5.1.3 Free space incident wave
QuickWave enables a free space excitation. It is available by using the auxiliary surface, so-called Plane Wave (PLW) Box simulation object. The free space excitation is generated only to the inside of the PLW Box. Two types of free space excitation available in QuickWave are described in the following sub-sections.
It should be noted at this point that the software enables free space illumination within dielectric or magnetic media. The parameters of surrounding medium (permittivity, permeability, conductivity, and magnetic loss) should be indicated in the Processing/Postprocessing dialogue and must be the same as respective entries seen for the surrounding medium in Project Media window. QW-3D does not check the consistency between the settings made in those two dialogues. Inconsistent settings will lead to physically inconsistent post-processing results.
In QW-3D the user can take advantage of another useful option for plane wave excitation. In some cases (e.g. periodic circuits) it is required to disable some of the PLW box walls from exciting the wave. This can be done through the Walls Activity option, where each of six PLW box walls can be deactivated.
Free space incident wave excitation is available for periodic circuits.
Free space incident wave excitation is not available in QW-V2D.
The free space excitation with a plane wave or Gaussian beam has been widely discussed on simulation examples in User Guide 3D: Plane wave excitation and scattering.
QuickWave enables free space excitation with a plane wave (available as TEM illumination in Plane Wave Box options). For this excitation type there are three angles to be chosen:
j (Phi) – azimuthal angle of the direction of wave propagation,
q (Theta) – elevation angle of the direction of wave propagation,
Polarisation – polarisation angle of the electric field.
With all these angles set to zero, the incident wave travels along the Z-axis and its electric field vector is oriented along the X-axis. In general, the direction of propagation determines a modified Z’ axis, and the electric field orientation determines a modified X’ axis, of the modified X’Y’Z’ coordinate system obtained from the original XYZ coordinate system by rotation with Euler angles Phi, Theta, Polarisation in the ZYZ Euler convention. For more details about Euler angles refer to Radiation patterns section.
An alternative explanation of the three angles is as follows. The direction of wave propagation is inclined by angle Theta from z-axis towards x-axis, and rotated by angle Phi from x-axis towards y-axis. Consider this direction to be ir direction of a spherical coordinate system, at the point where the wavefront first reaches the sphere. With Polarisation equal zero, the electric field will be oriented along iq direction at this point. Otherwise Polarisation is the angle between the unit vector iq and the electric field vector measured in the plane of unit vectors iq and ij.
Mathematically, the versor in the direction of wave propagation is:
[cosPhi sinTheta, sinPhi sinTheta, cosTheta]
and the versor in the direction of the electric field vector is:
[cosPol cosPhi cosTheta - sinPol sinPhi, cosPol sinPhi cosTheta + sinPol cosPhi, - cosPol sinTheta]
Next to the incident angles the Waveform, Amplitude, and Delay should be also determined. The sense of Amplitude and Delay is analogous as in the case of transmission line ports. Now Amplitude applies to a square root of surface power density, i.e., a square root of the Poynting vector amplitude of the incident wave. For example, a source of illumination TEM with Amplitude equal A injects a plane wave of surface power density equal A2 [W/mm2].
QuickWave allows for producing circular polarisation for a plane wave excitation. This can be achieved by using two Plane Wave Boxes and exciting two plane waves with perpendicular polarisations and an appropriate Delay between them.
5.1.3.2 2D and 3D Gaussian beam excitation
Illumination with a plane wave well approximates these physical cases where a spot size of the illuminating wave is larger than the scattering object's dimensions. There are, however, numerous cases where the actual finite size of the spot must be considered and may be smaller than the object's dimensions. This happens in measurements and scatterometry techniques.
Solutions to the Maxwell equations in free space that provide finite spots are Gaussian beams. The so-called 3D Gaussian beam propagating along a particular dimension focuses in the other two dimensions around a point called a neck centre, creating a Gaussian-shaped spot of size called a neck diameter (Gaussian field variation in the plane perpendicular to the direction of incidence); it then de-focuses beyond the neck.
The so-called 2D Gaussian beam propagates along one dimension, focuses in the second dimension, and remains invariant along the third (in the plane perpendicular to the direction of incidence, it has Gaussian field distribution in one direction and constant field in the direction perpendicular to it).
Both types of Gaussian beams are supported in QW-3D, and are available as B3D and B2D illumination in PLW box options. For these excitation types there are three angles to be chosen:
j (Phi) – azimuthal angle of the direction of wave propagation,
q (Theta) – elevation angle of the direction of wave propagation,
Polarisation – polarisation angle of the electric field.
With all these angles set to zero, the incident wave travels along the Z-axis and its electric field vector is oriented along the X-axis. In general, the direction of propagation determines a modified Z’ axis, and the electric field orientation determines a modified X’ axis, of the modified X’Y’Z’ coordinate system obtained from the original XYZ coordinate system by rotation with Euler angles Phi, Theta, Polarisation in the ZYZ Euler convention. For more details about Euler angles refer to Radiation pattern section.
An alternative explanation of the three angles is as follows. The direction of wave propagation is inclined by angle Theta from z-axis towards x-axis, and rotated by angle Phi from x-axis towards y-axis. Consider this direction to be ir direction of a spherical coordinate system, at the point where the wavefront first reaches the sphere. With Polarisation equal zero, the electric field will be oriented along iq direction at this point. Otherwise Polarisation is the angle between the unit vector iq and the electric field vector measured in the plane of unit vectors iq and ij.
Mathematically, the versor in the direction of wave propagation is:
[cosPhi sinTheta, sinPhi sinTheta, cosTheta]
and the versor in the direction of the electric field vector is:
[cosPol cosPhi cosTheta - sinPol sinPhi, cosPol sinPhi cosTheta + sinPol cosPhi, - cosPol sinTheta]
Additionally, for both B3D and B2D beams, the position of the neck centre of the beam (NeckX, NeckY, NeckZ in the project units) and neck diameter (N_dia in the project units) should be determined. For B2D, QW-3D allows defining also Angle of variation of the beam field in the plane perpendicular to the direction of propagation, in the same convention as Polarisation is defined.
Next to the incident angles and the neck parameters, the Waveform, Amplitude, and Delay should be also determined. The sense of Amplitude and Delay is analogous as in the case of transmission line ports. Now Amplitude applies to a square root of surface power density, i.e., a square root of the Poynting vector amplitude of the incident wave. For illumination type of B3D or B2D, surface power density of the incident wave varies in space, and Amplitude refers to its value at the neck. Note that both Gaussian beams are implemented with approximate relations after Ramo et al., "Fields and Waves in Communication Electronics", Chapter 14.12, which assume neck diameters bigger than wavelength. For narrower necks, the above described scaling is less rigorously obeyed, in particular, the position of the neck shifts opposite to the direction of beam propagation and surface power density at the neck decreases.