EM.Illumina

An EM.Illumina Primer

EM.Illumina in a Nutshell

EM.Illumina is a 3D electromagnetic simulator for modeling large free-space structures. It features a high frequency asymptotic solver based on Physical Optics (PO) for simulation of electromagnetic scattering from large metallic structures and impedance surfaces. You can use EM.Illumina to compute the radar cross section (RCS) of large target structures like aircraft or vehicles or simulate the radiation of antennas in the presence of large platforms.

EM.Illumina provides a computationally efficient alternative to full-wave solutions for extremely large structures when full-wave analysis becomes prohibitively expensive. Based on a high frequency asymptotic physical optics formulation, EM.Illumina assumes that a source like a short dipole radiator or an incident plane wave induces currents on a metallic structure, which in turn reradiate into the free space. In the case of an impedance surface, both surface electric and magnetic current are induced on the surface of the scatterer. A challenging step in establishing the PO currents is the determination of the lit and shadowed points on complex scatterer geometries. The conventional physical optics method (GO-PO) uses geometrical optics ray tracing from each source to the points on the scatterers to determine whether they fall into the lit or shadow regions. But this can become a time consuming task depending on the size of the computational problem. Besides GO-PO, EM.Illumina also offers a novel Iterative Physical Optics (IPO) formulation, which automatically accounts for multiple shadowing effects. The IPO technique can effectively capture dominant, near-field, multiple scattering effects from electrically large targets.

EM.Illumina is the high-frequency, asymptotic Physical Optics Module of EM.Cube, a comprehensive, integrated, modular electromagnetic modeling environment. EM.Illumina shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as CubeCAD with all of EM.Cube's other computational modules.

Click here to learn more about EM.Cube Modeling Environment.

Click here to learn more about the basic functionality of CubeCAD.

Physical Optics as an Asymptotic Technique

Asymptotic methods are usually valid at high frequencies as k₀ R = 2π R/λ₀ >> 1, where R is the distance between the source and observation points, k₀ is the free-space propagation constant and λ₀ is the free-space wavelength. Under such conditions, electromagnetic fields and waves start to behave more like optical fields and waves. Asymptotic methods are typically inspired by optical analysis. Two important examples of asymptotic methods are the Shoot-and-Bounce-Rays (SBR) method and Physical Optics (PO). The SBR method is a ray tracing method based on Geometrical Optics (GO) and forms the basis of the simulation engine of EM.Terrano.

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 conventional PO analysis, which involves only perfect electric conductors, only electric surface currents related to the tangential magnetic fields are considered.

Click here to lean more about the Theory of Physical Optics.

Building the Physical Structure

EM.Illumina's Navigation Tree.

Grouping Objects By Surface Type

EM.Illumina organizes physical objects by their surface type. Any object in EM.Illumina is assumed to be made of one of the three surface types:

1. Perfect Electric Conductor (PEC)
2. Perfect Magnetic Conductor (PMC)
3. Generalized Impedance Surface

EM.Illumina can only handle surface and solid CAD objects. Only the outer surface of solid objects is considered in the PO simulation. No line or 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. 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.

The PEC dialog.

The PMC dialog.

The Impedance Surface dialog.

Creating New Objects & Moving Them Around

Moving objects among different surface groups in EM.Illumina.

The objects that you draw in EM.Cube's project workspace always belong to the "Active" surface group. By default, the last object group that you created remains active until you change it. The current active group is always listed in bold letters in the Navigation Tree. Any surface group can be made active by right clicking on its name in the Navigation Tree and selecting the Activate item of the contextual menu. If you start a new EM.Illumina project and draw any object without having previously defined a surface group, a default PEC group is automatically created and added to the Navigation Tree to hold your new object.

You can move one or more selected objects to any material group. Right click on the highlighted selection and select Move To > Physical Optics > from the contextual menu. This opens another sub-menu with a list of all the available surface groups already defined in EM.Illumina. Select the desired surface group, and all the selected objects will move to that group. The objects can be selected either in the project workspace, or their names can be selected from the Navigation Tree. In the latter case, make sure that you hold the keyboard's Shift Key or Ctrl Key down while selecting a material group's name from the contextual menu. You can also move one or more objects from a PO surface group to EM.Cube's other modules, or vice versa. In that case, the sub-menus of the Move To > item of the contextual menu will indicate all the EM.Cube modules that have valid groups for transfer of the selected objects.

