# Diffractional Optics of Millimetre Waves (Series on Optics by I.V. Minin, O.V. Minin

By I.V. Minin, O.V. Minin

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Additional info for Diffractional Optics of Millimetre Waves (Series on Optics and Optoelectronics)

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Note that by changing the eikonal by a constant which is a multiple of n, we not only leave the ﬁeld of rays unchanged but the values of the ﬁeld also remain unchanged, that is, the value of the eikonal is in principle found only up to a constant which is a multiple of n. Let the incident radiation be of the form U0 ðx; y; zÞ ¼ A expðÿikzÞ, that is, its eikonal is È0 ðx; y; zÞ ¼ ÿz. We wish to focus this radiation on to a point with coordinates ð0; 0; FÞ. The eikonal of the reﬂected ﬁeld is, to within a constant, È1 ðx; y; zÞ ¼ ÿðx2 þ y2 þ ðz ÿ FÞ2 Þ1=2 : Copyright 2004 IOP Publishing Ltd Computation of the phase-inversion proﬁle 43 The equation of the equivalent reﬂecting focusing surfaces is z ÿ ðx2 þ y2 þ ðz ÿ FÞ2 Þ1=2 ¼ c þ m; m ¼ 0; Æ1; Æ2; .

A 253 349–357 [26] Richards B and Wolf E 1959 ‘Electromagnetic diﬀraction in optical systems. II. Structure of the ﬁeld in an aplanatic system’ Proc. Roy. Soc. A 253 358–380 [27] Minin I V 1982 Numerical Analysis of Diﬀraction of Electromagnetic Wave by Fresnel Zone Plates (Novosibirsk: NGU) [28] Holland J 1975 Adaptation in Natural and Artiﬁcial Systems (Ann Arbor, MI: University of Michigan Press) [29] Goldberg D E 1989 Genetic Algorithm in Search, Optimization and Machine Learning (Addison-Wesley) [30] Davis L (ed) 1991 Handbook of Genetic Algorithms (New York: Van Nostrand Reinhold) [31] Michalewicz Z 1992 Genetic Algorithms þ Data Structures ¼ Evolution Programs (Berlin: Springer) [32] Johnson J M and Rahmat-Samii Y 1997 ‘Genetic algorithms in engineering electromagnetics’ IEEE Antennas and Propagation Mag.

A) Geometric modelling of a diﬀraction element. 8. (b) Ray paths across an MWDO element that focuses the incident radiation of an oﬀ-axis radiation source into an annular area [20]. the diﬀraction element: Q ¼ ðA22 ÿ BÞ1=2 ÿ A2 ; A2 ¼ N; B2 ¼ Ã2 ÿ 2ÃðLu þ MÞ: The vector relations given above can be used for a rapid analysis of frequency and focusing properties of diﬀraction elements in various program complexes that are similar to those described in [7, 19–22] (ﬁrst of all, to analyse aberration characteristics).