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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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 MÞ: 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).

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