In EM.Cube, you can import external CAD models (such as STEP, IGES, STL models, etc.) only to CubeCAD. From CubeCAD, you can then move the imported objects to any other computational module including PO Module.

Discretizing the Physical Structure

EM.Illumina uses a triangular surface mesh to discretize the structure of your project workspace. The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. Alternatively, you can base the definition of the mesh density on "Cell Edge Length" expressed in project units.

Generating & Customizing PO Mesh

EM.Illumina's Mesh Settings dialog.

The Tessellation Options dialog.

The mesh generation process in EM.Illumina involves three steps:

1. Setting the mesh properties.
2. Generating the mesh.
3. Verifying the mesh.

The objects of your physical structure are meshed based on a specified mesh density expressed in cells/λ₀. The default mesh density is 10 cells/λ₀. To view the PO mesh, click on the button of the Simulate Toolbar or select Menu > Simulate > Discretization > Show Mesh or use the keyboard shortcut Ctrl+M. When the PO mesh is displayed in the project workspace, EM.Cube's mesh view mode is enabled. In this mode, you can perform view operations like rotate view, pan, zoom, etc. However, you cannot select or move or edit objects. While the mesh view is enabled, the Show Mesh button remains depressed. To get back to the normal view or select mode, click this button one more time, or deselect Menu > Simulate > Discretization > Show Mesh to remove its check mark or simply click the Esc Key of the keyboard.

"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.

To set the PO mesh properties, click on the button of the Simulate Toolbar or select Menu > Simulate > Discretization > Mesh Settings... or right click on the 3-D Mesh item in the Discretization section of the Navigation Tree and select Mesh Settings... from the contextual menu, or use the keyboard shortcut Ctrl+G. You can change the value of Mesh Density to generate a triangular mesh with a higher or lower resolutions. Some additional mesh parameters can be access by clicking the Tessellation Options button of the dialog. In the Tessellation Options dialog, you can change Curvature Angle Tolerance expressed in degrees, which as a default value of 15°. This parameter can affect the shape of the mesh especially in the case of solid CAD objects. It determines the apex angle of the triangular cells of the primary tessellation mesh which is generated initially before cell regularization. Lower values of the angle tolerance result in a less smooth and more pointed mesh of curved surface like a sphere.

Two ellipsoids of different compositions.

Trinagular surface mesh of the two ellipsoids.

More On Triangular Surface Mesh

The physical optics method assumes an unbounded, open-boundary computational domain, wherein the physical structure is placed against a free space background medium. As such, only finite-extent surfaces are discretized. EM.Cube's PO Module uses a triangular surface mesh to discretize all the surface and solid objects in the project workspace. As mentioned earlier, curve objects (or wires) are not allowed in PO Module. In the case of solids, only the surface of the object or its faces are discretized, as the interior volume is not taken into account in a PO analysis. In general, triangular cells are placed on the exterior surface of solid objects. In contrast, surface objects are assumed to be double-sided by default. The means that the PO mesh of a surface object indeed consists of coinciding double cells, one representing the upper or positive side and the other representing the lower or negative side. This may lead to a very large number of cells. EM.Cube's PO mesh has some more settings that allow you to treat all mesh cells as double-sided or all single-sided. This can be done in the Mesh Settings dialog by checking the boxes labeled All Double-Sided Cells and All Single-Sided Cells. This is useful when your project workspace contains well-organized and well-oriented surface objects only. In the single-sided case, it is very important that all the normals to the cells point towards the source. Otherwise, the surface objects will be assumed to lie in the shadow region and no currents will be computed on them. By checking the box labeled Reverse Normal, you instruct EM.Cube to reverse the direction of the normal vectors at the surface of all the cells.

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.

