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[[Image:Splash-po.jpg|right|750px720px]]<strong><font color="#bd5703" size="4">Fast Asymptotic Solver For Large-Scale Scattering Problems</font></strong><table><tr><td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link= An EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] </td><tr></table>[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Illumina_Documentation | EM.Illumina Primer Tutorial Gateway]]''' [[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''==Product Overview==

[[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 a full-wave analysis solution becomes prohibitively expensive. Based on a high frequency asymptotic physical optics formulation, EM.Illumina it assumes that a source like a short dipole radiator or an incident plane wave induces source generates 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 Ray tracing from each source to the points on the scatterers to determine whether they fall into the are lit or shadow regions. But this can become shadowed is a time consuming task depending on the size of the computational problem. Besides GO-POTo avoid this difficulty, [[EM.Illumina also offers ]]'s simulator uses 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.

{{Note|EM.Illumina is the high-frequency, asymptotic '''[[Physical Optics Module]]''' of '''[[EMImage:Info_icon.Cubepng|30px]]''', a comprehensive, integrated, modular electromagnetic modeling environment. EM.Illumina shares Click here to lean more about the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as '''[[CubeCADBasic Principles of Physical Optics | Theory of Physical Optics]]''' with all of [[EM.Cube]]'s other computational modules.}}

<table><tr><td> [[Image:Info_iconIllumina L2 Fig title.png|40px]] Click here to learn more about '''[[Getting_Started_with_EM.CUBE thumb| EMleft|420px|Analyzing scattering from a trihedral corner reflector using IPO solver.Cube Modeling Environment]]'''.</td>[[Image:Info_icon.png|40px]] Click here to learn more about the basic functionality of '''[[CubeCAD]]'''.</tr>=== Physical Optics as an Asymptotic Technique ===</table>

Asymptotic methods are usually valid at high frequencies as k₀ R = 2&pi; R/&lambda;₀ >> 1, where R is the distance between the source and observation points, k₀ is the free-space propagation constant and &lambda;₀is the free-space wavelength== EM. 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 Illumina as the Shoot-and-Bounce-Rays (SBR) method and Physical Optics (PO). The [[SBR Method|SBR method]] is a ray tracing method based on Geometrical Optics (GO) and forms the basis Module of the simulation engine of [[EM.Terrano]]. Cube ===

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[[EM. This concept Illumina]] is based on the fundamental equivalence theorem of electromagnetics and the Huygens principle. The electric surface currents are denoted by high-frequency, asymptotic '''J(r)Physical Optics Module''' and the magnetic surface currents are denoted by of '''M(r)[[EM.Cube]]''', where '''r''' is the position vectora comprehensive, integrated, modular electromagnetic modeling environment. [[EM. According to Illumina]] shares the Huygens principlevisual interface, 3D parametric CAD modeler, data visualization tools, the equivalent electric and magnetic surface currents are derived from the tangential components many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of magnetic and electric fields on a given surface, respectively[[EM. 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 consideredCube]]'s other computational modules.

[[Image:Info_iconEM.png|40pxIllumina]] Click here to lean more about the '''s simulator is seamlessly interfaced with [[Theory of Physical OpticsEM.Cube|EM.CUBE]]'''s other simulattion engines. This module is the ideal place to define Huygens sources. These are based on Huygens surface data that are generated using a full-wave simulator like [[EM.Tempo]], [[EM.Picasso]] or [[EM.Libera]].

[[Image:PO18(1).png|thumb|250px|=== Advantages & Limitations of EM.Illumina's Navigation Tree.]]=== Grouping Objects By Surface Type PO Solver ===

