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The paper presents a theoretical investigation of the propagation of strongly TE nonlinear magnetostatic surface waves propagating in a composite waveguide structure of a Ferrite (YIG) film, Left-handed substrate and nonlinear cover. The dispersion relation and the effect of nonlinearity on the propagation characteristics have been examined. It is found that the differential phase shift can be minimized for the smaller operating frequency and relatively thick film. The power flow has also been calculated for different values of operating frequency.

Consider a waveguide structure consisting of a pair of metamaterial and dielectric slabs inserted in vacuum. A plane polarized wave is obliquely incident on it. Metamaterials (sometimes termed left-handed materials (LHMs)) are materials whose real parts of permittivity Ɛ and permeability µ are both negative and consequently have negative index of refraction. The transmission of the electromagnetic waves through the structure is analyzed theoretically and numerically with the emphasis on the dissipation factor. Maxwell's equations are used to determine the electric and magnetic fields of the incident waves in each region. Then , Snell' s law is applied and the boundary conditions of the fields are imposed at each layer interface to obtain a number of equations with unknown parameters. The MAPLE is used to solve these equations for the unknown parameters to calculate the reflection and transmission coefficients. These coefficients are used to determine the reflected, transmitted and loss powers of the structure. In the numerical results the mentioned powers are computed and illustrated as a function of frequency, angle of incidence and slab thickness when the dissipation factor changes.

In this paper a waveguide structure consisting of a pair of left-handed material (LHM) and dielectric slabs inserted in vacuum is investigated theoretically. Maxwell’s equations are used to determine the electric and magnetic fields of the incident waves at each layer. Snell’s law is applied and the boundary conditions are imposed at each layer interface to calculate the reflected and transmitted powers of the structure. Numerical results are illustrated to show the effects of frequency, angle of incidence and LHM thickness on the transmitted power when the refractive index of the dielectric layer changes. The same procedure is repeated to show the variation of the transmitted power with the change in the mentioned parameters under different values of dissipation factor of the lossy LHM. Consequently, two cases of the LHM are considered, loss-less case and loss case. The results obtained, are in agreement with the law of conservation of energy.

This paper proposes a new planner metamaterial whose unit cell is infinity-shaped split ring resonator. The cell is composed of two identical infinity-shaped copper patterns etched parallel on both sides of dielectric laminate. The metamaterial is very thin and easy to fabricate. The High Frequency Structure Simulator (HFSS) software was used to design, optimize and simulate the metamaterial unit cell. The effective material properties were retrieved from the calculated transmission and reflection characteristics of the structure. The characteristics and properties of the new metamaterial were plotted to show the material behavior. The new structure has very wide band frequencies, about 11.35 GHz, with negative refractive index. Keywords: Negative refractive index (NRI), metamaterial, Left-handed material, effective medium parameters.

The optical transmission properties of a structure consisting of N identical pairs of left- and right-materials are investigated theoretically and numerically. Maxwell's equations are used to determine the electric and magnetic fields of the incident waves at each layer. Snell's law is applied and the boundary conditions are imposed at each layer interface to calculate Fresnel coefficients. Expressions for reflectance and transmittance of the structure are given in terms of these coefficients. In the numerical results the transmittance of the structure is computed and illustrated as a function of frequency under different values of N. Minimum transmittance is achieved by using high and low opposite refractive indices of left and right materials of each pair of the structure. The frequency band of this transmittance is reduced by decreasing N. Maximum transmittance is demonstrated by using two slabs of the same width and opposite refractive indices placed between two dielectric media of the same kind. The effect of frequency and angle of incidence is very weak in these structures as compared to their all-dielectric counterparts. Moreover the obtained results are in agreement with the law of conservation of energy. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/30264

Recently, the fabrication and optimization of nano-hole arrays in noble metal layers have attracted much attention both because of the interesting new physics associated with them and for their potential applications in nano-optics and biosensing. In particular nano-hole arrays in metal-dielectric-metal stacks, also known as "fish-net" type structures, are nowadays the best candidates to accomplish some suggestive physical phenomena like negative refractive index. Here we report a design and a parametrical analysis of a fishnet in the optical spectral range. In particular the dependence of both the magnetic and the electric resonance on the geometric features of the fishnet is investigated.

