polarized circular ports fiber

Solved with COMSOL Multiphysics 4.4Po l a r i z e d C i r c u l a r Po r t s

Introduction

This model is a demonstration of how to use numeric ports with a numerical solution of the port modes. It also illustrates a method to align the polarization of degenerate port modes and in particular how to model and excite circular waveguides in 3D.

Model Definition

A straight piece of circular waveguide with perfect metallic walls is excited by a TE11 mode at one end and ideally terminated at the other end. This is obtained by using two ports at each end which are tuned to mutually orthogonal polarizations of the TE11 mode. The electric field of the two TE11 modes differs by 90 degrees but due to circular symmetry, there is no a priori determined reference direction for the modes. However, when applying the finite element method, the mesh and shape functions will introduce some small numerical anisotropy that will determine the reference direction, that is the absolute polarization of the modes. In this model, the circular ports are geometrically segmented into equal halves and a mesh that is symmetric across the diameter is created. The result is that the eigenmode solver will find two TE11 modes with their electric fields respectively aligned or perpendicular to the introduced symmetry line.

The boundary mode analysis study for electromagnetic waves solves the eigenvalue problem for the boundary electric field:

where

is the eigenvalue. For time-harmonic problems, the electric field for out-of-plane propagation can be written as

where z is the known out-of-plane direction.

( 1 E ) E 0=

k02

rj-----=

E r t,( ) Re E r( )ejt z( )= 1 | P O L A R I Z E D C I R C U L A R P O R T S

Solved with COMSOL Multiphysics 4.4

2 | P O LThe spatial parameter, = z + j = , can have a real part and an imaginary part. The propagation constant is equal to the imaginary part, and the real part, z, represents the damping along the propagation direction.

With the stipulated excitation using the numerically established mode shapes as boundary conditions, the following equation is solved for the electric field vector E inside the waveguide:

Results and Discussion

The first TE11 mode of the inport is shown in Figure 1.

Figure 1: The first TE11 mode of the inport found by the eigenmode solver.

Note: Depending on the details of the mesh, which in turn may depend on the origin of the CAD geometry, a mode that is rotated 90 degrees may be found.

r1 E( ) k0

2r

j0---------

E 0=A R I Z E D C I R C U L A R P O R T S

Solved with COMSOL Multiphysics 4.4The first TE11 mode of the outport is shown in Figure 2.

Figure 2: The first TE11 mode of the outport found by the eigenmode solver.

Note: Depending on the details of the mesh, which in turn may depend on the origin of the CAD geometry, a mode that is rotated 90 degrees may be found. 3 | P O L A R I Z E D C I R C U L A R P O R T S


4 | P O LThe transmission coefficients between the inport and outport modes are shown inFigure 3.

Figure 3: The transmission coefficients between inport modes and outport modes are plotted as a function of frequency. As the port modes are misaligned by 45 degrees the transmission coefficients approach the -3dB level above cut-off.

Model Library path: RF_Module/Tutorial_Models/polarized_circular_ports

Modeling Instructions

From the File menu, choose New.

N E W

1 In the New window, click the Model Wizard button.

M O D E L W I Z A R D

1 In the Model Wizard window, click the 3D button.A R I Z E D C I R C U L A R P O R T S

Solved with COMSOL Multiphysics 4.42 In the Select physics tree, select Radio Frequency>Electromagnetic Waves, Frequency Domain (emw).

3 Click the Add button.

4 Click the Study button.

5 In the tree, select Custom Studies>Empty Study.

6 Click the Done button.

G L O B A L D E F I N I T I O N S

Add a parameter for the operating frequency.

Parameters1 On the Home toolbar, click Parameters.

2 In the Parameters settings window, locate the Parameters section.

3 In the table, enter the following settings:

G E O M E T R Y 1

The geometry is essentially a cylinder.

Cylinder 11 On the Geometry toolbar, click Cylinder.

2 In the Cylinder settings window, locate the Size and Shape section.

3 In the Radius edit field, type 0.01.

4 In the Height edit field, type 0.1.

Name Expression Value Description

frq c_const/0.03[m] 9.993E9 1/s Operating frequency 5 | P O L A R I Z E D C I R C U L A R P O R T S


6 | P O L5 Click the Build All Objects button.

6 Click the Wireframe Rendering button on the Graphics toolbar.

You need to add a reference direction for the port polarization by adding an extra line on the cylinder end. This is done in a work plane.

7 On the Geometry toolbar, click Work Plane.

Bzier Polygon 11 In the Model Builder window, under Component 1>Geometry 1>Work Plane 1

right-click Plane Geometry and choose Bzier Polygon.

