A non-scalar phenomenon of separation of plus and minus equal orders in wavelength observed under off-normal incidence with soft-X-ray-EUV multilayer-coated gratings

 

The experimentally observed and theoretically accounted for separation in wavelength of the same external (n > 0) and internal (n < 0) orders is intimately connected with specific features of dynamic propagation of short-wavelength radiation through a multilayer corrugated stack which is absent in a bulk diffraction grating. The separation encreases with the angle of incidence, wavelength and number of the diffraction order. The validity of approximating the efficiency of a multilayer grating operating at near-normal incidence in the soft-X-ray-EUV ranges with a product of the relative grating efficiency by the reflectance of its multilayer coating has been studied by the rigorous modified integral method (MIM). The widely used asymptotic approach has until recently been considered accurate enough for analysis of short-wavelength near-normal-incidence multilayer-coated gratings. While being capable of yielding close to true values of the maximum efficiency in diffraction orders, the approximate method does not predict the correct shape of the efficiency curves and cannot account for the noticeable spectral separation of the same, positive and negative, orders. Both perfect and real gratings employed in the soft-X-ray-EUV range are used to demonstrate the inapplicability of this approximation to an analysis of precise positions of efficiency maxima for the same external and internal diffraction orders, despite the small ratios of wavelength and groove depth to period, closeness of the refractive indices of the materials to their values in vacuum, and small layer thicknesses. The real groove boundary profiles and the rms roughness used in modeling were derived from AFM measurements. This conclusion is buttressed by experimental studies of the efficiency of various Mo/Si, Mo₄Ru₆/Be, and Mo/Y diffraction gratings performed with synchrotron radiation. The reasons for the observed substantial (a few Angstrom) separation in wavelength between the maxima of positive and negative orders of the same number and the part played by deviation from the exact normal incidence in this effect are discussed. Although carrying out high-precision efficiency calculations requires the use of sophisticated software and significantly increases the computation time compared to the commonly employed approximate approach, the revealed non-scalar effect may turn out advantageous in designing devices based on multilayer off-normal-incidence soft-X-ray-EUV gratings.

© 2005 EOS

 

The report was published in European Optical Society (Topical Meetings Digest Series). Click here to download the full text.