[[EM.Illumina organizes physical objects by their surface type]] provides a computationally efficient alternative to full-wave solutions for extremely large structures when full-wave analysis becomes prohibitively expensive. Any object in For simple scatterer geometries, [[EM.Illumina is assumed to be made of one of the three surface types: # Perfect Electric Conductor (PEC)# Perfect Magnetic Conductor (PMC)# Generalized Impedance Surface EM.Illumina can only handle surface and solid CAD objects. Only the outer surface of [[Solid Objects|solid objects]] is considered in the 's GO-PO simulationsolver is fairly adequate. No line or [[Curve Objects|curve objects]] are allowed in But for complex geometries that involve multiple shadowing effects, the project workspace; or else, they will IPO solver must be ignored during the PO simulationutilized. You The IPO technique can define several PECeffectively capture dominant, PMC or impedance surface groups near-field, multiple scattering effects from electrically large targets with different colors and impedance valuesconcave surfaces. All the objects created and drawn under a group share the same color and other properties.  [[Image:Info_icon.png|40px]] Click here You have to learn more about '''[[Defining_Materials_in_EM.Cube#Defining_a_New_Material_Group | Defining a New Surface Group]]'''. Once a new surface node has been created on the navigation tree, it becomes the "Active" surface group of the project workspace, which remember that Physical Optics is always listed in bold letters. When you draw a new CAD object such as a Box or a Sphere, it is inserted under the currently active surface typesimulator. There This is only one surface group that is active at any time. Any surface type can be made active by right clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create surface groups, and then draw new objects under the active surface group. However, if you start not a new EM.Illumina project from scratch, and start drawing a new object without having previously defined any surface groups, a new default problem for PEC surface group is created and added to the navigation tree to hold your new CAD object. [[Image:PO22(1).png|thumb|400px|Moving PMC objects among different surface groups in EM.Illumina.]] [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Moving_Objects_among_Material_Groups | Moving Objects among Material Groups]]'''. {{Note|In [[EM.Cube]], you can import external CAD models (such as STEPwhich have zero internal fields, IGES, STL models, etc.) only to [[CubeCAD]]. From [[CubeCAD]]or even impedance surfaces, where you can then move satisfy the imported objects to EM.Illumina.}} [[Image:Info_icon.png|40px]] Click here for a general discussion boundary conditions on one side of '''[[Defining Materials in EM.Cube]]'''. == Discretizing the Physical Structure == EM.Illumina uses a triangular surface mesh to discretize the structure of your project workspaceonly. The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across PO analysis cannot handle the entire structurefields inside dielectric objects. You can control the cell size using the "Mesh Density" parameter. By defaultAdditionally, 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.  [[File:PO4.png|thumb|300px|EM.Illumina's Mesh Settings dialog.]][[File:PO5.png|thumb|300px|The Tessellation Options dialog.]] The objects of your physical structure most coupling effects between adjacent scatterers are meshed based on a specified mesh density expressed in cells/&lambda;₀. The default mesh density is 10 cells/&lambda;₀. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Mesh_Generation_Schemes_in_EM.Cube#Working_with_Mesh_Generator | Working with Mesh Generator ]]'''. [[Image:Info_icon.png|40px]] Click here to learn more about EM.Illumina's '''[[Mesh_Generation_Schemes_in_EM.Cube#The_Triangular_Surface_Mesh_Generator | Triangular Surface Mesh Generator ]]'''ignored.

<td> [[Image:PO2PO Ship Pattern.png|thumb|450pxleft|Two ellipsoids 550px|Computed radiation pattern of different compositionsa short dipole radiator over a large metallic battleship.]] </td><td> [[Image:PO3.png|thumb|450px|Trinagular surface mesh of the two ellipsoids.]] </td>

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 Illumina Features at a triangular surface mesh to discretize all the surface and [[Solid Objects|solid objects]] in the project workspace. As mentioned earlier, [[Curve Objects|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|solid objects]]. In contrast, [[Surface Objects|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|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|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.Glance ==

<tableul> <trli> Metal (PEC) solids and surfaces in free space<td/li> [[Image:PO6.png|thumb|400px|Two overlapping PEC spheres.]] <li> PMC and impedance surfaces in free space</tdli> <tdli> [[Image:PO7.png|thumb|400px|Trinagular surface mesh of the two spheres.]] Import STL CAD files as native polymesh structures</tdli> <li> Huygens blocks imported from full-wave modules</trli></tableul>

=== Hertzian Dipole Sources Mesh Generation ===

A short Hertzian dipole is the simplest way <ul> <li> Surface triangular mesh with control over tessellation parameters</li> <li> Local mesh editing 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.polymesh objects</li></ul>

