== Methods Of Physical Optics ==
=== Physical Optics As An Asymptotic Technique ===
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.
Asymptotic methods are usually valid at high frequencies as k<sub>0</sub>R = 2ÏR2pR/λ?<sub>0 </sub>>> 1, where R is the distance between the source and observation points, k<sub>0 </sub>is the free-space propagation constant and λ?<sub>0 </sub>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, which is featured in EM.Cube's Propagation Module, is a ray tracing method based on Geometrical Optics (GO). An SBR analysis starts by shooting a number of ray tubes (or beams) off a source. It then traces all the rays as they propagate in the scene or bounce off the surface of obstructing scatterers. The uniform theory of diffraction (UTD) is used to model the diffraction of rays at the edges of the structure.
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.
=== Conventional Physical Optics (GO-PO) ===
The following analysis assumes a general impedance surface. To treat an object with an arbitrary geometry using PO, the object is first decomposed into many small elementary patches or cells, which have a simple geometry such as a rectangle or triangle. Then, using the tangent plane approximation, the electric and magnetic surface currents, '''J(r)''' and '''M(r)''', on the lit region of the scatterer are approximated by:
[[File:PO1(1).png]]
where '''E(r)''' and '''H(r)''' are the incident electric and magnetic fields on the object and '''n''' is the local outward normal unit vector as shown in the figure below. α a is a parameter related to the impedance Z of the surface (expressed in Ohms), which is defined in the following way:
[[File:PO2.png]]
where η?<sub>0</sub> = 120Ï Î© 120p O is the intrinsic impedance of the free space. Then, the electric and magnetic currents reduce to:
[[File:PO3.png]]
Two limiting cases of an impedance surface are perfect electric conductor (PEC) and perfect magnetic conductor (PMC) surface. For a PEC surface, Z = 0, α a = 1, and one can write:
[[File:PO4.png]]
while for a PMC surface, Z = â8, α a = -1, and one can write:
[[File:PO5.png]]
Another special case is a Huygens surface with equivalent electric and magnetic surface currents. In that case, Z = η?<sub>0</sub>, α a = 0, and one can write:
[[File:PO10.png]]
A major difficulty encountered in determining the PO currents of the scatterer is identification of lit and shadowed facets. Determination of lit and shadowed regions for simple, stand-alone, convex objects is rather simple. Denoting the incidence direction from a source to a point on the scatterer by the unit vector '''k''', the point is considered lit if '''n.k'''< 0, and shadowed if '''n.k'''> 0. These conditions, however, are only valid if there is a direct line of sight (LOS) between the source and the centroid of the cell under consideration. They cannot predict if there are any obstructing objects in the path of the incident beam or ray. For simple convex objects, a Geometrical Optics (GO) approach can be used to finds the optical LOS lines and determine the lit and shadowed areas on the object. The conventional PO can then be used to find the electric and magnetic surface currents.
=== Calculating Near & Far Fields In PO ===
Once the electric and magnetic surface currents are determined in the lit regions of the scatterer(s), they act as secondary sources and radiate into the free space. These secondary fields are the scattered fields that are superposed with the primary incident fields. The near fields at every point '''r''' in space are calculated from:
[[File:PO6.png]]
where ''''''G<sub>EJ</sub>''', '''G<sub>EM</sub>''', '''G<sub>HJ</sub>''', '''G<sub>HM</sub>'''''' are the dyadic Green's functions of electric and magnetic fields due to electric and magnetic currents, respectively. In EM.Cube's PO Module, the background structure is the free space. Therefore, all these dyadic Green's functions reduce to the simple free-space Green's function of the form exp(-jk<sub>0</sub>r)/(4Ïr4pr) and the near fields reduce to:
[[File:PO7.png]]
where R = | '''r'''-'''r''''|, k<sub>0</sub> = 2Ï2p/λ?<sub>0</sub> and Z<sub>0</sub> = 1/Y<sub>0</sub> = η?<sub>0</sub>.
When k<sub>0</sub>r >> 1, i.e. in the far-zone field of the scatterer, one can use the asymptotic form of the Green's functions and evaluate the radiation integrals using the stationary phase method to obtain far-field expressions for the electric and magnetic fields as follows:
[[File:PO8.png]]
=== Iterative Physical Optics (IPO) ===
The induced electric and magnetic surface currents on each point of the scatterer object can be calculated from the Magnetic and Electric Field Integral Equations (MFIE & EFIE):
For most practical applications, iterations up to the second order is sufficient. The iterative solution will not only account for double-bounce scattering over the lit regions but it also removes the lower order currents erroneously placed over concave shadowed areas.