2 In the Bzier Polygon settings window, locate the Polygon Segments section.

3 Find the Added segments subsection. Click the Add Linear button.

4 Find the Control points subsection. In row 1, set yw to 0.01.

5 In row 2, set yw to -0.01.

6 Click the Build Selected button.A R I Z E D C I R C U L A R P O R T S

Solved with COMSOL Multiphysics 4.47 Click the Zoom Extents button on the Graphics toolbar.

Work Plane 21 On the Geometry toolbar, click Work Plane.

2 In the Work Plane settings window, locate the Plane Definition section.

3 In the z-coordinate edit field, type 0.1.

Bzier Polygon 11 In the Model Builder window, under Component 1>Geometry 1>Work Plane 2

right-click Plane Geometry and choose Bzier Polygon.

2 In the Bzier Polygon settings window, locate the Polygon Segments section.

3 Find the Added segments subsection. Click the Add Linear button.

4 Find the Control points subsection. In row 1, set yw to 0.01.

5 In row 2, set yw to -0.01.

6 Click the Build Selected button.

7 Click the Zoom Extents button on the Graphics toolbar.

Plane GeometryRotate the reference direction for the second port 45 degrees.

Rotate 11 On the Work plane toolbar, click Rotate. 7 | P O L A R I Z E D C I R C U L A R P O R T S


8 | P O L2 Select the object b1 only.

3 In the Rotate settings window, locate the Rotation Angle section.

4 In the Rotation edit field, type 45.

5 Click the Build Selected button.

6 On the Home toolbar, click Build All.A R I Z E D C I R C U L A R P O R T S


M A T E R I A L SNext, add a material for the interior (air) of the waveguide.

Material 11 In the Model Builder window, under Component 1 right-click Materials and choose

New Material.

2 In the Material settings window, locate the Material Contents section.

3 In the table, enter the following settings:

E L E C T R O M A G N E T I C WAV E S , F R E Q U E N C Y D O M A I N

Set up one inport and three outports.

Port 11 On the Physics toolbar, click Boundaries and choose Port.

2 Select Boundaries 3 and 7 only.

3 In the Port settings window, locate the Port Properties section.

Property Name Value Unit Property group

Relative permittivity epsilonr 1 1 Basic

Relative permeability mur 1 1 Basic

Electrical conductivity sigma 0 S/m Basic 9 | P O L A R I Z E D C I R C U L A R P O R T S


10 | P O4 From the Type of port list, choose Numeric. The Numeric option means that the port mode will be computed in a separate study step.

5 From the Wave excitation at this port list, choose On.




4 From the Type of port list, choose Numeric.




4 From the Type of port list, choose Numeric.




4 From the Type of port list, choose Numeric.L A R I Z E D C I R C U L A R P O R T S


M E S H 1Meshing requires some special care in order to get port meshes that are symmetric with respect to the reference direction for the polarization. Without that extra care, the eigenmode solver will not find the desired mode.

Free Triangular 11 In the Model Builder window, under Component 1 right-click Mesh 1 and choose More

Operations>Free Triangular.

2 Select Boundary 3 only.

Size 11 Right-click Component 1>Mesh 1>Free Triangular 1 and choose Size.

2 In the Size settings window, locate the Element Size section.

3 From the Predefined list, choose Finer.

Copy Face 11 In the Model Builder window, right-click Mesh 1 and choose More Operations>Copy

Face.


3 In the Copy Face settings window, locate the Destination Boundaries section.

4 Click the Active button next to the Destination Group Focus selection list.

5 Select Boundary 7 only. 11 | P O L A R I Z E D C I R C U L A R P O R T S


12 | P OFree Triangular 21 Right-click Mesh 1 and choose More Operations>Free Triangular.


Size 11 Right-click Component 1>Mesh 1>Free Triangular 2 and choose Size.

2 In the Size settings window, locate the Element Size section.

3 From the Predefined list, choose Finer.

Copy Face 21 In the Model Builder window, right-click Mesh 1 and choose More Operations>Copy

Face.


3 In the Copy Face settings window, locate the Destination Boundaries section.

4 Click the Active button next to the Destination Group Focus selection list.


Finish the mesh by adding a volumetric mesh.

Size1 Right-click Mesh 1 and choose Free Tetrahedral.

2 In the Size settings window, locate the Element Size section.L A R I Z E D C I R C U L A R P O R T S

Solved with COMSOL Multiphysics 4.43 From the Predefined list, choose Fine.

4 Click the Build All button.

S T U D Y 1

Set up the custom study to perform boundary mode analysis for each port.

Step 1: Boundary Mode Analysis1 On the Study toolbar, click Study Steps and choose Other>Boundary Mode Analysis.

