COMSOL 6.2 - Gaussian Beam

Use the feature to release rays with a Gaussian distribution of intensity or power. Since the Geometrical Optics interface does not consider diffraction effects, the 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 is selected from the physics interface list.

The 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: , , and .

Enter the qw (SI unit: m) based on space dimension. By default the beam waist is located at the origin. Then enter the 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.

Select an option from the list:

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, 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 from the previous section.

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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.

For a , enter the 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 list:

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(the default), then enter a value or expression for the α (SI unit: rad). The default is 1 mrad.

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, then enter a value or expression for the w0 (SI unit: m). The default is 1 mm. In 2D, this option is instead called and the input is called the because the 2D beam is uniform in the out-of-plane direction, not rotationally symmetric about the beam axis.

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, then enter a value or expression for the zR (SI unit: m). The default is 1 mm.

If instead is selected, enter the 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 w0 (SI unit: m). The default is 1 mm. In 2D this is called the .

For all of the above settings, enter a value or expression for the c (dimensionless). The default is 2. 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 c = 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. The default value of 2 results in 99.97% of the total beam power being sampled by the rays. At about c = 4.2 the released power among all the rays matches the specified total source power to double precision but most of the released rays will individually have rather low power.

Select an option from the list (only available in 3D):

ar (dimensionless) is the ratio of major axis of ellipse to the minor axis. The major axis is always equal to the diameter of corresponding circular cross section. The default is 1, which is equivalent to circular cross section.

a (dimensionless) is direction of major axis in plane perpendicular to beam axis. By default the major axis is along positive x direction.

Select one of the following options from the Intensity specification list:

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(the default), then enter a value or expression for the Psrc (SI unit: W). The default is 1 W.

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, then enter a value or expression for the Pcir (SI unit: W). The default is 1 W.

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, then enter a value or expression for the I0 (SI unit: W/m2). The default is 1 W/mm2.

This section is a simplified version of the section for the Release node. The main differences are that the 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.

Components of the u (dimensionless). By default the vector points in the positive y direction. This must not be parallel to the beam axis.

For all dimensions, enter the δ0 (SI unit: rad, default 0).

This section is shown if is selected from the list in the physics interface section. Enter a value or expression for the λ0 (SI unit: m). The default is 660 nm.

This section is shown if is selected from the list in the physics interface section. Enter a value or expression for the ν0 (SI unit: Hz). The default is 4.54 × 1014 Hz.