of the selected type at normal incidence to the boundary, assuming that the material properties adjacent to the boundary are isotropic. That is, a plane wave at oblique incidence is partially reflected and so is a cylindrical wave or spherical wave unless the wave fronts are parallel to the boundary. For the Electromagnetic Waves, Frequency Domain interface, the Perfectly Matched Layer feature is available as a general way of modeling an open boundary.
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For cylindrical waves, specify around which cylinder axis the waves are cylindrical. Do this by specifying one point at the cylinder axis and the axis direction.
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For spherical waves, specify the center of the sphere around which the wave is spherical.
The domain material adjacent to the boundary where the Scattering Boundary Condition is applied can be lossy.
If the problem is solved for the eigenfrequency or the scattered field, the boundary condition does not include the incident wave.
In the scattered field formulation, the background field must be a solution to the wave equation in the domain adjacent to the Scattering Boundary Condition feature. If the background field is not a solution to the wave equation in the adjacent domain, there will be reflections at the boundary.
So, if the scattering problem consists of a scatterer embedded in a top superstrate and a bottom substrate, a structure similar to what is used in the tutorial model Plasmonic Wire Grating, the background field should be either a numerical or analytical solution to the two-layer superstrate-substrate problem. The tutorial model Scatterer on Substrate demonstrates how to compute a numerical background field that is used in a following scattered field formulation study.
Scattering Boundary Condition
Select an Incident field — No incident field (the default), Wave given by E field, Wave given by H field, or Gaussian beam. Enter the expressions for the components for the Incident electric field E0 or Incident magnetic field H0.
If the Incident field is set to Gaussian beam, select an Input quantity: Electric field amplitude (the default) or Power. If the Input quantity is Electric field amplitude, enter the component expressions for the Gaussian beam electric field amplitude Eg0 (SI unit: V/m). If the Input quantity is set to Power, enter the Input power (SI unit: W in 2D axisymmetry and 3D and W/m in 2D) and the component expressions for the Gaussian beam nonnormalized electric field amplitude Eg0 (SI unit: V/m). Also edit the Beam radius w0 (SI unit: m) and the Distance to focal plane p0 (SI unit: m). The default values are ((10*2)*pi)/ewfd.k0 and 0 m, respectively. The optical axis for the Gaussian beam is defined by a line including a reference point on the feature selection with a direction specified by the Incident wave direction (see below). By default, the reference point is the average position for the feature selection. However, by adding a Reference Point subnode any available point (or the average of several selected points) on the feature selection can be used as the reference point. The focal plane for the Gaussian beam is located the Distance to focal plane p0 from the reference point in the Incident wave direction.
If the Incident field is not set to No incident field, edit the Incident wave direction kdir for the vector coordinates. The default direction is in the opposite direction to the boundary normal. For 2D axisymmetry, the Incident wave direction kdir should be parallel or anti-parallel to the symmetry axis.
Select a Scattered wave type for which the boundary is absorbing — Plane wave (the default), Spherical wave, or Cylindrical wave.
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For the Electromagnetic Waves, Frequency Domain interface, select an Order —First order (the default) or Second order.
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For Cylindrical wave also enter coordinates for the Source point r0 (SI unit: m) and Source axis direction raxis (dimensionless). For 2D the Source axis direction is assumed to be in the z direction, whereas in 2D axisymmetry it is assumed to be along the axis of rotation.
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For Spherical wave enter coordinates for the Source point r0 (SI unit: m).
Mode Analysis
Expand the Mode Analysis section and check the Subtract propagation constant from material wave number check box to calculate the wave number for the scattered wave as
,
where kn is the wave number for the scattered wave propagating in the normal direction, k is the material wave number, and β is the propagation constant, determined from the mode analysis. If the check box is cleared (the default), kn = k.
For more information about the Gaussian beam theory, see Gaussian Beams as Background Fields and Input Fields.
Beam Splitter: Application Library path Wave_Optics_Module/Optical_Scattering/beam_splitter
Leaky Modes in a Microstructured Optical Fiber: Application Library path Wave_Optics_Module/Verification_Examples/microstructured_optical_fiber
Initial Values for Incident Wave
For the Electromagnetic Waves, Transient interface enter the components for the initial value of the Magnetic vector potential A0 (SI unit: Wb/m).
Second Harmonic Generation of a Gaussian Beam: Application Library path Wave_Optics_Module/Nonlinear_Optics/second_harmonic_generation
Dispersion and Absorption
This section is only available for the Electromagnetic Waves, Transient interface. To display it, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
Select the Dispersion and absorption model that will be used when calculating the wave number and attenuation constant for the incident and scattered waves — Low loss approximation (the default), or High loss. For High loss also enter a Carrier frequency f0 (SI unit: Hz). The default is 300 THz.
When the Dispersion and absorption model is set to Low loss approximation the refractive index is calculated from the relative permittivity and the relative permeability as
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Similarly, the absorption coefficient is calculated as
,
where Zc is the characteristic impedance.
When the Dispersion and absorption model is set to High loss, the real and the imaginary parts of the complex refractive index is solved for from the real and the imaginary parts of the relative permittivity, using the relations
and
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The absorption coefficient is then given by
.