Diffraction of multilayer gratings and zone plates in the x-ray region using the Born approximation

New devices combining the Bragg reflection from periodic multilayer structures with Fraunhofer or Fresnel diffraction arising from lateral patterning of the multilayer are now available for x-ray optics. Using the Green’s-function method, we establish an integral equation for the scattered amplitude that is valid in the framework of both Fraunhofer and Fresnel diffraction. The scattered amplitude is given in the first and the second Born approximations for multilayer mirrors, laminar and sawtooth-profile multilayer gratings, and linear multilayer zone plates. The main diffractive properties of these devices are deduced. The efficiencies are computed in the first and/or in the second Born approximation and are compared with efficiencies obtained from a rigorous electromagnetic theory when they are available.

[1]  Troy W. Barbee,et al.  Combined microstructure x‐ray optics , 1989 .

[2]  C. Malek,et al.  Multilayer gratings for the soft x‐ray region (invited) , 1992 .

[3]  X-UV synthetic interference mirrors : theoretical approach , 1988 .

[4]  M. Nevière,et al.  Multilayer coated gratings for x-ray diffraction: differential theory , 1991 .

[5]  V. Aristov,et al.  Principles of Bragg-Fresnel multilayer optics , 1988 .

[6]  J. Andre,et al.  Dynamical theory of diffraction at in-depth multilayered gratings , 1991 .

[7]  W. K. Warburton.  On the diffraction properties of multilayer coated plane gratings , 1990 .

[8]  T W Barbee,et al.  Multilayer-coated blazed grating performance in the soft x-ray region. , 1989, Applied optics.

[9]  T. Barbee,et al.  Performance of multilayer coated gratings at near normal incidence in the extreme ultaviolet , 1990 .

[10]  G. Barton.  Elements of Green's Functions and Propagation: Potentials, Diffusion, and Waves , 1989 .

[11]  Troy W. Barbee,et al.  Performance of a tungsten/carbon multilayer-coated, blazed grating from 150 to 1700 eV , 1990 .

[12]  J. Andre,et al.  Diffraction and scattering by lamellar amplitude multilayer gratings in the X-UV region , 1991 .

[13]  P. Dhez.  X and X-UV multilayered optics: principles, fabrication methods, tests and applications , 1990 .

[14]  T. J. Tanaka,et al.  Low-energy x-ray interaction coefficients: Photoabsorption, scattering, and reflection: E = 100–2000 eV Z = 1–94☆ , 1982 .

[15]  Janos Kirz,et al.  Phase zone plates for x rays and the extreme uv , 1974 .

[16]  C. Malek,et al.  A review of microfabrication technologies: application to x-ray optics. , 1991, Journal of X-ray science and technology.