In this thesis we investigate electromagnetic composite materials in order to realize media with the electromagnetic properties not achievable in the nature. The investigated composites are one dimensional and two dimensional photonic and plasmonic crystals. One dimensional structures consist of appropriately shaped slabs, whereas two dimensional structures consist of rods in air or cylindrical holes in a dielectric host. Beside the structures with the periodic arrangement of the unit cells, we consider graded structures obtained by a spatial variation of either cells’ geometry or dielectric permittivity. Photonic crystals are all dielectric structures whereas the plasmonic crystals are combination of dielectric and plasmonic materials, metals or semiconductors. Special class of the composite structures are the planar plasmonic crystals which consist of parallel ribbons made from plasmonic material on a dielectric substrate. All composites are considered in the metamaterial regime where unit cell size of the composites are not negligible in comparison to light wavelength, but the effective parameters can be still well defined. Homogenization of both one and two dimensional structures are done within the framework of Maxwell Garnett theory. Planar plasmonic crystals are not described by effective parameters, but they are considered as arrays of the same and subwavelength resonators with well defined plasmonic resonances so the resonant behaviour of the plasmonic crystals is the collective response of all resonators. Special attention is devoted to the choice of appropriate materials in the composites. The structures aimed for guiding of electromagnetic field should have as low as possible losses so the structures built form dielectrics only are the most preferably in this case. The plasmonic materials such as metals or semiconductors have to be used in the following cases: in the realization of extreme anisotropy in the dielectric permittivity and in the realization of resonant structures. The first method investigated for guiding of electromagnetic field is transformation optics. In this method, straight field trajectories in free space are appropriately transformed into the desired field trajectories. Maxwell equations are invariant under the applied coordinate transformations while the material parameters are scaled accordingly. The obtained material parameters are described with anisotropic and spatially inhomogeneous dielectric permittivity and magnetic permeability in a general case. Here we show the procedures for simplifying this material parameters by considering the concept of reduced parameters by retaining the same dispersion relation or the concept of the transformations with unit Jacobian matrix. As a result of the applied procedures, we show that it is possible to realize transformation optical devices by anisotropic and spatially inhomogeneous dielectric permittivity. The anisotropy can be then realized by layered slabs, while the inhomogeneity can be realized by proper gradation of slab thicknesses and permittivities. Due to large anisotropy in dielectric permittivity, unit cells have to contain at least one plasmonic slab. The utilization of the plasmonic materials introduces losses and makes the bandwidth narrow. For this reason, we consider the methods of transformation optics with conformal transformation and gradient refractive index optics where guiding of electromagnetic field is realized by inhomogeneous and isotropic refractive index. These structures can be then realized by two dimensional graded photonic crystals where gradation of refractive index is implemented by gradation of rod or hole radii. Due to utilization of dielectrics only, these structures are lossless and work in a broad bandwidth. In order to dynamically control trajectories of electromagnetic fields, we consider two dimensional graded plasmonic crystals with semiconductor rods. Permittivity of semiconductor rods can be tuned by modulating their charge carrier concentration. In this way it is possible to tune effective graded permittivity of whole graded plasmonic crystals. This enables a design of structures with dynamical beam steering and focusing. Beside guiding of electromagnetic fields, we investigate electromagnetic composite structures which control the field in the frequency domain. They are based on plasmonic photonic band gaps in two dimensional plasmonic crystals. The plasmonic gaps arise due to localized surface plasmon resonances in the rods when electric field is normal to them. Broad applications of these plasmonic crystals are supported by current development of new plasmonic materials whose plasma frequency can be well controlled by fabrication processes. In this way, it is possible to design plasmonic crystals with the plasmonic photonic band gaps from visible to near-infrared and even terahertz frequency range. The reason why we investigate the plasmonic photonic band gaps is twofold: they are