Surface mesh Generation in EM.Cube

Mesh Density & Local Mesh Control

EM.Illumina applies the mesh density specified in the Mesh Settings dialog on a global scale to discretize all the objects in the project workspace. Although the mesh density is expressed in cells per free space wavelength similar to full-wave method of moments (MoM) solvers, you have to keep in mind that the triangular surface mesh cells in PO Modules act slightly differently. The complex-valued, vectorial, electric and magnetic surface currents, J and M are assumed to be constant on the surface of each triangular cell. On plates and flat faces or surfaces, the normal vectors to all the cells are identical. Incident plane waves or other types of relatively uniform source fields induce uniform PO currents on all these cells. Therefore, a high resolution mesh may not be necessary on flat surface or faces. However, a high mesh density is very important for accurate discretization of curved objects like spheres or ellipsoids.

You can lock the mesh density of any surface group to any desired value different than the global mesh density. To do so, open the property dialog of a surface group by right clicking on its name in the Navigation Tree and select Properties... from the contextual menu. At the bottom of the dialog, check the box labeled Lock Mesh. This will enable the Density box, where you can set a desired value. The default value is equal to the global mesh density.

Two overlapping PEC spheres.

Trinagular surface mesh of the two spheres.

PO Module's Short Dipole Source dialog

PO Module's Plane Wave dialog

Excitation Sources

Hertzian Dipole Sources

A short Hertzian dipole is the simplest way of exciting a structure in EM.Illumina. A short dipole source acts like an infinitesimally small ideal current source. The total radiated power by your dipole source is calculated and displayed in Watts in its property dialog.

Click here to learn more about Hertzian Dipole Sources.

Plane Wave Sources

Your physical structure in EM.Illumina can be excited by an incident plane wave. In particular, a plane wave source is needed to compute the radar cross section of a target. A plane wave is defined by its propagation vector indicating the direction of incidence and its polarization. EM.Illumina provides the following polarization options: TMz, TEz, Custom Linear, LCPz and RCPz.

The direction of incidence is defined through the θ and φ angles of the unit propagation vector in the spherical coordinate system. The values of these angles are set in degrees in the boxes labeled Theta and Phi. The default values are θ = 180° and φ = 0° representing a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. In the TM_z and TE_z polarization cases, the magnetic and electric fields are parallel to the XY plane, respectively. The components of the unit propagation vector and normalized E- and H-field vectors are displayed in the dialog. In the more general case of custom linear polarization, besides the incidence angles, you have to enter the components of the unit electric Field Vector. However, two requirements must be satisfied: ê . ê = 1 and ê × k = 0 . This can be enforced using the Validate button at the bottom of the dialog. If these conditions are not met, an error message pops up. The left-hand (LCP) and right-hand (RCP) circular polarization cases are restricted to the normal incidence only (θ = 180°).

To define a plane wave source follow these steps:

• Right click on the Plane Waves item in the Sources section of the Navigation Tree and select Insert New Source... The Plane wave Dialog opens up.
• In the Field Definition section of the dialog, you can enter the Amplitude of the incident electric field in V/m and its Phase in degrees. The default field Amplitude is 1 V/m with a zero Phase.
• The direction of the Plane Wave is determined by the incident Theta and Phi angles in degrees. You can also set the Polarization of the plane wave and choose from the five options described earlier.
• If the Custom Linear option is selected, you also need to enter the X, Y, Z components of the E-Field Vector.

Huygens Sources

PO Module's Huygens Source dialog

At the end of a full-wave simulation in the EM.Cube's FDTD, MoM3D, Planar or Physical Optics Modules, you can generate Huygens surface data. According to Huygens' principle, if one knows the tangential electric and magnetic field components on a closed surface, one can determine the total electric and magnetic fields everywhere inside and outside that closed surface. Huygens surfaces are defined around a structure for recording the tangential components of electric and magnetic fields at the end of full-wave simulation of the structure. The tangential electric and magnetic fields are saved into ASCII data files as magnetic and electric currents, respectively. These current can be used as excitation for other structures. In other words, the electric and magnetic currents associated with a Huygens source radiate energy and provide the excitation for the PO Module's physical structure.

In order to define a Huygens source, you need to have a Huygens data file of .HUY type. This file is generated as an output data file at the end of an FDTD, MoM3D, Planar or PO simulation, if you have defined a Huygens Surface observable in one of those projects. When you define a Huygens source, you indeed import an existing Huygens surface into the project and set it as an excitation source.