=== General Huygens Sources ===
According to the electromagnetic equivalence theorem, if we know the tangential components of E and H fields on a closed surface, we can determine all the E and H fields inside and outside that surface in a unique way. Such a surface is called a Huygens surface. At the end of a full-wave FDTD or MoM solution, all the electric and magnetic fields are known everywhere in the computational domain. We can therefore define a box around the radiating (source) structure, over which we can record the tangential E and H field components. The tangential field components are then used to define equivalent electric and magnetic surface currents over the Huygens surface as:
[[File:PO16.png]]
where the summation over index ''j'' is carried out for all the elementary cells Î?<sub>j</sub> that make up the Huygens box. In EM.Cube Huygens surfaces are cubic and are discretized using a rectangular mesh. Therefore, Î?<sub>j</sub> represents any rectangular cell located on one of the six faces of Huygens box. Note that the calculated near-zone electric and magnetic fields act as incident fields for the scatterers in your PO Module project. The Huygens source data are normally generated in one of EM.Cube's full-wave computational modules like FDTD, Planar or MoM3D. Keep in mind that the fields scattered (or reradiated) by your physical structure do not affect the fields inside the Huygens source.
The far fields of the Huygens surface currents are calculated from the following relations:
[[File:PO17(1).png]]
== Physical Structure & Its Discretization ==
=== Grouping Objects By Surface Type ===
EM.Cube's Physical Optics (PO) Module organizes physical objects by their surface type. A regular object is assumed to be made of one of the three surface types:
Figure 1: PO Module's Navigation Tree and its PEC, PMC and Impedance Surface dialogs.
=== Creating New Objects & Moving Them Around ===
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 PO Module 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.
Figure 1: Moving objects between different surface groups in PO Module.
=== Generating & Customizing PO Mesh ===
The mesh generation process in PO Module involves three steps:
# Verifying the mesh.
The objects of your physical structure are meshed based on a specified mesh density expressed in cells/λ?<sub>0</sub>. The default mesh density is 20 cells/λ?<sub>0</sub>. To view the PO mesh, click on the [[File:manuals/emagware/emcube/modules/physical-optics/discretization-po-mesh/creating-and-viewing-the-mesh/mesh_tool_tn.png]] 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''' [[File:manuals/emagware/emcube/modules/physical-optics/discretization-po-mesh/creating-and-viewing-the-mesh/mesh_tool.png]] 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.
Figure 1: PO Module's Mesh Settings dialog.
=== 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.
Figure 2: Geometry and PO mesh of an overlapping sphere and ellipsoid.
=== Mesh Density & Local Mesh Control ===
EM.Cube's PO Module 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.
Figure 2: Triangular surface mesh of two PEC box objects with the orange PEC group having a locked mesh of higher density.
== Excitation Sources ==
=== Hertzian Dipole Sources ===
A short dipole is the simplest way of exciting a structure in EM.Cube's PO Module. A short dipole source acts like an infinitesimally small ideal current source. To define a short dipole source, follow these steps:
Figure 1: PO Module's Short Dipole Source dialog.
=== Importing Short Dipoles From MoM3D Module ===
The solution of a problem in one of EM.Cube's computational modules can serve as the excitation source for another problem in another computational module. An example of this is analyzing a wire antenna in the [[MoM3D Module]] and importing the wire current solution to PO Module to excite a large scatterer. Remember that you cannot define wires or curve objects in PO Module. However, you can have short dipole sources that act like differential wire elements carrying fixed currents. Using this concept, you can realize a complex wire antenna or radiator array as the source of your PO project.
Figure 1: Importing a Wire MoM current solution into the PO Module. In this structure, 90 wire cell currents representing a helical antenna were imported and placed above a large sinusoidal PEC surface.
=== Plane Wave Sources ===
Your physical structure in PO Module can be excited by an incident plane wave. In particular, a plane wave source can be used 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.Cube's PO Module provides the following polarization options:
* RCPz
The direction of incidence is defined through the θ ? and Ï f 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 Ï f = 0° representing a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. In the TM<sub>z</sub> and TE<sub>z</sub> 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 à 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 is generated. The left-hand (LCP) and right-hand (RCP) circular polarization cases are restricted to normal incidences only (θ?= 180°).
To define a plane wave source follow these steps:
Figure 1: PO Module's Plane Wave dialog.
