Defining Sources

Half Angle X & Y of Beam

For a Gaussian beam, this is the half angle to the 1/e2 value of the beam in the local X or Y direction. The Gaussian beam has an angular profile given by,

L =	Lpeake	–[2(x ⁄ θX)2	+ 2(y ⁄ θY )2]	,	(5.7)

where θX and θY are the half angles.

Half Angle R(adius)

Half Angle R is the half angle extent of the beam for Uniform and Lambertian profiles.

Beam Orientation

The orientation of the beam can be set independently of the grid’s orientation or it can be tied to the orientation of the grid. If set independently, it is specified by either:

•A normal (direction) vector and up vector (in global coordinates)

•Rotation angles (in global coordinates).

Perpendicular to Grid

With this setting, the orientation of the beam is perpendicular to the plane of the grid defined in the Grid Setup Tab.

Direction Vectors

The orientation of the beam is specified by two vectors. The normal vector points down the middle of the beam, and the up vector specifies the up or local Y direction of the beam, for Gaussian angular distributions. The default vectors are:

•Direction vector (0,0,1)

•Up vector (0,1,0)

Euler Angles

Euler rotation angles in global coordinates specify a normal vector parallel to the beam and an up vector. The normal vector starts out as the Z unit vector and the up vector as the Y unit vector. Then they are rotated by the angles specified, in the order X, Y, and Z. For example, an x rotation rotates the nominal Z unit vector about the x-axis. The resulting normal vector lies in the Y-Z plane.

Converge to/Diverge from Point

This mode defines a real point, Converge to, or a virtual point, Diverge from, which is used to aim the rays as they exit the grid. This selection provides a convenient way to define a point source, either real (Diverge from) or virtual (Converge to).

Wavelengths

Use this tab to specify the discrete wavelengths to be traced for the Grid Source. You can add a wavelength by typing the wavelength, in μm, into the text box, and

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Ray Tracing

clicking Add (or by pressing the Enter key). To delete wavelength(s), select them in the table and click Delete.

The columns in the wavelength table are described in Table 5.3. You can enter a relative weight for each wavelength in the Weight column, to tailor the source to your needs. The entries in the Flux and # Rays columns are calculated based on the settings in the Grid Setup tab and the weights.

Polarization Standard Expert

TracePro uses the Stokes vector-Mueller matrix representation of polarized light. The Stokes vector represents the Polarization State of the light, and the Mueller matrix represents how an optical device interacts with light. The interaction is calculated by multiplying the Mueller matrix by the Stokes vector as a column vector.

An advantage of using Stokes vectors over other methods is that unpolarized and partially polarized light can be represented. A detailed discussion of polarized light is beyond the scope of this manual, but such information can be found in many textbooks for example:

•E.L. O’Neill, Introduction to Statistical Optics, Dover (1992),

•E. Collett, Polarized Light, Dekker (1992),

•Shurcliff and Ballard, Polarized Light, van Nostrand (1964),

•Kliger, Lewis, and Randall, Polarized Light in Optics and Spectroscopy, Academic Press (1990)).

However, you can simulate polarized light in TracePro without knowing much about Stokes vectors and Mueller matrices. A tabulation of Mueller matrices of commonly used devices is given in the Technical Reference section. See Table 7.4 on page 7.51.

The polarization tab of the Grid Source dialog box lets you specify the initial Polarization State of rays emitted from the grid. The polarization tab has three areas. In the top area you can choose the Polarization State and degree of polarization. In the middle area you can enter the specifications for a custom polarization state. The bottom part is for information only. The Polarization State is depicted graphically and the calculated Stokes vector is also shown.

Polarization State

In order to fully specify the polarization state, you must enter:

•The polarization state, either a standard or custom one.

•The degree of polarization.

•The custom specifications, if you have chosen a custom polarization state.

•The orientation of the beam. This provides a reference direction or “Up Vector” for the polarization state.

The orientation of the beam is determined by the settings in the Grid Setup tab and the Beam Setup tab.

You can specify the Polarization State in one of three ways:

•Choose one of the standard polarization states.

•Specify a custom linear polarization state.

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Defining Sources

• Specify a custom elliptical polarization state.

Choose a standard polarization state by selecting from the drop-down list at the top of the dialog box. The standard polarization states available are:

•Unpolarized

•Horizontal Linear

•Vertical Linear

•+45 degrees Linear

•-45 degrees Linear

•Right Circular

•Left Circular

Unpolarized light

Unpolarized light has no organized polarization state. It consists of a collection of random polarization states. Unpolarized light is represented by the Stokes vector:

1

0

0

0 .

You can set the polarization state to unpolarized by either choosing Unpolarized from the drop-down list, or by setting the degree of polarization equal to zero with any of the polarized states.

Partially polarized light and the degree of polarization

If you specify the Polarization State, you also specify the degree of polarization. Completely unpolarized light is specified by a degree of polarization equal to 0. Fully polarized light has a degree of polarization equal to 1. Intermediate values provide a mix of polarized light, unpolarized light, or partial polarization.

Custom Polarization

Custom linear polarization states

Selecting Custom Linear from the Polarization State dropdown list enables two methods to set the orientation or rotation angle of the linear polarized state. By selecting Ellipse and Handedness from the Method dropdown list, you set the orientation of the linear polarization. For linear polarization, handedness has no meaning and the ellipse ratio collapses to 0.0. By selecting Amplitudes and Phase from the Method dropdown list, you can set the x and y amplitudes. For linear polarization the phase difference is zero.

Custom elliptical polarization states

Selecting Custom Elliptical from the Polarization State drop-down list enables two methods to set the polarization ellipse. By selecting Ellipse and Handedness from the Method dropdown list, you can set the handedness, ratio and orientation of the polarization ellipse. By selecting Amplitudes and Phase from the Method dropdown list, you can set the X and Y amplitudes and phase difference of the polarization ellipse. The labels on the entries change dynamically depending on

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