To create a new Huygens source, follow these steps:

• Right click on the Huygens Sources item in the Sources section of the Navigation Tree and select Import Huygens Source... from the contextual menu.
• The standard Windows Open Dialog opens up. The file type is set to .HUY by default. Browse your folders to find a Huygens surface data file with a .HUY file extension. Select the file and click the Open button of the dialog to import the data.
• Once imported, the Huygens source appears in the Project Workspace as a wire-frame box.
• You can open the property dialog of a Huygens source by right clicking on its name in the Navigation Tree and selecting Properties... From this dialog you can change the color of the Huygens source box as well as its location and orientation. You can enter new values for the X, Y, Z Center Coordinates and Rotation Angles of the Huygens box. You can also view the dimensions of the box.
• 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: (Left) A rotated imported Huygens source, and (Right) An array of imported Huygens sources defined to excite a PEC box.

Running PO Simulations

Running A Basic PO Analysis

EM.Illumina's Simulation Run dialog.

To open EM.Illumina's Simulation Run dialog, click the Run button of the Simulate Toolbar or select Menu > Simulate > Run...or use the keyboard shortcut Ctrl+R. To start the simulation click the Run button of this dialog. Once the PO simulation starts, a new dialog called Output Window opens up that reports the various stages of PO simulation, displays the running time and shows the percentage of completion for certain tasks during the PO simulation process. A prompt announces the completion of the PO simulation. At this time, EM.Cube generates a number of output data files that contain all the computed simulation data. These include current distributions, near field data, far field radiation pattern data as well bi-static or mono-static radar cross sections (RCS) if the structure is excited by a plane wave source.

Setting The Numerical Parameters

EM.Illumina's Simulation Engine Settings dialog.

Before you run a PO simulation, you can change some of the PO simulation engine settings. While in the PO Module's Simulation Run Dialog, click the Settings button next to the Select Engine dropdown list. In the Physical Optics Engine Settings Dialog, there are two options for Solver Type: Iterative and GOPO. The default option is Iterative. The GOPO solver is a zero-order PO simulator that uses Geometrical Optics (GO) to determine the lit and shadow cells in the structure's mesh. For the termination of the IPO solver, there are two options: Convergence Error and Maximum Number of Iterations. The default Termination Criterion is based on convergence error, which has a default value of 0.1 and can be changed to any desired accuracy. The convergence error is defined as the L2 norm of the normalized residual error in the combined J/M current solution of the entire discretized structure from one iteration to the next. Note that for this purpose, the magnetic currents are scaled by η₀ in the residual error vector.

You can also use higher- or lower-order integration schemes for the calculation of field integrals. EM.Cube's PO simulation engine uses triangular cells for the mesh of the physical surface structures and rectangular cells for discretization of Huygens sources and surfaces. For integration of triangular cells, you have three options: 7-Point Quadrature, 3-Point Quadrature and Constant. For integration of rectangular cells, too, you have three options: 9-Point Quadrature, 4-Point Quadrature and Constant.

PO Sweep Simulations

EM.Illumina's Frequency Settings dialog.

You can run EM.Cube's PO simulation engine in the sweep mode, whereby a parameter like frequency, plane wave incident angles or a user defined variable is varied over a specified range at predetermined samples. The output data are saved into data files for visualization and plotting. EM.Cube's PO Module currently offers three types of sweep:

1. Frequency Sweep
2. Angular Sweep
3. Parametric Sweep

To run a PO sweep, open the Simulation 'Run Dialog' and select one of the above sweep types from the Simulation Mode dropdown list of this dialog. If you select either frequency or angular sweep, the Settings button located next to the simulation mode dropdown list becomes enabled. If you click this button, the Frequency Settings Dialog or Angle Settings Dialog opens up, respectively. In the frequency settings dialog, you can set the start and end frequencies as well as the number of frequency samples. The start and end frequency values are initially set based on the project's center frequency and bandwidth. During a frequency sweep, as the project's frequency changes, so does the wavelength. As a result, the mesh of the structure also changes at each frequency sample. The frequency settings dialog gives you three choices regarding the mesh of the project structure during a frequency sweep:

1. Fix mesh at the highest frequency.
2. Fix mesh at the center frequency.
3. Re-mesh at each frequency.

You can run an angular sweep only if your project has a plane wave excitation. In this case, you have to define a plane wave source with the default settings. During an angular sweep, either the incident theta angle or incident phi angle is varied within the specified range. The other angle remains fixed at the value that is specified in the Plane Wave Dialog. You have to select either Theta or Phi as the Sweep Angle in the Angle Settings Dialog. You also need to set the start and end angles as well as the number of angle samples.

