Echelles: scalar, electromagnetic, and real-groove properties.

For lack of alternatives, echelle-grating diffraction behavior has in the past been modeled on scalar theory, despite observations that indicate significant deviations. To resolve this difficulty a detailed experimental, theoretical, and numerical study is performed for several echelles that work at low (18-13), medium (35-55), high (84-140), and very-high (to 660) diffraction orders. Noticeable deviations from the scalar model were detected both experimentally and numerically, on the basis of electromagnetic theory: (1) the shift of the observed blaze position was shown to decrease with the wavelength-to-period ratio, and it tends to zero more rapidly than the decrease of the maximum width, so that the TE- and TM-plane responses tend to merge into each other; (2) cut-off effects (Rayleigh anomalies) were found to play a significant role for high groove angles, where passing-off orders are close to the blaze order. A possibility for evaluation of the blaze angle from angular, rather than from spectral, measure nts is discussed.Several reasons for the differences between real and ideal echelles (material-index deviations, profile deformations, and groove-angle errors) are analyzed, and their effects on the performance of echelles is studied.