both very robust to disorder and they are very sensitive to the modulation of charge carrier concentration in the semiconductor rods. The first property candidates plasmonic crystals as robust photonic band gap media fabricated by the bottom-up technologies which always result in disordered structures. The second property of the plasmonic crystals enables design of very sensitive terahertz modulators and switches. The importance of the new plasmonic materials is shown in the example of planar one dimensional plasmonic crystals made from graphene ribbons. Graphene supports surface plasmon polaritons in wide range of infrared part of the spectrum where utilization of noble metals is not possible for this purpose. Patterning of graphene into ribbons enables efficient coupling of incident electromagnetic field into localized surface plasmon polaritons. We investigate the possibility to utilize these resonances for plasmonic sensors of dielectric environment at infrared frequencies. It is shown that graphene based sensors enable sensing of deep-subwavelength dielectric films as well as sensing of vibration modes in thin molecular films. As a possible method for graphene patterning, we use tapping mode atomic force microscopy, that is, dynamic plowing lithography of exfoliated graphene on silicondioxide substrates. The shape of the graphene sheet is determined by the movement of the vibrating probe of an atomic force microscope. There are two possibilities for lithography depending on the applied force. At moderate forces, the tip only deforms graphene and generates local strain in the order of 0.1%. For sufficiently large forces, the tip can hook graphene and then pull it, thus cutting the graphene along the direction of the tip motion. Electrical characterization by electric force microscopy allows to distinguish between the truly separated islands from those still connected to the surrounding graphene. U ovoj tezi su istraženi elektromagnetski kompozitni materijali u cilju realizacije sredina sa elektromagnetskim osobinama koje ne postoje u prirodnim materijalima. Istraživani kompoziti su jednodimenzionalni i dvodimenzionalni fotonski i plazmonski kristali. Jednodimenzionalne strukture se sastoje od slojeva odgovarajućeg oblika, dok se dvodimenzionalne strukture sastoje od štapića u vazduhu ili cilindričnih rupa u dielektriku. Pored struktura sa periodičnim ponavljanjem jediničnih ćelija, razmatraju se i gradirane strukture dobijene prostornom promenom geometrije ili dielektrične permitivnosti jediničnih ćelija. Fotonski kristali se sastoje isključivo od dielektrika, dok su plazmonski kristali kombinacija dielektričnih i plazmonskih materijala, metala ili poluprovodnika. Posebna klasa razmotrenih kompozitnih struktura su planarni plazmonski kristali koji se sastoje od paralelnih traka od plazmonskih materijala na dielektričnom substratu. Sve kompozitne strukture se razmatraju u režimu metamaterijala gde veličina jedinične ćelije nije zanemarljiva u odnosu na talasnu dužinu svetlosti, ali se efektivni parametri ipak mogu definisati. I jednodimenzionalne i dvodimenzionalne strukture su homogenizovane pomoću Maksvel Garnetove teorije. Planarni plazmonski kristali nisu opisani efektivnim parametrima, nego se razmatraju kao nizovi istih i podtalasnih rezonatora sa definisanim plazmonskim rezonancijama tako da rezonantne karakteristike plazmonskih kristala predstavljaju kolektivni odziv svih rezonatora. Posebna pažnja je posvećena izboru odgovarajućih materijala u kompozitima. Strukture namenjene vođenju elektromagnetskog polja treba da imaju što manje gubitke tako da u ovom slučaju strukture treba da budu isključivo dielektrične. Plazmonski materijali kao što su metali i poluprovodnici se moraju koristiti u sledećim slučajevima: u realizaciji visoke anizotropije dielektrične permitivnosti i u realizaciji rezonantnih struktura. Prvi metod koji je istraživan za vođenje elektromagnetskog polja je transformaciona optika. U ovom metodu, prave linije polja u slobodnom prostoru se na odgovarajući način transformišu u linije polja sa željenim oblikom. Maksvelove jednačine su invarijantne prilikom koordinatnih transformacija dok se materijalni parametri menjaju u skladu sa primenjenom transformacijom. Dobijeni materijalni parametri su opisani anizotropnom i prostorno nehomogenom dielektričnom permitivno šću i magnetskom peremabilnošću u opštem slučaju. Ovde je data procedura kojom se nalaze jednostavniji materijalni parametri pomoću koncepta redukovanih parametara pri čemu se zadržava ista disperzija ili pomoću koncepta transformacija sa jediničnim Jakobijanom. Kao rezultat primenjenih procedura, pokazuje se da je moguće realizovati uređaje na bazi transformacione optike pomoću anizotropne i prostorno nehomogene dielektrične permitivnosti. Anizotropija je onda realizovana slojevima ploča, dok se nehomogenost može realizovati odgovarajućom gradacijom debljine ili permitivnosti ploča.parametri menjaju u skladu sa primenjenom t