FEATool Multiphysics
v1.14
Finite Element Analysis Toolbox

The classic doubleslit experiment considers a planar and periodic oscillating wave which hits and passes two narrow slits. Assuming the slits are narrow enough, the passing waves will bend and cause an interference pattern, while diffraction will attenuate the off axis resulting amplitude.
In the example the Helmholtz equation is used to model the wave phenomena
\[ ( \frac{\partial^2 A}{\partial x^2} + \frac{\partial^2 A}{\partial y^2} )  k^2 A = 0 \]
where A is the amplitude of the wave,and k the wave number (k = 2·π/λ).
This model is available as an automated tutorial by selecting Model Examples and Tutorials... > Classic PDE > Interference and Diffraction from the File menu. Or alternatively, follow the stepbystep instructions below.
Enter A
into the Dependent Variable Names edit field.
0.8
into the radius edit field.0.8
into the x_{min} edit field.0.8
into the x_{max} edit field.0.8
into the y_{min} edit field.0
into the y_{max} edit field.Press the  / Subtract geometry objects Toolbar button.
0.080.02
into the x_{min} edit field.0.08+0.02
into the x_{max} edit field.0.2
into the y_{min} edit field.0
into the y_{max} edit field.0.080.02
into the x_{min} edit field.0.08+0.02
into the x_{max} edit field.0.2
into the y_{min} edit field.0
into the y_{max} edit field.Press the + / Add geometry objects Toolbar button.
Enter 0.015
into the Grid Size edit field, and press the Generate button to call the grid generation algorithm.
Enter (Ax_x + Ay_y)  k^2*A_t = 0
into the Equation for A edit field.
Name  Expression 

wl  0.08 
k  pi*2/wl 
First set homogenous Neumann conditions for all boundaries.
Enter 0
into the Dirichlet/Neumann coefficient edit field.
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.
Enter k*i*A + 2*k*i
into the Dirichlet/Neumann coefficient edit field.
The outlet is assumed nonreflective and n·∇(A) + k·i·A = 0.
Enter k*i*A
into the Dirichlet/Neumann coefficient edit field.
After the problem has been solved FEATool will automatically switch to postprocessing mode and here display the computed wave amplitude A. The interference pattern can be clearly seen with four lines where the waves have been canceled out completely.
The Point/Line Evaluation tool can be used to visualize the interference and diffraction pattern at the boundary.
Press OK to finish and plot the amplitude curve.
The interference and diffraction custom equation model has now been completed and can be saved as a binary (.fea) model file, or exported as a programmable MATLAB mscript text file, or GUI script (.fes) file.