Changes

Many larger-scale electromagnetic problems deal with the modeling of radar scattering from large metallic structures (targets like aircraft or vehicles) or the radiation of antennas in the presence of large scatterer platforms. Although a full-wave analysis of such open-boundary computational problems using the method of moments (MoM) is conceptually feasible, it may not be practical due to the enormous memory requirements for storage of the resulting moment matrices. To solve this class of problems, you may instead pursue asymptotic electromagnetic analysis methods.

In the Physical Optics (PO) method, a scatterer surface is illuminated by an incident source, and it is modeled by equivalent electric and magnetic surface currents. This concept is based on the fundamental equivalence theorem of electromagnetics and the Huygens principle. The electric surface currents are denoted by '''J(r)''' and the magnetic surface currents are denoted by '''M(r)''', where '''r''' is the position vector. According to the Huygens principle, the equivalent electric and magnetic surface currents are derived from the tangential components of magnetic and electric fields on a given surface, respectively. This will be discussed in more detail in the next sections. In a classic PO analysis which involves only perfect electric conductors, only electric surface currents, related to the tangential magnetic fields, are considered.

PO Module can only handle surface and solid objects. No curve objects are allowed in the project workspace; or else, they will be ignored during the PO simulation. You can define several PEC, PMC or impedance surface groups with different colors and impedance values (for the last type). All the objects created and drawn under a group share the same color and other properties. A new surface group can be defined by simply right clicking on one of the three '''PEC''', '''PMC''' or '''Impedance Surface''' items in the '''Physical Structure''' section of the Navigation Tree and selecting '''Insert New PEC...''', '''Insert New PMC...''', or '''Insert New Impedance Surface...''' from the contextual menu. A dialog for setting up the group properties opens up. In this dialog you can change the name of the group or its color. In the case of a surface impedance group, you can set the values for the real and imaginary parts of the '''Surface Impedance''' in Ohms.

Figure 1: PO Module's Navigation Tree and its PEC, PMC and Impedance Surface dialogs.

# Verifying the mesh.

"Show Mesh" generates a new mesh and displays it if there is none in the memory, or it simply displays an existing mesh in the memory. This is a useful feature because generating a PO mesh may take a long time depending on the complexity and size of objects. If you change the structure or alter the mesh settings, a new mesh is always generated. You can ignore the mesh in the memory and force EM.Cube to generate a mesh from the ground up by selecting '''Menu > Simulate > Discretization > Regenerate Mesh''' or by right clicking on the '''3-D Mesh''' item of the Navigation Tree and selecting '''Regenerate''' from the contextual menu.

'''As a general rule, EM.Cube's PO mesh generator merges all the objects that belong to the same surface group using the Boolean Union operation.''' As a result, overlapping objects are transformed into a single consolidated object. This is particularly important for generating a contiguous and consistent mesh in the transition and junction areas between connected objects. In general, objects of the same CAD category can be "unioned". For example, surface objects can be merged together, and so can solid objects. However, a surface object and a solid in general do not merge. Objects that belong to different groups on the Navigation Tree are not merged during mesh generation even if they are all of PEC type and physically overlap.

Figure 2: Geometry and PO mesh of an overlapping sphere and ellipsoid.

* By default, the Huygens data are imported as a single Huygens source. You can create an arbitrary array of Huygens sources for your PO project. To do so, in the "Create Array" section of the Huygens source dialog, enter desired values for the '''Number of Elements''' and '''Element Spacing''' along the X, Y and Z directions. You will see an array of wire-frame box appear in the project workspace.

Figure 1: PO Module's Huygens Source dialog.

Figure 2: (Left) A rotated imported Huygens source, and (Right) An array of imported Huygens sources defined to excite a PEC box.

Figure 1: PO Module's Field Sensor dialog.<br />

Figure 2: Near field plots of electric and magnetic fields on a sensor plane.

EM.CUBE's current distribution plots are interactive. When you move the mouse over a current plot, tiny dots appear on its surface. These dots correspond to the points on the sensor plane where the current data have been calculated. Upon mouse-over, you can highlight one of these points. A small tooltip appears on the plot that shows the current value at that point. In other words, you can read the plot values using mouse-over. The legend of a current plot also shows the minimum and maximum current values, the current unit (A/m on metallic traces, V/m on slot traces and A/m² on embedded objects) as well as the mean current and the standard deviation.

Reading current values from a current distribution map by mouse-over.