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 "Parametric Modeling, Sweep & Optimization" section of EM.Cube Manual or see the "Parametric Sweep" sections of the FDTD or Planar Module manuals.

Working with PO Simualtion Data

At the end of a Physical Optics simulation, EM.Illumina generates a number of output data files that contain all the computed simulation data. The primary output data in Physical Optics are the electric and magnetic surface current distributions on the surface of your structure. Once these quantities are known, EM.Illumina can compute near-field distributions as well as far-field quantities such as radiation patterns and radar cross section (RCS). EM.Illumina does not generate any output data on its own unless you define observables for your simulation project.

Visualizing Current Distributions

You can easily examine the 3D color-coded intensity plots of current distributions in the project workspace. Current distributions are visualized on the surface of the PO mesh cells, and the magnitude and phase of the electric and magnetic surface currents are plotted for all the objects. In order to view these currents, you must first define a current distribution observable before running the PO simulation. To do this, right click on the Current Distributions item in the Observables section of the Navigation Tree and select Insert New Observable.... The Current Distribution Dialog opens up. Accept the default settings and close the dialog. A new current distribution node is added to the Navigation Tree. Unlike the Planar Module, in the PO Module you can define only one current distribution node in the Navigation Tree, which covers all the objects in the project workspace. After a PO simulation is completed, new plots are added under the current distribution node of the Navigation Tree. Separate plots are produced for the magnitude and phase of each of the electric and magnetic surface current components (X, Y and Z) as well as the total current magnitude. The magnitude maps are plotted on a normalized scale with the minimum and maximum values displayed in the legend box. The phase maps are plotted in radians between -p and p. Note that sometimes the current distribution plots may hide inside smooth and curved objects, and you cannot see them. You may have to freeze such objects or switch to the mesh view mode.

Click here to learn more about Visualizing 3D Current Distribution Maps.

PO Module's Current Distribution dialog.

The current distribution plot of a PEC sphere illuminated by an obliquely incident plane wave.

Near-Field Visualization

EM.Cube allows you to visualize the near fields at a specific field sensor plane. Calculation of near fields is a post-processing process and may take a considerable amount of time depending on the resolution that you specify. To define a new Field Sensor, follow these steps:

• Right click on the Field Sensors item in the Observables section of the Navigation Tree and select Insert New Observable...
• The Label box allows you to change the sensor’s name. you can also change the color of the field sensor plane using the Color button.
• Set the Direction of the field sensor. This is specified by the normal vector of the sensor plane. The available options are X, Y and Z, with the last being the default option.
• By default EM.Cube creates a field sensor plane passing through the origin of coordinates (0,0,0) on the XY plane. You can change the location of the sensor plane to any point by typing in new values for the X, Y and Z Center Coordinates. You can also change these coordinates using the spin buttons.
• The initial size of the sensor plane is 100 × 100 project units. You can change the dimensions of the sensor plane to any desired size. You can also set the Number of Samples along the different directions. These numbers determine the resolution of near field maps. Keep in mind that large numbers of samples may result in long computation times.

After closing the Field Sensor Dialog, a new field sensor item immediately appears under the Observables section in the Navigation Tree. Once a PO simulation is finished, a total of 14 plots are added to every field sensor node in the Navigation Tree. These include the magnitude and phase of all three components of E and H fields and the total electric and magnetic field values. Click on any of these items and a color-coded intensity plot of it will be visualized on the project workspace. A legend box appears in the upper right corner of the field plot, which can be dragged around using the left mouse button. The values of the magnitude plots are normalized between 0 and 1. The legend box contains the minimum field value corresponding to 0 of the color map, maximum field value corresponding to 1 of the color map, and the unit of the field quantity, which is V/m for E-field and A/m for H-field. The values of phase plots are always shown in Radians between -p and p.To display the fields properly, the structure is cut through the field sensor plane, and only part of it is shown. If the structure still blocks your view, you can simply hide or freeze it. You can change the view of the field plot with the available view operations such as rotate view, pan, zoom, etc.

