Graphical representation of the diffraction grating equation
Example of diffraction orders produced at a given wavelength by a reflecting diffraction grating in the plane of dispersion.
Range of directions defining the signs of and .
Graphical regions (shaded) producing specific orders. equals in classical diffraction.
Graphical representation of orders produced from a grating. The numbers shown in a given area are the orders produced in it. White (shaded) areas produce an odd (even) number of orders. The zeroth order is produced alone at the right-hand side. From right to left a consecutive positive (negative) order is produced for each segment of negative (positive) slope crossed. and are the starting and ending limits used in Sec. IV C.
The four vertices of area (from Fig. 4) producing , , , 0, and .
Multiple values of (arrow lengths) for a given point of interest. Here the values are negative (positive) for and ( and ).
Scanning curves with different values of for (a) and (b) . The angle is illustrated at the top for three configurations.
Illustration of overlapping orders. Scanning curves for and (dark lines and ) with . When a widely polychromatic beam (horizontal gray line starting, for example, at ) is scanned, different values of lead to (1) no detected order, (2) a single detected order, or (3) multiple detected orders (overlapping) in the analyzed direction of diffraction. The useful portion of the scan starts when and ends when .
Graphical area that solves the problem presented in Sec. I. The scan must be performed with (see Eq. (16) for ). The quantity must be chosen to make (related to the known lowest wavelength ) lie in the area of solutions delimited by and . To avoid overlapping, the scan must end at . The scanning curves shown for different values of are four examples of solutions.
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