EM.CUBE offers two different ways of visualizing electric and magnetic current distributions: as a confetti plot or a cone plot. The first type is a scalar intensity plot and shows the current amplitude and phase using colored triangular mesh cells. The second type is a vectorial plot showing cones (or arrows) directed along the visualized current component. In the case of the total electric current distribution, the cone plot shows the overall direction of the currents at any point on the surface of objects. To set the type of a current plot, open the current distribution plot's property dialog by right clicking its name in the Navigation Tree and selecting '''Properties...''' from the contextual menu. In the Plot Type section, choose one of the two radio buttons labeled '''Confetti''' or Cone. In the latter case, you can set the size of the vector cones using the box labeled '''Max Size'''. You can set the plot type at the time of defining the current distribution before running the PO simulation. You can also change the plot type afterwards and switch between the confetti and cone types back and forth.

A vectorial (cone-type) current distribution plot of the PEC sphere: (Left) overlaid on mesh and (Right) with the sphere object frozen.

Current distribution maps are displayed with some default settings and options. You can customize the individual maps (total, magnitude, phase, etc.). To do so, open the '''Output Plot Settings Dialog''' by right clicking on the specific plot entry in the Navigation Tree and selecting '''Properties...''' or by double clicking on the surface of the plot's legend box. Two '''scale''' options are available: '''Linear''' and '''dB'''. With the '''Linear''' (default) option selected, the current value is always normalized to the maximum total current in that plane, and the normalized scale is mapped between the minimum and maximum values. If the '''dB''' option is selected, the normalized current is converted to dB scale. The plot limits (bounds) can be set individually for every current distribution plot. In the '''Limits''' section of the plot's property dialog, you see four options: '''Default''', '''User Defined''', '''95% Conf.''' and '''95% Conf.'''. Select the user defined option and enter new values for the '''Lower''' and '''Upper''' limits. The last two options are used to remove the outlier data within the 95% and 99% confidence intervals, respectively. In other words, the lower and upper limits are set to ? ± 1.96? and ? ± 2.79? , respectively, assuming a normal distribution of the data. Three color maps are offered: '''Default''', '''Rainbow''' and '''Grayscale'''. You can hide the legend box by deselecting the box labeled '''Show Legend Box'''. You can also change the foreground and background colors of the legend box.

The output plot settings dialog.

In a parametric sweep, one or more user defined variables are varied at the same time over their specified ranges. This creates a parametric space with the total number of samples equal to the product of the number of samples for each variable. The user defined variables are defined using EM.Cube's '''Variables Dialog'''. For a description of EM.Cube variables, please refer to the &quot;Parametric Modeling, Sweep &amp; Optimization&quot; section of EM.Cube Manual or see the &quot;Parametric Sweep&quot; sections of the FDTD or [[Planar Module]] manuals.

Figure 1: PO Module's Frequency Settings and Angle Settings dialogs.

At the end of a frequency sweep, angular sweep or parametric sweep simulation in EM.Cube's PO Module, the output data are saved for visualization and plotting. In particular, if you have defined current distribution, field sensor or far field observables in your project, multiple 3D plots, as many as the total number of sweep samples, are added to the Navigation Tree. In a single simulation run, a total of 14 current distribution plots, 14 field sensor plot and 3 radiation pattern plots or 3 RCS plots are generated under every observable node defined in the Navigation Tree. However, after a sweep simulation, only one plot is saved for each sweep sample. This is done to keep the resulting plots manageable. Thus, only the total radiation pattern or total RCS are saved for each sweep sample. In the case of a current distribution observable, you have the choice to save either the magnitude of total electric current distribution '''|J_s|'''or the magnitude of total magnetic current distribution '''|M_s|'''. To change this, open the '''Current Distribution Dialog''' by right clicking on the observable's name in the Navigation Tree and selecting '''Properties...''' from the contextual menu. In the '''Current Display - Multiple Plots''' section of this dialog, select one of the radio sensors labeled '''Electric Current (J)''' or '''Magnetic Current (M)'''. Similarly, in the case of a field sensor observable, you have the choice to save either the total E-field magnitude plot or the total H-field magnitude plot. To change this, open the '''Field Sensor Dialog''' by right clicking on a field sensor's name in the Navigation Tree and selecting '''Properties...''' from the contextual menu. In the '''Field Display - Multiple Plots''' section of this dialog, select one of the radio sensors labeled '''E-Field''' or '''H-Field'''.

Figure 1: Selecting the current or field types for sweep data visualization in PO Module's Current Distribution and Field Sensor dialogs.