Raspršenje elektromagnetskoga vala na anizotropnim planarnim i cilindričnim strukturama: doktorski rad - Bojanjac, Dario; Šipuš, Zvonimir (Zagreb: D. Bojanjac ; Fakultet elektrotehnike i računarstva, 2015)
U radu se analizira raspršenje elektromagnetskih valova na tankim zakrivljenim dielektričnim objektima te planarnim i cilindričnim anizotropnim strukturama. Kod tankih zakrivljenih dielektričnih objekata provedena je analiza koja omogućuje redukciju modela raspršenja skalarnog vala s trodimenzionalnog objekta na aproksimativni dvodimenzionalni objekt. Skalarni valovi javljaju se kod problema raspršenja na trodimenzionalnim objektima i kod problema raspršenja transverzalno električnih (TE) i transverzalno magnetskih (TM) valova u dvodimenzionalnim elektromagnetskim problemima. Primjenom izvedenog reduciranog modela smanjeni su zahtjevi na numeričko rješavanje problema jer se za jednu dimenziju smanjuje objekt promatranja što rezultira smanjenjem dimenzije elemenata u diskretizaciji objekta pa time i njihov broj te zahtjevi na memoriju i snagu računala. U slučaju jednoosnog anizotropnog homogenog prostora s planarnom i cilindričnom simetrijom izvedena je Greenova funkcija koja omogućuje unaprjeđenje G1DMULT s izotropne homogene višeslojne strukture na višeslojnu strukturu s jednoosno anizotropnim slojevima. G1DMULT algoritam uspješno se primjenjuje dugi niz godina na probleme analize konformnih mikrotrakastih antena te analizu svjetlovoda i leća antena. Unaprijeđeni algoritam primijenjen je na računanje efektivnih parametara metamaterijalnih jednoslojnih i višeslojnih struktura. Izveden je algoritam koji omogućuje rješavanje problema raspršenja elektromagnetskih valova uslijed kosog upada na cilindar načinjen od savršenog metala koji se nalazi unutar višeslojnog anizotropnog plašta. Problemi koji se javljaju kod analize opisanog problema leže u činjenici da je model problema opisan sustavom diferencijalnih jednadžbi, a ne jednom jednadžbom kao što je slučaj kod okomitog upada elektromagnetskog vala na spomenutu strukturu. Numeričko rješenje za potpuni problem nije moguće dobiti na efikasan način zato što je problem raspršenja problem u slobodnom prostoru što predstavlja veliki zahtjev na korištenu numeričku metodu. U radu je iskorišteno poznavanje rješenja izvan promatranog objekta na način da je rješenje izvan objekta rastavljeno u sumu planarnih valova koja je na vanjskom rubu anizotropnog plašta spojena s numeričkim rješenjem unutar strukture. Na taj način je reducirana domena na kojoj je potrebno numerički rješavati problem. Izvedena metoda je primijenjena na analizu raspršenja elektromagnetskih valova na Schurigovom i Caijevom plaštu nevidljivosti uslijed kosog upada. Pokazano je da izvedeni plaštevi nevidljivosti rade dobro samo za okomiti upad elektromagnetskog vala dok za relativno male pomake od normale na cilindar raspršenje od takvog objekta postaje veće od raspršenja na čistom cilindru načinjenom od savršenog metala, tj. predloženi plaštevi nevidljivosti ne rade za kosi upad elektromagnetskog vala.
Ključne riječi: raspršenje elektromagnetskih valova, jednoosno anizotropan materijal, potpuno anizotropan materijal, cilindrični objekt, redukcija dimenzije, Greenova funkcija
In the thesis emphasis is on electromagnetic scattering on anisotropic structures and on electromagnetic scattering on curved homogeneous structures. Electromagnetic wave scattering on anisotropic structures has become a very interesting topic in the last couple of years. The main application is connected to metamaterials, metasurfaces and other anisotropic media. Metamaterials and metasurfaces are artificial electromagnetic structures made from small scatterers on a distance smaller than wavelength. Because the distance is small between the elements it is possible to use homogenization techniques in order to analyze and produce objects made from metamaterials. The result of homogenization procedure are usually anisotropic parameters and in order to further analyze considered object it is necessary to be able to accurately describe scattering from anisotropic structures.

