transformation of cyclic non-circular trigonometrical functions and the ... Melnikov G.S., Tverdova A.E. Methods of non-circular trigonometry in problems of.
FRACTAL OPTICS - EXTRAPARAXIAL OPTICS OF MULTIPLE REFLECTIONS. SOLUTION OF APPLIED PROBLEMS.
G.S. Melnikov, S.A. Larionov FGI VNC "Vavilov State Optical Institute" 199034, St.Petersburg, 12, Birzhevaya Liniya Tel.: (812) 311-22-01, Fax: (812) 218-80-65, E-mail @ ILPH.SPB.SU
The term "fractal optics" has been introduced and substantiated in work [1]. Investigations of discrete digital methods of optical transformations based upon the potentialities of fractal optics go back in 1986, when the first description of raster effects of extraparaxial optics in elements of cylindrical group [2, 3] were discovered in the "Vavilov State Optical Institute". Formulation of first applied problems that can be solved by methods of fractal optics is described in review paper [4]. Some solutions are described in applications for RF patents [5, 6]. The paper deals with the generalization of results of theoretical studies for description of fractal propagation pathes of photon trains in segmented elements (SE) of cylindrical group. It is shown that SE of tubular-cylindrical type can be considered as a general case of light conducting elements of cylindrical group and are bifractal systems. Considering gnoseologic grounds of fractality it is shown that fractality roots go into structural presentation of numerical continuum by means of alternating Laurent series. It is proved that distribution within numerical continuum of integers, irrational, fractionary-rational and transcedental numbers follows principles of transformation of cyclic non-circular trigonometrical functions and the functions themselves are directly connected with the fractality coefficients. It is shown that geometric mode pathes of elementary particles within extraparaxial range of optical elements are described by multiparametric "macrowave" equations of amplitude-angular modulation. In this case modulation carrier frequency is less than modulation function frequency and is connected with angular frequency of rotation of ensembles of light particles along curvilinear reflection surfaces. The modulation function has a wavelength connected with free path length of a photon train between two reflections from curvilinear surfaces. There is a number of certain sketchy solutions of applied problems described in [4] suggested basing upon theoretical description of effects of fractal optics: - multimode multilevel Fabry-Perot interferometer (optical analog of VLSI) and optical synchrogenerator with a fractionary-rational change of mesh size of time delays grid; - multichannel data transmission line through a single fibre with frequency-division and angular multiplexing; - some sketchy solutions of illumination systems.
Literature
1. Melnikov G.S. On creation of digital optical data processors for remote monitoring of water// Report in V St. Petersburg International Conference "Regional Informatics-96" (RI-96), sec. 14, 15, 05. 1996. 2. Melnikov G.S., Tverdova A.E. Methods of non-circular trigonometry in problems of extraparaxial optics// Report in IV All-Union Conference "Theoretic and Applied Optics"., L., GOI. 1986. 3. Melnikov G.S., Kosmachev A.F., Shishkin M.Yu. // Thesis of Report in IV All-Union Conference "Theoretic and Applied Optics"., L., GOI. 1986. 4. Melnikov G.S., Larionov S.A., Mikheev P.A. Tsvetkov E.A. // News? of AS, v. 59, No 12, 1995. 5. Melnikov G.S. , Larionov S.A., Mikheev P.A. Tsvetkov E.A. // Method of creation of light flux time delays. Priority certificate of VNIIGPE 95 114222/25 (024015) of 7 August 1995.