The direction of incidence is defined through the &theta; <ul> <li> Electric and magnetic surface current distributions on metallic or impedance surfaces</li> <li> Near field intensity plots (vectorial - amplitude &phiamp; angles of the unit propagation vector phase)</li> <li> Huygens surface data generation for use in the spherical coordinate systemPO or other [[EM. The values of these angles are set in degrees in the boxes labeled '''Theta''' and '''Phi'''. The default values are &theta; = 180° and &phi; = 0° representing a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. In the TMCube]] modules<sub/li>z </subli> Far field radiation patterns: 3D pattern visualization and 2-D Cartesian and TEpolar graphs<sub/li>z </subli> polarization cases, the magnetic and electric fields are parallel to the XY plane, respectively. The components of the unit propagation vector and normalized E Bi- static 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 satisfiedmonostatic radar cross section: '''ê . ê''' = 1 3D visualization and '''ê × k''' = 0 . This can be enforced using the '''Validate''' button at the bottom 2D graphs</li> <li> Custom output parameters defined as mathematical expressions 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 (&theta; = 180°).standard outputs</li></ul>

* 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 Variety of the dialog, you can enter the '''Amplitude''' of the incident electric field Surface Types 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'''EM.Illumina ===

{| class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed|-| style="width:30px;" | [[File:po_phys17pec_group_icon.png]]|thumbstyle="width:250px;" |[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC) Surface]]| style="width:300px;" |PO ModuleModeling perfect metal surfaces| style="width:250px;" | Solid and surface objects|-| style="width:30px;" | [[File:pmc_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube's Huygens Source dialogMaterials, Sources, Devices & Other Physical Object Types#Perfect Magnetic Conductor (PMC) |Perfect Magnetic Conductor (PMC) Surface]]| style="width:300px;" | Modeling perfect magnetic surfaces| style="width:250px;" | Solid and surface objects|-| style="width:30px;" | [[File:voxel_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Impedance Surface |Impedance/Dielectric Surface]]| style="width:300px;" | Modeling impedance surfaces as an equivalent to the surface of dielectric objects | style="width:250px;" | Solid and surface objects|-| style="width:30px;" | [[File:Virt_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]| style="width:300px;" | Used for representing non-physical items | style="width:250px;" | All types of objects|}

At the end of a full-wave simulation Click on each category to learn more details about it in the [[Glossary of EM.Cube]]'s FDTDMaterials, MoM3DSources, Planar or Devices & Other 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 ModuleObject Types]]'s physical structure.

In order to define a Huygens source, you need to have a Huygens data file of '''[[EM.HUY''' typeIllumina]] can only handle surface and solid CAD objects. This file is generated as an output data file at Only the end outer surface of an FDTD, MoM3D, Planar or solid objects is considered in the 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 No line or curve objects are allowed in the project and set it as an excitation sourceworkspace; or else, they will be ignored during the PO simulation.

* Right click on You can define several PEC, PMC or impedance surface groups with different colors and impedance values. All the '''Huygens Sources''' item in objects created and drawn under a group share the '''Sources''' section of the Navigation Tree same color and select '''Import Huygens Sourceother properties...''' 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 Once a Huygens new surface data file with a '''.HUY''' file extension. Select node has been created on the file and click navigation tree, it becomes the '''Open''' button "Active" surface group of the dialog to import the data.* Once importedproject workspace, the Huygens source appears which is always listed in the Project Workspace bold letters. When you draw a new CAD object such as a wire-frame boxBox or a Sphere, it is inserted under the currently active surface type.* You There is only one surface group that is active at any time. Any surface type can open the property dialog of a Huygens source be made active by right clicking on its name in the Navigation Tree navigation tree and selecting the '''Properties...Activate''' From this dialog you can change the color item of the Huygens source box as well as its location and orientationcontextual menu. You can enter new values for the XIt is recommended that you first create surface groups, Y, Z '''Center Coordinates''' and '''Rotation Angles''' of then draw new objects under the Huygens boxactive surface group. You can also view the dimensions of the box.* By defaultHowever, the Huygens data are imported as if you start a single Huygens sourcenew EM. You can create an arbitrary array of Huygens sources for your PO Illumina project. To do sofrom scratch, in the &quot;Create Array&quot; section of the Huygens source dialog, enter desired values for the '''Number of Elements''' and '''Element Spacing''' along the Xstart drawing a new object without having previously defined any surface groups, Y a new default PEC surface group is created and Z directions. You will see an array of wire-frame box appear in added to the project workspacenavigation tree to hold your new CAD object.

[[FileImage:PO34Info_icon.png|400px30px]] Click here to learn more about '''[[File:PO35.pngBuilding Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules |400pxMoving Objects among Different Groups]]'''.

