Photon Engineering FRED, Interferometry and Beam Propagation

Beam Propagation and Interferometry

FRED uses a Gaussian beam decomposition algorithm to propagate coherent optical fields through the system geometry.

This proven, powerful technique makes it possible to model beam propagation through interferometers, holographic systems, lasers systems, etc with accuracy and generality.

The basic idea behind the Gaussian beam decomposition algorithm is that an arbitrary optical field can be decomposed into a set of elementary Gaussian beams. Each Gaussian beam is traced through the system and, at the desired plane in space, the individual Gaussian beams are summed together coherently to regenerate the optical field. The clever part of the algorithm comes from an observation made by Arnaud in the 1960’s: a Gaussian beam can be rigorously propagated through an optical system by tracing geometrical rays! (In Arnaud’s formalism, the geometric representation of a Gaussian beam involves three sets of rays:

1. The “base” ray, the central ray in the Gaussian beam. This ray contains the optical path length (phase) and polarization data for the single Gaussian beam. (It is also the geometric ray with which optical engineers are familiar.)
2. The “waist” rays. The waist rays are initially propagated parallel to base ray and are displaced from the base ray by an amount that is proportional to the waist dimensions of the Gaussian beam. In order to calculate astigmatic effects, there need to be at least 2 waist rays/Gaussian beam: one displaced in x and the other in y. In order to calculate comatic effects, there need to be at least 4 waist rays/Gaussian beam: displaced by ± x and ± y.
3. The “divergence” rays. These rays diverge from the center of the waist and asymptotically approach the far-field divergence of the Gaussian beam. As with the waist rays, there are typically 2 or 4 divergence rays traced with a single base ray to detect astigmatic and comatic effects.

The waist and divergence rays are sometimes referred to in the literature as “secondary” or “parabasal” rays.

(Top) Two beam interference
(Below)
Interfereogram of spherically aberrated beam

In FRED, the implementation of this algorithm is largely hidden from the user. The user specifies the type of optical field (plane wave, diverging/converging wave, astigmatic laser diode, user-defined, etc) to be propagated and FRED creates and traces the secondary rays in the background. At the conclusion of the raytrace, FRED uses the ray information to recreate each Gaussian beam, and then sums the coherent field at the observation plane; the result is an irradiance, power density, or scalar field distribution at the user-specified spatial resolution.

FRED's Gaussian beam decomposition algorithm has been further enhanced to model arbitrary polarized beams as well.

For more information on FRED's coherent Gaussian Beam propagation read the Coherent Application note here and the Laser Application note here.