Gaussian Beam
Use the Gaussian Beam feature to release rays with a Gaussian distribution of intensity or power. Since the Geometrical Optics interface does not consider diffraction effects, the Gaussian Beam node can be used in two different asymptotic limits: to release a collimated beam over short distances, or to treat the beam waist as a point source and trace rays over very long distances.
This feature is only available when either the ray intensity or power is solved for; it will not be available if None is selected from the physics interface Intensity computation list.
The Gaussian Beam node does not require a selection because it is not necessary to release the rays at a boundary or even within a domain; the waist may be located at an arbitrary location in the geometry (2D or 3D) or an arbitrary location along the z-axis (2D axisymmetric).
See Release for information on the following sections: Release Times, Initial Phase, and Initial Value of Auxiliary Dependent Variables.
Beam Position and Direction
Enter the Beam waist position qw (SI unit: m) based on space dimension. By default the beam waist is located at the origin. Then enter the Beam axis r (dimensionless) based on space dimension. By default this is the positive z direction in 3D or the positive x direction in 2D.
In a 2D axisymmetric geometry, the position and orientation of the Gaussian beam is more restricted compared to 2D and 3D geometries. The beam must be symmetric about the z-axis or else it would not actually be a Gaussian beam in the 3D volume of revolution.
Enter the Beam waist z-coordinate zw (SI unit: m). The default is 0. Then, from the Beam direction list, select Positive z-axis (the default) or Negative z-axis.
Beam Dimensions
Select an option from the Beam type list:
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Point source (small Rayleigh range), the default, is appropriate when the rays in the model propagate very large distances compared to the beam waist radius or Rayleigh range. The beam waist is treated as a point source, from which rays emanate outward in a cone. The symmetry axis of the cone is the Beam axis from the previous section.
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Collimated source (large Rayleigh range) is appropriate when the rays propagate for only a short distance compared to the Rayleigh range. The rays are released from a grid of points and initially propagate in the same direction.
Releasing Rays from a Point Source
For a Point source, enter the Number of polar angles Nθ (dimensionless). The default is 10. In a 2D or 2D axisymmetric geometry, the actual number of rays released is equal to Nθ, while in 3D the total number of rays released is 3Nθ(Nθ + 1) + 1. because rays released at a larger polar angle require a finer sampling of azimuthal angles to ensure uniform sampling within the solid angle subtended by the beam.
To control the width of the beam, select one of the following from the Beam dimensions list:
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Specify beam divergence half-angle (the default), then enter a value or expression for the Beam divergence half-angle α (SI unit: rad). The default is 1 mrad.
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Specify beam waist radius, then enter a value or expression for the Beam waist radius w0 (SI unit: m). The default is 1 mm. In 2D, this option is instead called Specify beam waist half-width and the input is called the Beam waist half-width because the 2D beam is uniform in the out-of-plane direction, not rotationally symmetric about the beam axis.
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Specify Rayleigh range, then enter a value or expression for the Rayleigh range zR (SI unit: m). The default is 1 mm.
Releasing Rays from a Collimated Source
If instead Collimated source is selected, enter the Number of radial positions Nc (dimensionless) in a 3D or 2D axisymmetric geometry, or the Number of rays per release N (dimensionless). For any dimension, the default is 10. In 3D the total number of rays released is 3Nc(Nc + 1) + 1 because rays released at greater radial distances from the center of the beam waist require a finer sampling of azimuthal angles, to ensure uniform sampling within the beam cross section. Then enter the Beam waist radius w0 (SI unit: m). The default is 1 mm. In 2D this is called the Beam waist half-width.
Beam Cutoff Ratio
For all of the above settings, enter a value or expression for the Beam cutoff ratio c (dimensionless). The default is 1. The cutoff ratio does not affect the other beam parameters but it affects how rays are sampled from the beam.
Theoretically the irradiance and power of light within a Gaussian beam remains nonzero out to an arbitrarily large radial distance. But for practical purposes the beam must be truncated at some point, so that rays will only be released within a finite distance from the center of the beam waist (for collimated sources) or within a finite angle (for point sources).
Changing the value of c changes the maximum distance or angle from the beam axis at which rays are released. For the default value of 1, rays will be released at radial positions out to the waist radius w0 (for a collimated source) or in a cone with angles up to the beam divergence half-angle α (for a point source). In a 3D or 2D axisymmetric beam, the released rays then comprise a fraction of 1 - e2 or about 87% of the total beam power. In a 2D sheet beam, this fraction is about 95%.
If the value of c is increased, rays will be released at greater distances from the beam axis (for a collimated beam) or at greater angles (for a point source) and the total power over all of the released rays will be greater than the fractions given above. Setting c = 2 results in 99.97% of the total beam power being sampled by the rays. , but most of the released rays will individually have rather low power. At about c = 4.2 the released power among all the rays matches the specified total source power to double precision.
Intensity and Power
Select one of the following options from the Intensity specification list:
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Specify total beam power (the default), then enter a value or expression for the Total source power Psrc (SI unit: W). The default is 1 W.
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Specify encircled power, then enter a value or expression for the Encircled power Pcir (SI unit: W). The default is 1 W.
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Specify Intensity at beam waist, then enter a value or expression for the Peak intensity at beam waist I0 (SI unit: W/m2). The default is 1 W/mm2.
Initial Polarization
This section is a simplified version of the Initial Polarization section for the Release node. The main differences are that the Gaussian Beam must always release polarized rays, and that the initial polarization direction must be entered directly rather than based on the directions of the principal wavefront curvatures.
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In 3D enter the following:
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Components of the Initial polarization reference direction u (dimensionless). By default the vector points in the positive y-direction. This must not be parallel to the beam axis.
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Initial polarization parallel to reference direction a1,0 (dimensionless, default 1).
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Initial polarization perpendicular to reference direction a2,0 (dimensionless, default 0).
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In 2D axisymmetric models enter the following:
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Initial polarization, in plane arz,0 (dimensionless, default 1)
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Initial polarization, out of plane aφ,0 (dimensionless, default 0).
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In 2D enter the following:
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Initial polarization, in plane axy,0 (dimensionless, default 1)
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Initial polarization, out of plane az,0 (dimensionless, default 0)
For all dimensions, enter the Initial phase difference δ0 (SI unit: rad, default 0).
Vacuum Wavelength
This section is shown if Polychromatic, specify vacuum wavelength is selected from the Wavelength distribution of released rays list in the physics interface Ray Release and Propagation section. Enter a value or expression for the Vacuum wavelength λ0 (SI unit: m). The default is 660 nm.
Initial Ray Frequency
This section is shown if Polychromatic, specify frequency is selected from the Wavelength distribution of released rays list in the physics interface Ray Release and Propagation section. Enter a value or expression for the Initial ray frequency ν0 (SI unit: Hz). The default is 4.54 × 1014 Hz.
Gaussian Beam Theory