Figure: (Left) A rotated imported Huygens source{{Note|In [[EM.Cube]], and you can import external CAD models (Rightsuch as STEP, IGES, STL models, etc.) An array of only to CubeCAD. From CubeCAD, you can then move the imported Huygens sources defined objects to excite a PEC boxEM.Illumina.}}

== Running <table><tr><td> [[File:PO Simulations ==MAN1.png|thumb|left|480px|EM.Illumina's navigation tree.]] </td></tr></table>

=== Running A Basic PO Analysis =EM.Illumina's Excitation Sources ==

[[File:PO27.png|thumb|400px|EM.Illumina's Simulation Run dialog.]]To open EM.Illumina's Simulation Run dialog, click the '''Run''' [[File:run_icon.png]] button provides three types of the '''Simulate Toolbar''' or select '''Menu &gt; Simulate &gt; 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 sources for certain tasks during the PO simulation process. A prompt announces the completion excitation of the PO your physical optics 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.:

{| class="wikitable"|-! scope="col"| Icon! scope= Setting The Numerical Parameters "col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:hertz_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]| style="width:300px;" | Almost omni-directional physical radiator| style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:plane_wave_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]| style="width:300px;" | Used for modeling scattering | style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:huyg_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules | style="width:300px;" | Imported from a Huygens surface data file|}

[[File:PO28.png|thumb|350px|EM.Illumina's Simulation Engine Settings dialog.]]Before you run a PO simulation, you can change some of the PO simulation engine settings. While Click on each category to learn more details about it in the [[PO Module]]'s '''Simulation Run Dialog''', click the '''Settings''' button next to the '''Select Engine''' dropdown listGlossary of EM. 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 structureCube's mesh. For the termination of the IPO solverMaterials, there are two options: '''Convergence Error''' and '''Maximum Number of Iterations'''. The default Termination Criterion is based on convergence errorSources, 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 Devices &eta;₀ in the residual error vectorOther Physical Object Types]].

You can also use higher- or lower-order integration schemes for A short Hertzian dipole is the calculation simplest way of field integralsexciting 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. Your physical structure in [[EM.CubeIllumina]]'s PO simulation engine uses triangular cells for can also be excited by an incident plane wave. In particular, you need a plane wave source to compute the mesh radar cross section of a target. The direction of incidence is defined by the physical surface structures &theta; and rectangular cells for discretization &phi; angles of Huygens sources and surfacesthe unit propagation vector in the spherical coordinate system. For integration The default values of triangular cells, you have three options: '''7-Point Quadrature''', '''3-Point Quadrature''' the incidence angles are &theta; = 180° and '''Constant'''. For integration of rectangular cells, too, you have three options: '''9&phi; = 0° corresponding to a normally incident plane wave propagating along the -Point Quadrature''', '''4Z direction with a +X-Point Quadrature''' polarized E-vector. Huygens sources are virtual equivalent sources that capture the radiated electric and '''Constant'''magnetic fields from another structure that was previously analyzed in another [[EM.Cube]] computational module.

=== PO Sweep Simulations =EM.Illumina's Simulation Data & Observables ==

[[Image:po_phys52.png|thumb|300px|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 does not produce any output data on its own unless you define one or a user defined variable is varied over a specified range at predetermined samplesmore observables for your simulation project. The primary output data in the Physical Optics method are saved into data files for visualization the electric and plottingmagnetic surface current distributions on the surface of your structure. At the end of a PO simulation, [[EM.CubeIllumina]]'s generates a number of output data files that contain all the computed simulation data. Once the current distributions are known, [[PO ModuleEM.Illumina]] currently offers three types of sweep:can compute near-field distributions as well as far-field quantities such as radiation patterns and radar cross section (RCS).

