Setting Laser Beam Spatial Profiles

VISRAD utilizes a hybrid analytic/ray-trace model to compute the laser power spatial distribution onto a target grid. The analytic model provides the spatial profile for the intensity at a surface element, while the ray-trace component is used to test occultation by other surface elements and energy loss of light escaping the mesh through holes. This hybrid model avoids "speckled" distribution patterns that can occur when using a purely ray-trace model.

The spatial profile model in VISRAD supports the use of circular beam profiles, square beam profiles, and elliptical beam profiles. The model has the following features:

• At the focal plane, the spatial profile is characterized by either:
  • a uniform beam (either circular or square, depending on the beam shape at the final optics), or
  • a "modified supergaussian" formula
• At the final optics the beam profile is spatially uniform.
• The spatial profile transitions smoothly from its profile at the final optics to the focal plane by utilizing parameters that vary along the beam's symmetry axis ("z-axis").

Note that at present, the spatial profile at the focal plane is based on parameters/data provided by the laser facilities. However, away from the focal plane, the analytic formulae used are not currently constrained by experimental data.

Note also that when rendering laser beam cones in the Main Graphics Window, VISRAD draws each cone using a specified number of polygons. To adjust the number of polygons used in rendering each cone, use the Lasers tab of the Preferences dialog.

Distributed Polarization Rotator (DPR) Modeling

For the OMEGA laser system, DPR modeling is available. When simulating a beam with DPR "on" (i.e., with distributed polarization rotators (DPR) in), the beam is split into two cones, which have a separation of 85 microns at the focal plane. The beam power is split evenly between the two cones. The images below show examples of a beam with DPR on (left) and off (right). Issues related to DPR modeling are:

• DPR modeling can only be turned on for any beam. Note, however, that for many OMEGA DPPs, the spatial model parameters (i.e., beam spot size, supergaussian exponent) are based on fits to data which had DPR on (in which case, turning DPR modeling on is not necessary)..
• DPR modeling is not supported for Custom laser beams (including the 2w/3w/4w probe beams), or for laser beams of target chambers other than OMEGA.
• A column indicating DPR status (on/off) is included in the Laser Beam Summary Table. The DPR status is also included in the exported/imported laser beam data files (CSV and XML).
• By default, VISRAD shows both of the DPR cones. Users can specify that only the DPR+ cones or the DPR- cones be displayed. To do this, select the Laser | OMEGA DPR Cones menu item.

Beam Profile Modeling

VISRAD utilizes beam profile formulae that allow for a continuous transition from a square or circular spatially uniform profile at the final optics to an elliptical supergaussian profile at the focal plane. The beam intensity is given by:

where I₀(z) is normalized at each z to provide the correct total beam power, and

              (1)

where x, y, and z are the position in the beam's coordinate system (z = 0 is at the focal plane). The left term of Eq. (1) represents the contribution to a that provides a square profile, while the right term provides an elliptical (or circular) profile.

For the square component, DL(z) represents the edge length of the square beam at a distance z from the focal plane, and the exponent M(z) varies smoothly from a value of 10 at the focal plane to 1000 when z is large*.

For rectangular beams (e.g., NIF ARC beams), Eq. (1) utilizes the width, DL_W(z), and height, DL_H(z), of the beam edge.

In the right term of Eq. (1), the parameter a(z) and b(z) are the major and minor radii of the ellipse, respectively, and are a function of the axial distance from the point of focus. They are given by:

a(z) = a_o [ ( z / z_A ) ² + 1 ]^1/2,

b(z) = b_o [ ( z / z_B ) ² + 1 ]^1/2,

where a_o and b_o are the 1/e major and minor radii in the focal plane, and z_A and z_B are constants that depend on the focal length (F_L) and f# of the system:

z_A = F_L [ ( F_L / ( 2 a_o f# ) ² - 1 ] ^-1/2,

z_B = F_L [ ( F_L / 2 b_o f# ) ² - 1 ] ^-1/2.

The primes on x and y in the right term of Eq. (1) account for the fact that the axes of the elliptical profile can be rotated. The supergaussian index, n(z), is given by:

n(z) = n_o [ 1 + k ( z / z_o ) ^a ] ,

where n_o is the value at best focus (z = 0), and a and k are constants (a = 1, k = 0.2). The use of a z-dependent value for the supergaussian index provides for a continuous transition from a supergaussian profile in the near field to a uniform spatial profile in the far field. For uniform beams (i.e., independent of r), n(z) = 0.

The quantity f_SQ(z) represents the fractional contribution to a that provides a square profile and is given by:

where G is a constant (currently set to 1.0). For a beam that is circular at the final optics, f_SQ(z) is always zero.

Beam Profile Parameters

The Spatial Profile tab is used to specify the spatial distribution parameters of the laser beam. Available spatial profile models include:

• Uniform
• Custom Supergaussian
• DPPs for OMEGA
• DPPs for OMEGA EP
• CPPs for NIF
• Phase Plates for LMJ
• Phase Plates for GEKKO

For phase plates, the supergaussian profile parameters are editable. Values stored previously in VISRAD workspaces are read in and used. When the Spatial profile model is changed, default values for the supergaussian profiles are entered. To reset the profile parameters to their default values, select the Use default values button.

When the Custom Supergaussian model is selected, the user must enter the appropriate values for the supergaussian exponent, n, and the spot size. The spot size can be specified in terms of the 1/e radius (i.e., d_o), the half-max radius, or the radius at which the intensity falls to 5% of its peak value.

The size of the envelope containing the beam can be adjusted using Advanced parameters. Typically, a value of ~ 2 - 3 is suitable. Io(z) is normalized so that the envelope contains the appropriate power at each z. The user can also adjust the ratio of the lens radius to the value of d(z) at the final optics. The effect of this is to change z_o.

• minor radius at best focus
• either specific Rotation angle of the minor axis with respect to vertical (positive angles => clockwise), or the Orientation port.

A rotation angle of zero corresponds to the case where the major axis is nearly horizontal; for a square beam, it is coincident with the upper edge of the square beam as it enters the target chamber.

Elliptical beam profile rotation angles can be specified using an OMEGA Port. Mapping of rotation angles of individual beams based on a specified Orientation port is currently supported for the following elliptical DPPs:

• E-IDI-300 (Pent and Hex ports)
• E-SG4-865 (Hex ports)
• E-SG10-300 (Hex ports).

Uniform Beam Profiles

When a Uniform spatial profile is selected, the intensity, at a given position along the z-axis of the beam, is spatially uniform (in x and y directions).

For conical beams, the shape of the beam at focus can be either circular or elliptical. R_max and R_min determine that size of the beam at focus.

For square beams (such as standard NIF beams) or rectangular beams (such as NIF ARC beams), R_max refers to the furthest extend from the center of the beam (i.e., to the corner of the square or rectangle). The shape is not affected by the value of R_min.

Sample Profiles for Circular Beams

The images below show the change in the beam intensity profile for disks at 0 cm (left), 2 cm, and 10 cm (right) from target chamber center (TCC). The spatial profile is seen to become nearly flat-topped at 10 cm from TCC. (In each case, the size of the disk was adjusted so that its edge corresponded to where the intensity was 1% of its peak value.)

Sample Profiles for Circular Beams with Elliptical Phase Plates

Sample Profiles for Square Beams with Elliptical Phase Plates

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* The form of M(z) is chosen to provide a sharp edge to the square profile at positions far from the focal plane, and a more rounded edge at the focal plane.

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