Polarization/Angles

GSOLVER is a full vector implementation. The incident illumination k - vector is determined by two polar angles (theta and phi) and a wavelength. The polarization state is determined by two angles, alpha and beta. The incident ray is drawn for a positive theta, and negative phi.

(incident k-vector description)

The Cartesian coordinate system is indicated by [x,y,z] in the figure. The polar angles are given by theta and phi. The default grating period is along the +x-direction (the cross and transverse dimension is along the +y-direction). Theta, for the incident ray, is positive with respect to the -x axis. On reflection theta is positive with respect to the +x axis.

A positive theta, for reflected orders, is a deviation from +z towards +x (phi=0).

A negative theta, for transmitted orders, is a deviation from -z towards +x (phi=0). This angle convention is used by the angles dialog in calculating angles.

The EDITOR view uses a coordinate system which changes the sign of the z and y axis.

The incident plane wave illumination is fully specified with five parameters: wavelength, and four angles, theta, phi, alpha, and beta.

(polarization definition)

Alpha and beta determine the state of polarization. The red line in the figure is the principle E-field (E1) direction. For phi=alpha=beta=0 it is the TE direction. The secondary E-field (E2) (which is 90degrees out of phase with the principle E-field) is shown in green. E1, E2, and k form an orthogonal system. E1/E2 are rotated about the k direction by alpha. The relative magnitude of E2 with respect to E1 is determined by beta. Tan(beta)=E2/E1.
(orders convention)
The figures indicate the order naming convention used by GSOLVER. In this figure, the incident ray (blue) has positive theta. The specular reflected order (0R) has positive theta (equal to the incident ray theta). The +1R order theta is more positive (unless it is evanescent, then it is imaginary). The -1R order is more negative than 0R. The 0T transmitted order theta is negative (measured with respect to the -z axis, moving towards the +x axis). The +1T order is more negative, and the -1T order is less negative.

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