2 In the Boundary Mode Analysis settings window, locate the Study Settings section.

3 In the Search for modes around edit field, type 0.4. The shift controls which mode is found. Finding the desired mode normally requires some trial and error.

4 In the Mode analysis frequency edit field, type frq.

Step 2: Boundary Mode Analysis 21 On the Study toolbar, click Study Steps and choose Other>Boundary Mode Analysis.


3 In the Search for modes around edit field, type 0.5. Use a larger shift to find the second TE11 mode and change to the second port.

4 In the Port name edit field, type 2. 13 | P O L A R I Z E D C I R C U L A R P O R T S


14 | P O5 In the Mode analysis frequency edit field, type frq.

Repeat the procedure for the remaining ports.



3 In the Search for modes around edit field, type 0.4.

4 In the Port name edit field, type 3.




3 In the Search for modes around edit field, type 0.5.

4 In the Port name edit field, type 4.


Finish the study by adding a frequency sweep.

Step 5: Frequency Domain1 On the Study toolbar, click Study Steps and choose Frequency Domain>Frequency

Domain.

2 In the Frequency Domain settings window, locate the Study Settings section.

3 Click the Range button.

4 Go to the Range dialog box.

5 From the Entry method list, choose Number of values.

6 In the Start edit field, type 0.5*frq.

7 In the Stop edit field, type 1.5*frq.

8 In the Number of values edit field, type 11.

9 Click the Add button.

Solve first for only the boundary modes and inspect the solution to make sure the desired modes have been found. In order to do that, the solver sequence needs to be displayed.L A R I Z E D C I R C U L A R P O R T S

Solved with COMSOL Multiphysics 4.4Solver 11 On the Study toolbar, click Show Default Solver.

Compute the first boundary mode field, that is, for port 1.

2 In the Model Builder window, expand the Solver 1 node.

3 Right-click Store Solution 2 and choose Compute to Selected.

R E S U L T S

Electric Field (emw)The default plot group shows the 3D fields which so far are zero. Add a plot group and display the boundary mode fields.

3D Plot Group 21 On the Home toolbar, click Add Plot Group and choose 3D Plot Group.

2 In the Model Builder window, under Results right-click 3D Plot Group 2 and choose Surface.

3 In the Surface settings window, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Electromagnetic Waves, Frequency Domain>Boundary mode analysis>Tangential boundary mode electric field norm

(emw.normEbm_1).

4 In the Model Builder window, right-click 3D Plot Group 2 and choose Arrow Surface.

5 In the Arrow Surface settings window, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Electromagnetic Waves, Frequency Domain>Boundary mode analysis>Tangential boundary mode electric field

(emw.tEbm1x,...,emw.tEbm1z).

6 Locate the Coloring and Style section. In the Number of arrows edit field, type 1000.

7 From the Color list, choose Black. 15 | P O L A R I Z E D C I R C U L A R P O R T S


16 | P O8 On the 3D Plot Group 2 toolbar, click Plot.

9 Right-click 3D Plot Group 2 and choose Rename.

10 Go to the Rename 3D Plot Group dialog box and type Electric field BMA 1 in the New name edit field.

11 Click OK.

S T U D Y 1

Solver 1Compute the remaining port modes.

1 In the Model Builder window, under Study 1>Solver Configurations>Solver 1 right-click Store Solution 5 and choose Compute to Selected.

R E S U L T S

Electric field BMA 1Display the remaining port modes. Save some effort by duplicating previous plots.

In the Model Builder window, under Results right-click Electric field BMA 1 and choose Duplicate.L A R I Z E D C I R C U L A R P O R T S

Solved with COMSOL Multiphysics 4.4Electric field BMA 1.2In the Model Builder window, under Results right-click Electric field BMA 1.2 and choose Duplicate.

Electric field BMA 1.2.2In the Model Builder window, under Results right-click Electric field BMA 1.2.2 and choose Duplicate.

Electric field BMA 1.2The stored port modes will reside in different data sets so update this.

1 In the Electric field BMA 1.2 plot group, in the 3D Plot Group settings window, locate the Data section.

2 From the Data set list, choose Solution 3.

3 In the Model Builder window, expand the Electric field BMA 1.2 node, then click Surface 1.


(emw.normEbm_2).

5 In the Model Builder window, under Results>Electric field BMA 1.2 click Arrow Surface 1.

6 In the Arrow Surface settings window, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Electromagnetic Waves, Frequency Domain>Boundary mode analysis>Tangential boundary mode electric field

(emw.tEbm2x,...,emw.tEbm2z). 17 | P O L A R I Z E D C I R C U L A R P O R T S


18 | P O7 On the Electric field BMA 1.2 toolbar, click Plot.

