Abstract

A zone-plate transfer function of importance in practical optical systems is the output efficiency, I⁽¹⁾/I_OUT, where I⁽¹⁾ is the total power diffracted into the first order by the zone plate. We apply variational analysis to derive a special symmetry-restricted zone-plate profile that maximizes this output efficiency. Our solution, which we have named the generalized symmetry-restricted output efficiency maximizing zone plate, is demonstrably the optimum such symmetry-restricted solution for materials of arbitrary indices of refraction $\widehat{n}\hspace{0.17em}[\widehat{n}=(1-\delta )+ik]$, where k is the absorption constant and δ is the phase-difference constant. For purely absorbing materials, i.e., for δ = 0, we show that a simple extension of our general solution in the far field leads to the well-known, but less-efficient, Gabor zone plate, which also has the desirable property of suppressing all diffracted orders higher than the first and minus first. Our theoretical solution, which is optimum in both the near and far fields, is of importance for research in the soft-x-ray range, where most materials are in fact both absorbers and phase shifters, i.e., where neither k nor δ is evanescent.

© 1985 Optical Society of America

Outline of a variational formulation of zone-plate theory

Roman Tatchyn, Paul L. Csonka, and Ingolf Lindau
J. Opt. Soc. Am. B 1(6) 806-811 (1984)

Optimization of planar metallic nonrefracting transmission-grating profiles for mth-order intensity maximization in the soft-x-ray range

R. Tatchyn, P. L. Csonka, and I. Lindau
J. Opt. Soc. Am. 72(12) 1630-1638 (1982)

Simulation of high-resolution x-ray zone plates

Alexei N. Kurokhtin and Alexei V. Popov
J. Opt. Soc. Am. A 19(2) 315-324 (2002)

Phase zone plates for x rays and the extreme uv

Janos Kirz
J. Opt. Soc. Am. 64(3) 301-309 (1974)

Higher-order suppressed phase zone plates

Hakaru Kyuragi and Tsuneo Urisu
Appl. Opt. 24(8) 1139-1141 (1985)