Detecting the Orientation of a Metallic Cylinder Embedded in a Dielectric Shell

A metallic cylindrical rod is hidden inside a spherical dielectric shell and its orientation is unknown. By studying the polarization-dependent scattered field of a cylindrical object and performing a parametric sweep as a function of polarization angle, the rod is detected for the polarization angle where the scattered field is highest. The model uses a linearly polarized plane wave for the background field and computes the far-field radiation patterns.

Figure 1: A copper rod inside a spherical polystyrene foam shell. Some parts are removed for visualization purposes.

Model Definition

A cylindrical copper rod is enclosed in a 2 cm thick polystyrene foam (εr = 1.03) dielectric shell that is filled with air. The copper rod lies in the xy-plane, but its orientation is unknown. The dielectric shell is surrounded by air and the entire model domain is enclosed by perfectly matched layers.

The model is solved using the scattered field formulation, while the built-in linearly polarized plane wave is used for background field. The wave vector of the background field is pointing toward the -z direction after it is transformed from the +x-directional initial wave by a 90 degree pitch angle. The polarization is determined by the parameterized value of the yaw angle that varies from 0 to 175 degrees.

The copper rod is modeled using the Impedance boundary condition and its inner volume is removed from the model domain. This is done because the skin depth is much smaller than the size of the rod. The rod's scattered field is computed on the boundaries configured by the Far-Field Domain node and its Far-Field Calculation subfeature by performing a near-field to far-field transformation.

A perfectly matched layer (PML) domain is outside of the surrounding air domain and acts as an absorber of the scattered field. The PML is placed at a half-wavelength away from the dielectric shell.

Results and Discussion

Figure 2 shows the radar cross section (RCS) of the example in dB scale. The maximum occurs when the yaw angle for the polarization is 30 degrees, while the minimum value occurs at 120 degrees. The maximum scattering is known to take a place when the polarization is parallel to the cylinder. This means the cylinder is oriented at 30 degrees, with respect to the x-axis.

Figure 2: The maximum radar cross section (RCS) is observed at 30 degrees. With respect to the orientation of the cylinder, when the polarization angle of the background field is rotated 45 degrees, the RCS is 3dB lower than the maximum.

Figure 3 shows the electric field norm in the xy-plane at the maximum scattering angle. The electric field resembles that of a dipole antenna. The background field induces the oscillating current along the rod which then radiates as a dipole.

Figure 3: The electric field norm in the xy-plane at the maximum scattering angle

RF_Module/Scattering_and_RCS/cylinder_orientation

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
alpha	0[deg]	0 rad	Polarization angle

Geometry 1

Sphere 1 (sph1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.34.

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (m)
Layer 1	0.03

Click

Click the

button in the toolbar.

Sphere 2 (sph2)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.16.

Locate the section. In the table, enter the following settings:


Layer name	Thickness (m)
Layer 1	0.02

Cylinder 1 (cyl1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.01.

In the text field, type 0.15.

Locate the section. In the text field, type -0.075.

Locate the section. From the list, choose .

Rotate 1 (rot1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

In the text field, type 30.

Click

Click the

button in the toolbar.

The finished geometry should look like this.

Definitions

Perfectly Matched Layer 1 (pml1)

In the toolbar, click

Select Domains 1–4, 12, 13, 16, and 19 only.

In the window for , locate the section.

From the list, choose .

Electromagnetic Waves, Frequency Domain (emw)

In the window, under click .

In the window for , locate the section.

Click

In the dialog box, type 1-10, 12-19 in the text field.

Click .

In the window for , locate the section.

From the list, choose .

In the text field, type 90[deg].

In the text field, type alpha.

Far-Field Domain 1

In the toolbar, click

and choose .

Impedance Boundary Condition 1

In the toolbar, click

and choose .

In the window for , locate the section.

Click

In the dialog box, type 25-29, 62 in the text field.

Click .

Materials

Material 1 (mat1)

In the window, under right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	1	1	Basic
Relative permeability	mur_iso ; murii = mur_iso, murij = 0	1	1	Basic
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	0	S/m	Basic

Material 2 (mat2)

Right-click and choose .

In the window for , locate the section.

Click

In the dialog box, type 6-9, 14-15, 17-18 in the text field.

Click .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	1.03	1	Basic
Relative permeability	mur_iso ; murii = mur_iso, murij = 0	1	1	Basic
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	0	S/m	Basic