8 In the Model Builder window, right-click Electric field BMA 1.2 and choose Rename.


10 Click OK.

Electric field BMA 1.2.21 In the Electric field BMA 1.2.2 plot group, in the 3D Plot Group settings window,

locate the Data section.


3 In the Model Builder window, under Results>Electric field BMA 1.2.2 click Surface 1.


(emw.normEbm_3).

5 In the Model Builder window, under Results>Electric field BMA 1.2.2 click Arrow Surface 1.

6 In the Arrow Surface settings window, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Electromagnetic Waves, L A R I Z E D C I R C U L A R P O R T S

Solved with COMSOL Multiphysics 4.4Frequency Domain>Boundary mode analysis>Tangential boundary mode electric field


7 On the Electric field BMA 1.2.2 toolbar, click Plot.

8 In the Model Builder window, right-click Electric field BMA 1.2.2 and choose Rename.


10 Click OK.

Electric field BMA 1.2.2.21 In the Electric field BMA 1.2.2.2 plot group, in the 3D Plot Group settings window,

locate the Data section.


3 In the Model Builder window, under Results>Electric field BMA 1.2.2.2 click Surface 1.


(emw.normEbm_4).

5 In the Model Builder window, under Results>Electric field BMA 1.2.2.2 click Arrow Surface 1. 19 | P O L A R I Z E D C I R C U L A R P O R T S


20 | P O6 In the Arrow Surface settings window, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Electromagnetic Waves, Frequency Domain>Boundary mode analysis>Tangential boundary mode electric field


7 On the Electric field BMA 1.2.2.2 toolbar, click Plot.

8 In the Model Builder window, right-click Electric field BMA 1.2.2.2 and choose Rename.


10 Click OK.

S T U D Y 1

After inspecting and verifying the port modes, proceed to solve the entire study.

1 On the Home toolbar, click Compute.

R E S U L T S

Electric Field (emw)Inspect the electric field norm and rename the plot group.L A R I Z E D C I R C U L A R P O R T S

Solved with COMSOL Multiphysics 4.41 In the Model Builder window, under Results right-click Electric Field (emw) and choose Rename.

2 Go to the Rename 3D Plot Group dialog box and type Electric field FD in the New name edit field.

3 Click OK.

Next, inspect the S-parameters representing transmission.

1D Plot Group 61 On the Home toolbar, click Add Plot Group and choose 1D Plot Group.

2 In the 1D Plot Group settings window, click to expand the Legend section.

3 From the Position list, choose Lower right.

4 On the 1D Plot Group 6 toolbar, click Global.

5 In the Global settings window, click Replace Expression in the upper-right corner of the y-axis data section. From the menu, choose Electromagnetic Waves, Frequency Domain>Ports>S-parameter, dB>S-parameter, dB, 31 component (emw.S31dB).

6 Click Add Expression in the upper-right corner of the y-axis data section. From the menu, choose Electromagnetic Waves, Frequency Domain>Ports>S-parameter, dB>S-parameter, dB, 41 component (emw.S41dB). 21 | P O L A R I Z E D C I R C U L A R P O R T S


22 | P O7 Click to expand the Coloring and style section. Locate the Coloring and Style section. Find the Line markers subsection. From the Marker list, choose Cycle.

As expected, the transmitted energy is evenly divided between the outport modes.

Derived ValuesNext, display numerical values for the transmission at the highest frequency.

1 On the Results toolbar, click Global Evaluation.

2 In the Global Evaluation settings window, locate the Data section.

3 From the Parameter selection (freq) list, choose Last.

4 Click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Electromagnetic Waves, Frequency Domain>Ports>S-parameter, dB>S-parameter, dB, 31 component (emw.S31dB).

5 Click the Evaluate button.

6 On the Results toolbar, click Global Evaluation.

7 In the Global Evaluation settings window, locate the Data section.

8 From the Parameter selection (freq) list, choose Last.L A R I Z E D C I R C U L A R P O R T S

Solved with COMSOL Multiphysics 4.49 Click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Electromagnetic Waves, Frequency Domain>Ports>S-parameter, dB>S-parameter, dB, 41 component (emw.S41dB).

10 Click the Evaluate button.

As expected, the result is about -3 dB for both modes. 23 | P O L A R I Z E D C I R C U L A R P O R T S


24 | P O L A R I Z E D C I R C U L A R P O R T S

Polarized Circular PortsIntroductionModel DefinitionResults and DiscussionModeling Instructions

polarized circular ports fiber

Documents

r p o r t ssolved

r i z e d c i r c u

e r ejt z

te11 modes

inport modes

outport modes

electric field vector

aswhere z