Poisson spot played an important role in the discovery of the Optical Wave nature of light and is a common way to demonstrate that light behaves as an Optical Wave, here is how to simulate and demo it by an optical wave simulation.
In optics, the Arago spot, Poisson spot, or Fresnel spot is a bright point that appears at the center of a circular object’s shadow due to Fresnel diffraction. In 1818 Poisson was a judge in a competition held by the French Academy of Sciences. Fresnel entered the competition with an optical Wave diffraction theory of light. Poisson, a supporter of the particle theory of light, said that it was absurd to expect a bright spot to appear after a central obscuration. The debate was resolved when the president of the organization was able to experimentally recreate the bright spot and Fresnel won the competition.
The basic experimental setup requires a “point source”, such as an illuminated pinhole or a diverging laser beam. The dimensions of the setup must comply with the requirements for Fresnel diffraction. Namely, the Fresnel number must satisfy
where
d is the diameter of the circular object,
ℓ is the distance between the object and the screen, and
λ is the Optical Wavelength of the source.
Finally, the edge of the circular object must be sufficiently smooth.
Arago spot experiment. A point source illuminates a circular object, casting a shadow on a screen. At the shadow’s center a bright spot appears due to diffraction, contradicting the prediction of geometric optics.
In this validation experiment, we want to launch a 632nm Gaussian beam into the system, as if it’s fed by a fiber optic. The fiber NA is 0.05. This corresponds to a beam divergence angle of about 2.9° and a Gaussian beam waist semi-diameter of about 4.2 µm, using the equations below.
The diameter of the circular aperture is 0.8mm. The distance between light source, lens, and screen is setting as below:
In this simulation, we need to take note：
- Check that each beam has an adequate guard band (at least 3x the beam size) and an adequate resolution across the beam.
- To improve resolution when the beam is traveling from a focus to a lens, or from a lens to a focus, you need to increase the grid width at the previous surface.
- To improve resolution in space where the beam is roughly collimated, you need to go to the first surface in the group and reduce the grid size.
- It’s recommended to start a POP run with more pixels because in general it improves the resolution at every surface.
Let’s validate the beam performance and size on the surface:
The beam size after fiber ( surface 1), the beam size is 4.02um.
The beam size after lens ( surface 6), the beam size is 2.46mm.
The beam size after circular block disk ( surface 9), the beam size is 2.44mm.
The beam performance @ screen (surface 12).
Change the display color to inverse grey color, we could see the optical wave diffraction pattern.
Yes! We see a bright spot on the screen, and it is quite match with the experiment result. Poisson spot is simulated and validated by an optical wave simulation.
The design file used in this particle is attached, please download it here.How to validate Poisson spot
Reference Source:
- https://www.zemax.com/
- Zemax Optical Design Program User’s Guide, Zemax Development Corporation
- https://en.wikipedia.org/wiki/Main_Page
