Abstract
Reflectivities at nongrazing incidence angles, and in particular at normal or near-normal incidence, may be enhanced by causing multiple reflections to add in phase, in a manner analogous to Bragg reflection from a crystal. The Bragg condition for mth-order constructive interference is (Figure 4.1) that the angle θ that the incident radiation, of wavelength λ, makes with the crystal planes is equal to 0m where
and d is the spacing between the planes. Typical crystals have spacings of a few tenths of a nanometer and therefore condition (4.1) cannot be satisfied for soft X rays with wavelengths of 1-10 nm. It is necessary to manufacture structures with the required spacings, and these are known as multilayer mirrors.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. H. Underwood and T. W. Barbee, Jr., Synthetic multilayers as Bragg diffractors for x-rays and extreme ultraviolet: Calculations of performance, in: Low Energy X-Ray Diagnostics (D. T. Attwood and B. L. Henke, eds.), AIP Conference Proceedings No. 75, pp. 170–178, American Institute of Physics, New York (1981)
J. H. Underwood and T. W. Barbee, Jr., Layered synthetic microstructures as Bragg diffractors for x-rays and extreme ultraviolet: Theory and predicted performance, Appl. Opt., 20, 3027–3034 (1981).
L. G. Parratt, Surface studies of solids by total reflection of x-rays, Phys. Rev., 45, 359–369 (1954).
A. E. Rosenbluth and P. Lee, Bragg condition in absorbing x-ray multilayers, Appl. Phys. Lett., 40, 466–468 (1982).
R. Marmoret and J. M. Andre, Bragg reflectivity of layered synthetic microstructures in the x-ray anomalous scattering region, Appl. Opt., 22, 17–19 (1983).
P. Lee, X-ray diffraction in multilayers, Opt. Commun., 37, 159–164 (1981).
B. Videl and P. Vincent. Metallic multilayers for x-rays using classical thin-film theory, Appl. Opt., 23, 1794–1801 (1984).
AH. Saxena and B. P. Schoenborn, Multilayer neutron monochromators. Acta Crystallogr. Sect. A, 33, 805–813 (1977).
C. G. Darwin, The theory of x-ray reflexion, Philos. Mag. Series 6, 27, 315–332 (1914).
C. G. Darwin, The theory of x-ray reflexion, Part II, Philos. Mag. Series 6, 27, 675–690 (1914).
G. G. Darwin, Reflection of x rays from imperfect crystals, Philos. Mag. Series 6, 43, 800–829 (1922).
P. P. Ewald, The crystal-optics of x rays (I), Ann. Phys. (Leipzig), 54, 519–556 (1917).
P. P. Ewald, The crystal-optics of x rays (II), Ann. Phys. (Leipzig), 54, 557–597 (1917).
P. P. Ewald, Bragg’s reflection law for Röntgen rays, Phys. Z, 21, 617–619 (1920).
P. P. Ewald, The refractive index for x rays and the deviations from Bragg’s law of reflection, Z. Phys., 30, 1–13 (1924).
P. P. Ewald, Reflection of Röntgen rays, Phys. Z., 26, 29–32 (1925).
W. H. Zachariasen, Theory of X-Ray Diffraction in Crystals, pp. 111–155, Wiley, New York (1945).
B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro and B. K. Fujikawa, The atomic scattering factor, f1 + if2, for 94 elements and for the 100 to 2000 eV photon energy region, in: Low Energy X-Ray Diagnostics (D. T. Attwood and B. L. Henke, eds.), AIP Conference Proceedings No. 75, pp. 340 - 388, American Institute of Physics, New York (1981).
J. A. Prins, Reflection of x-rays by absorbing ideal crystals, Z. Phys., 63, 477–493 (1930).
A. V. Vinogradov and B. Y. Zeldovich, X-ray and far UV multilayer mirrors: Principles and possibilities, Appl. Opt., 16, 89–93 (1977).
E. Spiller, High quality Fabry-Perot mirrors for the ultraviolet, Optik (Stuttgart), 39, 118–125 (1973).
R.-P. Haelbich, A. Segmüller, and E. Spiller, Smooth multilayer films suitable for x-ray mirrors, Appl. Phys. Lett., 34, 184–186 (1979).
P. Debye, Interference of Rontgen rays and heat motion, Ann. Phys. (Leipzig), 43, 49–95 (1914).
E. Spiller, A scanning soft x-ray microscope using normal incidence mirrors, in: X-Ray Microscopy (G. Schmahl and D. Rudolph, eds.), Springer Series in Optical Sciences, Vol. 43, pp. 226–231, Springer, Berlin (1984).
E. Spiller, Evaporated multilayer dispersion elements for soft x-rays, in: Low Energy X-Ray Diagnostics (D. T. Attwood and B. L. Henke, eds.), AIP Conference Proceedings No. 75, pp. 124–130, American Institute of Physics, New York (1981).
K. Schawarzchild, Untersuchungen zur Geometrischen Optik, Abh. Ges. Wiss. Goettingen Math. Phys. Kl. N.F. 4, No. 1–3 (1905).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1986 Plenum Press, New York
About this chapter
Cite this chapter
Michette, A.G. (1986). Reflective Optics for Soft X Rays II Multilayer Mirrors. In: Optical Systems for Soft X Rays. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2223-8_4
Download citation
DOI: https://doi.org/10.1007/978-1-4613-2223-8_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-9304-0
Online ISBN: 978-1-4613-2223-8
eBook Packages: Springer Book Archive