This video is taken from the FDTD 100 course on Lumerical University.

## Transcript

The Gaussian source type injects a beam with either Gaussian field profile or Cauchy-Lorentz

beam profile.

This type of beam is typically used to represent an incident beam where you want to include

the full field profile of the beam in the simulation region.

There are two methods to calculate the field profile of the beam: the scalar approximation

method, and the thin lens method.

The scalar approximation method assumes that the beam doesn't include any field components

in the direction of propagation so all fields are polarized in the transverse plane normal

to the propagation axis.

This approximation is valid as long as the beam waist diameter is much larger than the

wavelength of the source.

The parameters of the scalar approximation beam are either the combination of the beam

waist radius and the distance between the source injection plane and the focal plane

of the beam, or the beam radius at the source injection plane and the divergence angle of

the beam.

These beam properties are illustrated in this diagram.

The "distance from waist" setting can be set to a negative number if the focal plane

is in front of the injection plane in order to specify a converging beam, or it can be

set to a positive value to specify a beam which is diverging as it propagates from the

injection plane.

For more highly focused beams where the beam waist diameter is on the order of, or smaller

than the source wavelength, the scalar approximation breaks down.

In this case the thin lens method should be used instead.

Note that the thin lens method is only available when the Gaussian type beam is selected, and

it is not available for the Cauchy-Lorentz beam.

The thin lens method injects a fully-vectorial beam where the beam profile is calculated

by a sum of plane waves travelling at different angles representing the resulting beam from

a lens of a given numerical aperture and a given ratio between the incident diameter

of the illuminated portion of the lens to the total lens diameter.

This method of calculating the field profile is based on a published method from M. Mansuripur.

The beam waist size is not one of the input parameters that you can specify when using

the thin lens method, so to generate a beam with a given beam waist radius, you can set

the distance from focus property to 0 to calculate the field profile at the focal plane, and

vary the numerical aperture until the calculated beam has the desired waist radius.

The calculated beam profile can be viewed by clicking the "visualize beam data"

button in the "beam options tab".

For broadband simulations, the "multifrequency beam calculation" option should be selected

which allows the injected beam profile to vary over the broadband range to maintain

the desired beam properties over all wavelengths.

For example, the images here show a beam incident from the bottom right of the plot on a surface

and the angle of the beam propagation varies with frequency when the multifrequency beam

calculation option is not selected.

When injecting a beam, one thing to be careful of is avoiding clipping the beam at the edges

since this can lead to diffractive effects.

You should always use the "visualize beam data" button to plot the field profile and

make sure that the field amplitude of the beam decays to 0 by the edges of the source

region.

Some applications which make use of the Gaussian source are photonic integrated circuits, heat

assisted magnetic recording, CMOS image sensors, and microscopy imaging.

A Gaussian source can be used to represent an incident laser source, or it can be used

to represent the light from an objective lens with a given numerical aperture.

In the next unit we will demonstrate the setup of a Gaussian beam source and how to test

whether the scalar approximation is valid.