Keep in mind that since Physical Optics is an asymptotic method, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.

Click here to learn more about Visualizing 3D Near Field Maps.

PO Module's Field Sensor dialog

Near field plot of electric field on a sensor plane.

Near field plot of magnetic field on a sensor plane.

Computing Radiation Patterns

Unlike the FDTD method, Physical Optics is an open-boundary technique. You do not need a far field box to perform near-to-far-field transformations. Nonetheless, you still need to define a far field observable if you want to plot radiation patterns. A far field can be defined by right clicking on the Far Fields item in the Observables section of the Navigation Tree and selecting Insert New Radiation Pattern... from the contextual menu. The Radiation Pattern dialog opens up. You can accept most of the default settings in this dialog. The Output Settings section allows you to change the Angle Increment in the degrees, which sets the resolution of far field calculations. The default value is 5 degrees. After closing the radiation pattern dialog, a far field entry immediately appears with its given name under the Far Fields item of the Navigation Tree. After a PO simulation is finished, three radiation patterns plots are added to the far field node in the Navigation Tree. These are the far field component in θ direction, the far field component in φ direction and the total far field. The 3D plots can be viewed by clicking on their name in the navigation tree. They are displayed in EM.Cube's project workspace and are overlaid on the project's structure.

Click here to learn more about the theory of Far Field Computations.

Click here to learn more about Visualizing 3D Radiation Patterns.

Click here to learn more about Plotting 2D Radiation Graphs.

EM.Illumina's Radiation Pattern dialog.

3D radiation pattern of a parabolic dish reflector excited by a short dipole at its focal point.

Computing Radar Cross Section

When the physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. EM.Cube calculates the radar cross section (RCS) of a target. Three RCS quantities are computed: the θ and φ components of the radar cross section as well as the total radar cross section, which are dented by σ_θ, σ_φ, and σ_tot. In addition, EM.Cube's PO Module calculates two types of RCS for each structure: Bi-Static RCS and Mono-Static RCS. In bi-static RCS, the structure is illuminated by a plane wave at incidence angles θ₀ and φ₀, and the RCS is measured and plotted at all θ and φ angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles θ₀ and φ₀, and the RCS is measured and plotted at the echo angles 180°-θ₀; and φ₀. It is clear that in the case of mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles θ and φ are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded.

To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. Right click on the Far Fields item in the Observables section of the Navigation Tree and select Insert New RCS... to open the Radar Cross Section Dialog. Use the Label box to change the name of the far field or change the color of the far field box using the Color button. Select the type of RCS from the two radio buttons labeled Bi-Static RCS and Mono-Static RCS. The former is the default choice. The resolution of RCS calculation is specified by Angle Increment expressed in degrees. By default, the θ and φ angles are incremented by 5 degrees. At the end of a PO simulation, besides calculating the RCS data over the entire (spherical) 3D space, a number of 2D RCS graphs are also generated. These are RCS cuts at certain planes, which include the three principal XY, YZ and ZX planes plus one additional constant f-cut. This latter cut is at f = 45° by default. You can assign another azimuth angle in degrees in the box labeled Non-Principal Phi Plane.

At the end of a PO simulation, the thee RCS plots σ_θ, σ_φ, and σ_tot are added under the far field section of the Navigation Tree. These plots are very similar to the three 3D radiation pattern plots. You can view them by clicking on their names in the navigation tree. The RCS values are expressed in m². For visualization purposes, the 3D plots are normalized to the maximum RCS value, which is also displayed in the legend box. Keep in mind that computing the 3D mono-static RCS may take an enormous amount of computation time.

Click here to learn more about Visualizing 3D RCS.

Click here to learn more about Plotting 2D RCS Graphs.

EM.Illumina's Radar Cross Section dialog.

RCS of a PEC sphere illuminated by an laterally incident plane wave.

 

Back to the Top of the Page

Back to EM.Cube Main Page