=== Huygens Sources ===
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.
Figure 2: (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 ===
To open PO Module's Simulation Run dialog, click the '''Run''' [[File:manuals/emagware/emcube/modules/physical-optics/running-po-simulations/running-a-po-analysis/run_icon.png]] 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.
Figure 1: PO Module's Simulation Run dialog.
=== Setting The Numerical Parameters ===
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 η?<sub>0</sub> 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'''.
Figure 1: PO Module's Simulation Engine Settings dialog.
=== Visualizing Current Distributions ===
At the end of a PO simulation, EM.Cube's PO engine generates a number of output data files that contain all the computed simulation data. The main output data are the electric and magnetic 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 -Ï p and Ïp. 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.
[[File:PO37.png]]
Figure 2: 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:
* The initial size of the sensor plane is 100 Ã 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 -Ï p and Ïp.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.'''
[[File:PO42(4).png]]
Figure 2: Near field plots of electric and magnetic fields on a sensor plane.
=== Visualizing 3D 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 Ï f direction and the total far field defines as:
[[File:FDTD129.png]]
Figure 2: 3D radiation pattern of a parabolic dish reflector excited by a short dipole at its focal point.
=== 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, which is defined in the following manner:
[[File:FDTD130.png]]
Three RCS quantities are computed: the θ ? and Ï f components of the radar cross section as well as the total radar cross section, which are dented by Ïs<sub>θ?</sub>, Ïs<sub>Ïf</sub>, and Ïs<sub>tot</sub>. 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 θ?<sub>0</sub> and Ïf<sub>0</sub>, and the RCS is measured and plotted at all θ ? and Ï f angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles θ?<sub>0</sub> and Ïf<sub>0</sub>, and the RCS is measured and plotted at the echo angles 180°-θ?<sub>0</sub>; and Ïf<sub>0</sub>. 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 Ï f 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 Ï f 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 Ïf-cut. This latter cut is at Ï 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 Ïs<sub>θ?</sub>, Ïs<sub>Ïf</sub>, and Ïs<sub>tot</sub> 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 m<sup>2</sup>. 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.
[[File:PO47.png]]
Figure 2: RCS of a PEC sphere illuminated by an laterally incident plane wave.
=== Customizing 3D Plots ===
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/m<sup>2</sup> on embedded objects) as well as the mean current and the standard deviation.
Similar to current distribution plots, field plots (total, magnitude, phase, etc.) are displayed with some default settings and options, which can be further customized individually. To do so, open the '''Output Plot Settings''' dialog by right clicking on a specific plot entry in the Navigation Tree and selecting '''Properties...''' or by double clicking on the surface of the plot's legend box. The settings are identical to those of current distribution plots. Two scale options, linear and dB, are available. You can also change the lower and upper limits of the individual field plots as well as their color map.
=== 2D Radiation Pattern & RCS Graphs ===
At the end of a PO simulation, the radiation pattern data E<sub>θ</sub>, E<sub>φ</sub>, and E<sub>tot</sub> in the three principal XY, YZ and ZX planes as well as an additional user defined phi plane cut are available for plotting on 2-D graphs. There are a total of eight 2-D pattern graphs in the data manager: 4 polar graphs and 4 Cartesian graphs of the same pattern data. To open data manager, click the '''Data Manager''' [[File:manuals/emagware/emcube/modules/physical-optics/visualizing-simulation-data/2-d-radiation-graphs/data_manager_icon.png]] button of the '''Compute Toolbar''' or select '''Compute [[File:manuals/emagware/emcube/modules/physical-optics/physical-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]]Data Manager''' from the menu bar or right click on the '''Data Manager''' item of the Navigation Tree and select Open Data Manager... from the contextual menu or use the keyboard shortcut '''Ctrl+D'''. In the Data manager Dialog, you will see a list of all the data files available for plotting. These include the four polar pattern data files with a '''.ANG''' file extension and the four Cartesian pattern data file with a '''.DAT''' file extension. Select any data file by clicking and highlighting its '''ID''' in the table and then click the '''Plot''' button to plot the graph.
The 2-D radiation patterns in the XY, YZ and ZX plane cuts.
=== PO Sweep Simulations ===
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:
Figure 1: PO Module's Frequency Settings and Angle Settings dialogs.
=== Animation Of PO Data ===
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<sub>s</sub>|'''or the magnitude of total magnetic current distribution '''|M<sub>s</sub>|'''. 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'''.