To run a PO sweep, open the '''{| class="wikitable"|-! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:currdistr_icon.png]]| style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube''''''Run Dialog''' s Simulation Observables & Graph Types#Current Distribution |Current Distribution]]| style="width:300px;" | Computing electric surface current distribution on PEC and select one impedance surfaces and magnetic surface current distribution on PMC and impedance surfaces| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of the above sweep types from the ''EM.Cube's Simulation Mode''' dropdown list Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]] | style="width:300px;" | Computing electric and magnetic field components on a specified plane in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[File:farfield_icon.png]]| style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[Glossary of this dialogEM. If you select either frequency or angular sweep, the 'Cube''Settings''' button located next to s Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the simulation mode dropdown list becomes enabled. If you click this buttonradiation pattern and additional radiation characteristics such as directivity, the Frequency Settings Dialog or Angle Settings Dialog opens upaxial ratio, side lobe levels, respectivelyetc. In | style="width:250px;" | None|-| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Far-Field Scattering Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] | style="width:300px;" | Computing the frequency settings dialog, you can set the start bistatic and end frequencies as well as the number monostatic RCS of frequency samplesa target| style="width:250px;" | Requires a plane wave source|-| style="width:30px;" | [[File:huyg_surf_icon. The start png]]| style="width:150px;" | Equivalent electric and end frequency values are initially set based on the projectmagnetic surface current data| style="width:150px;" | [[Glossary of EM.Cube's center frequency and bandwidth. During Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]| style="width:300px;" | Collecting tangential field data on a frequency sweep, box to be used later as the project's frequency changes, so does the wavelength. As a result, the mesh of the structure also changes at each frequency sampleHuygens source in other [[EM. The frequency settings dialog gives you three choices regarding the mesh of the project structure during a frequency sweepCube]] modules| style="width:250px;" | None|}

# Fix mesh at Click on each category to learn more details about it in the highest frequency[[Glossary of EM.# Fix mesh at the center frequency.# Re-mesh at each frequencyCube's Simulation Observables & Graph Types]].

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 Current distributions are visualized on the default settings. During an angular sweepsurface of PO mesh cells, either and the incident theta angle or incident phi angle is varied within magnitude and phase of the specified rangeelectric and magnetic surface currents are plotted for all the objects. The other angle remains fixed at A single current distribution node in the navigation tree holds the current distribution data for all the value that is specified objects in the '''Plane Wave Dialog'''project workspace. You have to select either '''Theta''' or '''Phi''' as Since the '''Sweep Angle''' in currents are plotted on the Angle Settings Dialogsurface of the individual mesh cells, some parts of the plots may be blocked by and hidden inside smooth and curved objects. You also need To be able to view those parts, you may have to set freeze the start and end angles as well as obstructing objects or switch to the number of angle samplesmesh view mode.

In a parametric sweep, one or more user defined <table><tr><td> [[variables]] are varied at the same time over their specified rangesImage:PO38. This creates a parametric space with the total number png|thumb|390px|The current distribution plot 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 [[EMPEC sphere illuminated by an obliquely incident plane wave.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.</td></tr></table>

At the end of a {{Note|Keep in mind that since Physical Optics simulationis an asymptotic method, 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 sensors must be placed at adequate distances (RCSat least one or few wavelengths)away from the scatterers to produce acceptable results. EM.Illumina does not generate any output data on its own unless you define observables for your simulation project. }}

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 need to view these currents, you must first define a current distribution far field observable before running if you want to plot the PO simulation. To do this, right click on the '''Current Distributions''' item in the '''Observables''' section radiation patterns 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 workspaceyour physical structure. After a PO simulation is completedfinished, new three 3D radiation patterns plots are added under displayed in the current distribution node of the Navigation Treeproject workspace and are overlaid on your physical structure. Separate plots These are produced for the magnitude Theta and phase of each Phi components of the far-zone electric and magnetic surface current components (X, Y and Z) fields 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 modefar field.

[[Image:Info_icon.png{{Note|40px]] Click here The 3D radiation pattern is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps | Visualizing 3D Current Distribution Maps]]'''which the far radiation zone is defined. Oftentimes, this might not be the radiation center of your physical structure.}}

<td> [[Image:PO37PO46.png|thumb|300px360px|PO Module's Current Distribution dialog.]] </td><td> [[Image:PO38.png|thumb|500px|The current distribution plot 3D radiation pattern of a PEC sphere illuminated parabolic dish reflector excited by an obliquely incident plane wavea short dipole at its focal point.]] </td>

=== NearWhen your physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[EM.Illumina]] can calculate two types of RCS for each structure: '''Bi-Field Visualization ===Static RCS''' and '''Mono-Static RCS'''. In bi-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀, and the RCS is measured and plotted at all &theta; and &phi; angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀, and the RCS is measured and plotted at the echo angles 180°-&theta;₀; and &phi;₀. 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 &theta; and &phi; are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded.

