The Poisson spot, also known as the Arago spot or Fresnel spot, is a bright point that appears at the center of a circular object’s shadow due to Fresnel diffraction. This phenomenon played a crucial role in the discovery of the optical wave nature of light. The Poisson spot provides experimental proof that light behaves as an optical wave rather than a particle.
This article will explain how to simulate and demonstrate the Poisson spot using an optical wave simulation in OpticStudio.
The Historical Background of the Poisson Spot
In 1818, Poisson challenged the wave theory of light proposed by Fresnel. Poisson, a proponent of the particle theory, argued that it was absurd to expect a bright spot in the center of a shadow created by a circular object. To test this, the president of the French Academy of Sciences conducted an experiment in which the bright spot was indeed observed, validating Fresnel’s theory and disproving Poisson’s argument.
Experimental Setup
The basic experimental setup involves a point source (such as a pinhole or a diverging laser beam) illuminating a circular object. The diffraction pattern formed at the center of the shadow creates the Poisson spot.
To ensure Fresnel diffraction occurs, the Fresnel number must satisfy the following condition:
where
- d is the diameter of the circular object
- ℓ is the distance between the object and the screen
- λ is the optical wavelength of the source
In the experiment, the edge of the circular object must be sufficiently smooth to observe the diffraction effect clearly.
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.
Simulating the Poisson Spot in OpticStudio
To simulate this experiment, we set up a 632nm Gaussian beam, typically fed by a fiber optic with a Numerical Aperture (NA) of 0.05 using the equation below. This corresponds to a divergence angle of about 2.9° and a Gaussian beam waist semi-diameter of approximately 4.2 µm.
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) is 4.02um.
The beam size after lens (surface 6) is 2.46mm.
The beam size after circular block disk (surface 9) is 2.44mm.
The beam performance at 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 quite matches with the experiment result. Poisson spot is simulated and validated by an optical wave simulation.
Reference
- https://www.zemax.com/
- The design file used in this article is attached. How to validate Poisson spot