Poisson's Spot

Introduction

To download the associated FRED file: poissons-spot.frd

FRED allows for simulation of physical optics phenomena such as diffraction and interference. With this capability, components such as Gaussian laser beams and interferometers can be accurately modeled and incorporated into optical systems.

The FRED Model

FRED performs diffraction and interference calculations using a technique called Gaussian Beam Decomposition. The coherent beam superposition technique works by modeling arbitrary optical fields with the coherent summation of smaller fundamental beams. In FRED, these smaller fundamental beams are Gaussian beamlets. It has been demonstrated that Gaussian beams can be represented and propagated with real rays [1]. Those rays can be traced through an optical system while maintaining the Gaussian beam representation. Near and far field diffraction can be calculated coherently summing the Gaussian beams, which are represented by real rays traced through the system.

As an example, the Poisson’s Spot experiment is modeled in FRED. A simple coherent plane wave optical source is created, followed by a small circular obstruction. Coherent irradiance behind the obstruction is evaluated at two different distances to show development of the diffraction pattern.

Figure 1. Poisson’s spot irradiance pattern. A 588 nm coherent plane wave source shines behind a circular obstruction with 0.1 mm radius. Coherent irradiance is evaluated at two different distances: On the left side, light 2 mm beyond the obstruction does not undergo significant diffraction. On the right side, light 40 mm beyond the obstruction undergoes Fresnel diffraction and exhibits a characteristic Poisson Spot on axis.

1] Arnaud, Jacques, “Representation of Gaussian beams by Complex Rays”,Applied Optics, Vol. 24, No. 4, p. 538-543, Feb 1985