[[EM.Cube]] allows To calculate RCS, first you have to visualize the near fields at define an RCS observable instead of a specific field sensor planeradiation pattern. Calculation At the end of near fields is a post-processing process PO simulation, the thee RCS plots &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot are added under the far field section of the navigation tree. Keep in mind that computing the 3D mono-static RCS may take a considerable an enormous amount of computation 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...'''* {{Note| 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 3D RCS plot is specified by always displayed at the normal vector origin of the sensor plane. The available options are '''X'''spherical coordinate system, '''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 with respect to any desired size. You can also set which 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 far radiation zone is finished, a total of 14 plots are added to every field sensor node in the Navigation Treedefined. 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 plotOftentimes, which can this might not be dragged around using the left mouse button. The values scattering center 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 your physical 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. {{Note|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.}} [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Near-Field_Maps | Visualizing 3D Near Field Maps]]'''.

<td> [[Image:PO42(4)PO48.png|thumb|300px420px|PO Module's Field Sensor dialog]] </td><td> [[Image:PO43.png|thumb|400px|Near field plot of electric field on a sensor plane.]] </td><td> [[Image:PO44.png|thumb|400px|Near field plot RCS of magnetic field on a sensor PEC sphere illuminated by an laterally incident planewave.]] </td>

=== Computing Radiation Patterns =Discretizing the Physical Structure in EM.Illumina ==

Unlike the FDTD method, Physical Optics is an open-boundary techniqueEM. You do not need Illumina uses a far field box triangular surface mesh 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 discretize the '''Far Fields''' item in the '''Observables''' section structure of the Navigation Tree and selecting '''Insert New Radiation Patternyour project workspace...''' from The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the contextual menu. The Radiation Pattern dialog opens upentire structure. You can accept most of control the cell size using the "Mesh Density" parameter. By default settings in this dialog. The Output Settings section allows you to change , the '''Angle Increment''' mesh density is expressed in terms of the degrees, which sets the resolution of far field calculationsfree-space wavelength. The default value mesh density is 5 degrees10 cells per wavelength. After closing In the radiation pattern dialogPhysical Optics method, a far field entry immediately appears with its given name under the electric and magnetic surface currents, '''Far FieldsJ''' and '''M''' item of the Navigation Tree. After a PO simulation is finished, three radiation patterns plots are added assumed to be constant on the far field node in the Navigation Treesurface of each triangular cell. These are the far field component in &theta; directionOn flat surfaces, the far field component in &phi; direction and unit normal vectors to all the total far fieldcells are identical. Incident plane waves or other relatively uniform source fields induce uniform PO currents on all these cells. The 3D plots can Therefore, a high resolution mesh may not be viewed by clicking necessary on their name in the navigation treeflat surface or faces. Accurate discretization of curved objects like spheres or ellipsoids, however, requires a high mesh density. They are displayed in <table><tr><td> [[File:PO4.png|thumb|left|480px|EM.Cube]]Illumina's project workspace and are overlaid on the project's structureMesh Settings dialog. ]]</td></tr></table>

[[Image:Info_iconSince EM.png|40px]] Click here Illumina is a surface simulator, only the exterior surface of solid CAD objects is discretized, as the interior volume is not taken into account in a PO analysis. By contrast, surface CAD objects are assumed to learn more about be double-sided. In other words, the theory default PO mesh of a surface object 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.Illumina's mesh generator has settings that allow you to treat all mesh cells as double-sided or all single-sided. You can do that in the Mesh Settings dialog by checking the boxes labeled ''[[Computing_the_Far_Fields_%26_Radiation_Characteristics| Far Field Computations]]'All Double-Sided Cells''' and '''All Single-Sided Cells'''. This is useful when your project workspace contains well-organized and well-oriented surface CAD objects only. In the single-sided case, it is very important that all the normals to the cells point towards the source. Otherwise, your surfaces fall in the shadow region, and no currents will be computed on them. By checking the box labeled '''Reverse Normal''', you instruct EM.Illumina to reverse the direction of the normal vectors globally at the surface of all the cells.

[[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Data_Visualization_and_ProcessingPreparing_Physical_Structures_for_Electromagnetic_Simulation#Visualizing_3D_Radiation_Patterns Working_with_EM.Cube.27s_Mesh_Generators | Visualizing 3D Radiation PatternsWorking with Mesh Generator]]'''.

[[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Data_Visualization_and_ProcessingPreparing_Physical_Structures_for_Electromagnetic_Simulation#2D_Radiation_and_RCS_Graphs The_Triangular_Surface_Mesh_Generator | Plotting 2D Radiation GraphsEM.Illumina's Triangular Surface Mesh Generator ]]'''.