In the second chapter an approximate method for solving the scattering problem on a curved thin dielectric object is proposed. It is assumed that the permittivity of an object in asymptotic regime is scaled with thickness since otherwise at certain moment the object will become invisible for an incoming wave because it will be too thin and with too small permittivity to be noticeable. The starting point of the method is the Helmholtz partial differential equation which is transformed to the Lippmann-Schwinger integral equation using convolution with the Greens function. Lippmann-Schwinger integral equation is a Fredholm second type integral equation for which there is a lot of developed theory which is usefull in the process of asymptotic analysis. In order to utilize the information about the small thickness of the structure, asymptotic analysis in terms of small parameter is applied. Solution to a full three dimensional problem is then described as an asymptotic series in terms of thickness. Using this procedure, the starting integral equation on three dimensional structure is reduced to an integral equation on two dimensional structure. Transition from Helmholtz partial differential equation to Lippmann-Schwinger integral equation reduces computational time, however in order to solve the problem it is still necessary to numerically solve it on a three dimensional object. After the asymptotic analysis and by obtaining first order asymptotic solution it will be enough to solve the problem only on a two dimensional domain. Error estimate and convergence for described approximation will be presented and it will be verified on an electromagnetic scattering problem.

In the third chapter Greens functions for uniaxially anisotropic multilayer planar and cylindrical structures are derived. Those functions are used for upgrading G1DMULT algorithm previously developed by prof. Zvonimir Sipus and prof. Per-Simon Kildal. Using G1DMULT algorithm it is possible to calculate radiation from homogeneous isotropic multilayer structures, and with the upgrade involving the developed Greens functions it is possible to analyze uniaxially anisotropic structures. This algorithm was previously used for analysis of conformal microstrip antennas, optical fibers and lenses. One of the biggest applications is analysis of microstrip antennas on spherical structures on which scientists from Department for Wireless Communications worked for several years. The need for upgrading G1DMULT algorithm came from the idea of analyzing metamaterial structures. In this chapter it is shown that this upgrade allows analysis of uniaxially anisotropic structures because in that case it is possible to decompose scattered electromagnetic field on transversel electric and transversel magnetic modes. In uniaxially anosotropic strucuteres there is no coupling between those two modes. If the structure is such that the modes are coupled then it is necessary to analyze it using the procedure proposed in the following chapter. Upgraded G1DMULT algorithm is used for the analysis of scattering from periodic strips and from artificial anisotropic dielectrics.

In the fourth chapter analysis of electromagnetic scattering from biaxially anisotropic structures is given. The considered problem is a circular cylindrical metallic rod inside a multilayer biaxially anisotropic dielectric object. In the case of oblique incidence of electromagnetic waves it is not possible to decouple transversel electric and transversel magnetic modes because both modes are needed in order to satisfy boundary conditions. For that reason the mathematical model of the described situation is given with system of partial differential equations and not with only one equation, and consequently the analysis from the third chapter cannot be applied. Method developed in this chapter is based on Fourier series and finite differences. Using Fourier series it is possible to switch from solving system of partial differential equations to solving a system of ordinary differential equation for every mode. Because of small dimensions of structures there are only few modes for which it is needed to solve the system. Outside the structure it is possible to solve the scattered field as a summation of outgoing plane waves. It is possible to analytically describe wave outside the object because mathematical model is given with only one equation of Bessel type. That solution is given in terms of plane wave expansion. Inside the structure finite difference method is used for solving the field. On the boundary of cylindrical object the outside and the inside problems are matched through boundary conditions. Matching these two solutions gives final boundary condition for numerical solution of the problem. Using this method oblique incidence from metamaterial cloaks is analyzed. Circular cylindrical cloaks were usually analyzed only for normal incidence because in that case it is possible to use simpler algorithms such as the algorithm described in previous chapter. Since the normal incidence case can be solved using the G1DMULT algorithm it is used as a reference for algorithm developed in this chapter. Results for oblique incidence are compared for oblique incidence solution for a metallic circular cylinder inside one layer of dielectric material. Using the developed algorithm it is shown that cloaks known from the literature work only for normal incidence. In the case of oblique incidence there is a great detoriation of radar cross section for increased angle of incidence. When angle of incidence is shifted for 20 or more degrees relative to the normal incidence, radar cross section for cloaked metal cylinder is larger then the radar cross section of bare metal. This means that cloaks from the literature work only for normal incidence of electromagnetic wave or for very small displacement from the normal incidence.
Keywords: electromagnetic wave scattering, uniaxially anisotropic materials, biaxially anisotropic materials, cylindrical object, reduction of dimension, Green's function
Bibliografija: str. 91 - 98.