Light and Matter Waves

When light and matter waves pass through an object or an opening, they diffract. The intensity can be calculated with Huygens' Principle along with the ideas of the superposition principle. These different ideas will be simulated with python(x,y). These simulations will help us visualize how the waves behave. We will begin by observing how the electric field from a point source changes with a detector. The detector will detect through all of the points in the space being observed.


When the slit space(y) is 12mm and a wavelength(λ) of 2mm and there is one point source the will be seen in this form.

y = 12 mm, λ = 4 mm 1 point source

y = 12 mm, λ = 8 mm 1 point source

y = 12 mm, λ = 2 mm 2 point sources

y = 12 mm, λ = 4 mm 2 point sources

y = 24 mm, λ =4 mm 2 point sources

y = 12 mm, λ = 8mm 2 point sources 

y = 24 mm, λ = 8mm 2 point sources 

In the next set of pictures we changed the amount of sources and the number of detectors in the wave.

There are 50 sources (s) and 500 detectors (d)

This is when M = 5 and N = 7

This is when M = 50 and N = 500

This is when M = 51, N = 500, the slit distance = 1μm and the slit width = 5μm

This is when M = 51, N = 600, the slit distance = 0.5 μm and the slit width = 10μm 

This is when M = 51, N = 600, the slit distance is 50mm and the slit width is 25μm

This is when the length of the wave is 600nm

This is when the length of the wave is 700nm

This is when the screen distance is 5 mm

This is when the screen width is 50 mm 

This is when the screen width is 5 mm

There are different lines of code that help us program these different simulations. The code below helps us calculate our coordinate system that we used. 

N = 100

dX = screendist/N

dY = screendist/N
Xcoords = arange(0, screendist+2*dX, dX)

Ycoords = arange(-screendist/2, screendist/2 + 2*dY, dY)

[xd,yd] = meshgrid(Xcoord,Ycoord)

When we are graphing 2D images of our 3D graphs, it gives us a representation of how the graph behaves and any differential area. It is easier visually, to interpret a 2D graph versus a 3D graph. Some of graphs go to a zero point because this is when destructive interference occurs at its most intense amount. 

The maximums of the graphs change as you go away from the center. The further the detector is away, the harder it is to detect the waves. When the detector is close it can tell us a lot of information of how the waves behave.