<td> [[Image:PO45POShip1.png|thumb|300px600px|EM.Illumina's Radiation Pattern dialogGeometry of a metallic battleship model with a short horizontal dipole radiator above it.]] </td></tr><tr><td> [[Image:PO46POShip2.png|thumb|500px600px|3D radiation pattern Trinagular surface mesh of a parabolic dish reflector excited by a short dipole at its focal pointthe metallic battleship model.]] </td>

=== Computing Radar Cross Section =Running PO Simulations in EM.Illumina ==

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 &theta; and &phi; components of the radar cross section as well as the total radar cross section, which are dented by &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot. In addition, [[EM.Cube]]Illumina'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 &theta;₀ and &phi;₀, and the RCS is measured and plotted at all &theta; and &phi; angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀, and the RCS is measured and plotted at the echo angles 180°-&theta;₀; and &phi;₀. 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 &theta; and &phi; are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded.Simulation Modes ===

To calculate RCS, first Once you have to define an RCS observable instead of a radiation patternset up your structure in [[EM. Right click on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree Illumina]], have defined sources and select '''Insert New RCS...''' to open the Radar Cross Section Dialog. Use the '''Label''' box to change observables and have examined the name quality of the far field or change the color of the far field box using the structure'''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 defaults mesh, the &theta; and &phi; angles you are incremented by 5 degrees. At the end of ready to run a PO Physical Optics 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'''[[EM.Illumina]] offers five simulation modes:

At the end {| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of a Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running A Single-Frequency PO simulation, Analysis | Single-Frequency Analysis]]| style="width:270px;" | Simulates the thee RCS plots &sigmaphysical structure "As Is"| style="width:80px;_{&theta" | Single run| style="width:250px;}, &sigma" | Runs at the center frequency fc| style="width:80px;_{&phi" | None|-| style="width:120px;}, and &sigma" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]| style="width:270px;_tot are added under " | Varies the far field section operating frequency of the Navigation TreePO solver | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a specified set of frequency samples| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. These plots are very similar to the three 3D radiation pattern plotsCube#Running_Parametric_Sweep_Simulations_in_EM. You can view them by clicking on their names in Cube | Parametric Sweep]]| style="width:270px;" | Varies the navigation treevalue(s) of one or more project variables| style="width:80px;" | Multiple runs| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. The RCS values are expressed in m²Cube#Performing_Optimization_in_EM. For visualization purposes, Cube | Optimization]]| style="width:270px;" | Optimizes the 3D plots are normalized value(s) of one or more project variables to achieve a design goal | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the maximum RCS value, which is also displayed in the legend boxcenter frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. Keep in mind that computing Cube#Generating_Surrogate_Models | HDMR Sweep]]| style="width:270px;" | Varies the 3D mono-static RCS may take an enormous amount value(s) of computation time.one or more project variables to generate a compact model| style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|}

You can set the simulation mode from [[Image:Info_iconEM.png|40pxIllumina]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_RCS | Visualizing s "Simulation Run Dialog". A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. If you run a simulation without having defined any observables, no data will be generated at the end of the simulation. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D RCS]]'''simulation data from the navigation tree.

=== Running A Single-Frequency PO Analysis === To open [[Image:Info_iconEM.png|40pxIllumina]] Click here to learn more about 's Simulation Run dialog, click the '''Run'''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D RCS GraphsFile:run_icon.png]]button of the '''Simulate Toolbar''' or select '''Menu &gt; Simulate &gt; Run...'''or use the keyboard shortcut {{key|Ctrl+R}}. To start the simulation click the {{key|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.

<td> [[Image:PO47Illumina L1 Fig10A.png|thumb|300pxleft|480px|EM.Illumina's Radar Cross Section Simulation Run dialog.]] </td><td> [[Image:PO48.png|thumb|500px|RCS of a PEC sphere illuminated by an laterally incident plane wave.]] </td>

<p>=== Setting The Numerical Parameters === Before you run a PO simulation, you can change some of the PO simulation engine settings. While in the [[EM.Illumina]]'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 &nbspeta;<sub>0</psub>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'''. <table><tr><td> [[File:PO28.png|thumb|left|480px|EM.Illumina's Simulation Engine Settings dialog.]]</td></tr></table> <br /> <hr> [[Image:Top_icon.png|48px30px]] '''[[EM.Illumina#An_EM.Illumina_Primer Product_Overview | Back to the Top of the Page]]''' [[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Illumina_Documentation | EM.Illumina Tutorial Gateway]]'''

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