Abstract

Transmission zone plates composed of materials describable by the complex index of refraction $\widehat{n}[\widehat{n}=(1-\delta )+ik]$ modulate both the amplitude and the phase of the light passing through them. In this paper, a general variational approach to the design of zone-plate profiles that maximize system transfer functions, such as I^(m)/I_IN or I^(m)/I_OUT (where I_IN and I_OUT are the total input and output powers and I^(m) is the mth-order diffracted power), is presented in terms of the real and imaginary components of $\widehat{n}$. The variational problem, as formulated here, is shown to generate some important classical zone-plate configurations as special solutions and to lead naturally to the derivation of the most general zone-plate configurations possible. Some specific optimum solutions are derived for gold in the soft-x-ray range and are tabulated for convenient reference.

© 1984 Optical Society of America

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