FEATool Multiphysics
v1.10 Finite Element Analysis Toolbox |

Two Material Wave Guide Interface

Simulation of a wave guide interface with two different materials. The changing diffraction pattern of planar time harmonic waves is investigated using the Helmholtz equation

\[ -( \frac{\partial^2 A}{\partial x^2} + \frac{\partial^2 A}{\partial y^2} ) - k^2 A = 0 \]

This model is available as an automated tutorial by selecting **Model Examples and Tutorials...** > **Electromagnetics** > **Two Material Wave Guide Interface** from the **File** menu. Or alternatively, follow the step-by-step instructions below.

- To start a new model click the
**New Model**toolbar button, or select*New Model...*from the*File*menu. - Select the
**Custom Equation**physics mode from the*Select Physics*drop-down menu. Enter

`A`

into the*Dependent Variable Names*edit field.- Press
**OK**to finish the physics mode selection.

The geometry consists of two rectangles for the different materials.

- Select
**Rectangle**from the*Geometry*menu. - Enter
`-0.12`

into the*x*edit field._{min} - Enter
`0`

into the*x*edit field._{max} - Enter
`-0.01`

into the*y*edit field._{min} - Enter
`0.01`

into the*y*edit field._{max} - Press
**OK**to finish and close the dialog box. - Select
**R1**in the geometry object*Selection*list box. - Press the
**Copy and/or transform selected geometry object***Toolbar*button. - Select the
**Make copy of geometry object**check box. - Enter
`0.12 0`

into the*Space separated string of displacement lengths*edit field. - Press
**OK**to finish and close the dialog box. - Switch to
**Grid**mode by clicking on the corresponding*Mode Toolbar*button. - Press the
**Refine***Toolbar*button. - Switch to
**Equation**mode by clicking on the corresponding*Mode Toolbar*button. - Press the
**edit**button.

Enter the Helmholtz equation in the *Edit Equations* dialog box.

- Enter
`-(Ax_x + Ay_y) - k^2*A_t = 0`

into the*Equation for A*edit field. - Press
**OK**to finish and close the dialog box. - Press
**OK**to finish the equation and subdomain settings specification. - Press the
**Constants***Toolbar*button, or select the corresponding entry from the*Equation*menu, and add the following modeling constants for the speed of light, frequency, and wave number in the*Model Constants and Expressions*dialog box. Note that the wave number is scaled by a factor of two in the left subdomain (entering a space separated list allows prescribing constants on a per subdomain basis).

Name | Expression |
---|---|

c | 3e9 |

f | 1e11 |

sfac | 2 1 |

k | sfac*2*pi*f/c |

- Switch to
**Boundary**mode by clicking on the corresponding*Mode Toolbar*button.

Set homogenous Dirichlet conditions *A = 0* for the absorbing walls.

An incoming planar wave is featured at the inlet with the complex boundary condition *n·∇(A) + k·i·A = 2·k·i* which can be implemented as a Neumann boundary condition.

- Select boundary number
**5**in the*Boundaries*list box. - Select the
**Neumann, g_A**radio button. - Enter
`-k*i*A + 2*k*i`

into the*Dirichlet/Neumann coefficient*edit field.

The outlet is assumed non-reflective and *n·∇(A) + k·i·A = 0*.

- Select number
**3**in the*Boundaries*list box. - Select the
**Neumann, g_A**radio button. - Enter
`-k*i*A`

into the*Dirichlet/Neumann coefficient*edit field. - Press
**OK**to finish the boundary condition specification. - Switch to
**Solve**mode by clicking on the corresponding*Mode Toolbar*button. - Press the
**=***Toolbar*button to call the solver. After the problem has been solved FEATool will automatically switch to postprocessing mode and plot the computed solution.

After the problem has been solved FEATool will automatically switch to *Postprocessing* mode and show real part of the computed amplitude of the electric field. One can clearly see how the wave and frequency changes in the second material.

The *two material wave guide interface* electromagnetics model has now been completed and can be saved as a binary (.fea) model file, or exported as a programmable MATLAB m-script text file, or GUI script (.fes) file.