We studied the radial distribution of the electromagnetic field and the spectrum of the eigenfrequencies in coated microspheres with alternating quasiperiodic layers having left-handed (LH) materials included. At an increase of the quasiperiodicity parameter $\gamma$, the boundaries of the spectral band gaps acquire the intended shape. When $\gamma$ exceeds the inverse golden mean value, a structure with extremely narrow separated resonant peaks with nearly complete transmittance arises. We find that the field peaks in the radial distribution forbidden band is located not in the center of the microsphere, but in the layers that cover such a microsphere.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Metamaterials exhibiting negative refraction have attracted a great amount of attention in recent years mostly due to their exquisite electromagnetic properties. These materials are artificial structures that exhibit characteristics not found in nature. It is possible to obtain a metamaterial by combining artificial structures periodically. We investigated the unique properties of Split Ring Resonators, High impedance Surfaces and Frequency Selective Surfaces and composite metamaterials. We have successfully demonstrated the practical use of these structures in antennas and circuits. We experimentally confirmed that composite metamaterial can improve the performance of the structures considered in this thesis, at the frequencies where electromagnetic band gap transmission takes place

We have determined the scattering parameters of optical structures incorporating both left-handed metamaterials (LHM) and conventional ("right-handed") materials (RHM) for the case when the refractive index at the LHM-RHM interface is graded, for oblique incidence at an arbitrary angle and for arbitrary spectral dispersion. We derived an accurate analytical solution to Helmholtz’ equation for the case of the refractive index gradient varying as a hyperbolic tangent where the steepness of the index transition may be arbitrary, even of the order of vacuum wavelength. We determined the expressions for the field intensity along the LHM-RHM structure with refractive index gradient. We show that there is an excellent agreement between our analytical results and the accurate numerical simulations done by finite element method. QC 20120117

Negatif kırılma, düz lens, süper lens ve görünmezlik pelerini gibi uygumaları bulunan metamalzemeler oldukça farklı elektromanyetik özelliklere sahiptirler. Bu tezde, negatif kırılma indisine sahip metamalzemelerin karakterizasyonu gerçekleştirilmiş ve mikrodalga uygulamalarından birkaçı gösterilmiştir. Bu metamalzemeler negatif permeabiliteye sahip yarıklı halka rezonatörleri ile negatif permitiviteye sahip ince tel yapıları bir araya getirilerek oluşturulmuştur. Yarıklı halka rezonatörlerinin rezonans karakteristikleri deneysel ve teorik olarak incelenmiştir. Yarıklı halka rezonatörleri ile tel yapılarının bir araya getirilmesi sonucu permitivite ve permeabilite değerlerinin eksi olduğu frekanslarda bir geçirgenlik bandı gözlemlenmiş ve bu bant boyunca metamalzemenin dalga vektörü, elektrik alan ve manyetik alanları için sol-el kuralına uyduğu belirlenmiştir. Bu metamalzemenin negatif kırılma indisine sahip olduğu üç farklı ve birbirinden bağımsız deneysel yöntem kullanılarak gösterilmiştir. Bu deneysel yöntemler; prizma şeklindeki metamalzemeden kırılma deneyi, düz metamalzeme levhadan dalganın yer değişiminin gözlemlenmesi ve farklı uzunluklardaki metamalzemelerden faz farkının ölçülmesidir. Mikrodalga boyutlarında çalışan ve düzgün yüzeye sahip lens başarıyla gösterildi. Ayrıca, negatif indise sahip metamalzeme bazlı süperlenslerin dalgaboyu altı görüntüleme ve çözünürlük için kullanılabileceği deneysel olarak ispatlanmıştır. Rekor seviyede dalgaboyunun sekizde biri çözünürlük elde edilmiştir. Ağ şeklindeki alternatif metamalzemelerin de negatif indis ve negatif faz hızına sahip olduğu başarıyla gösterilmiştir. Son olarak tek bir dalgaboyu altı delikten yarıklı halka rezonatörü kullanarak arttırılmış iletim (transmiyon) çalışılmıştır. Metamaterials offer novel electromagnetic properties and promising applications including negative refraction, flat-lenses, superlenses, cloaking devices. In this thesis, we characterized the negative-index metamaterials that is composed of periodic arrangements of split-ring resonators (providing negative permeability) and thin wire (providing negative permittivity) arrays. The resonances of split-ring resonators (SRR) are investigated experimentally and theoretically. By combining SRR and wire arrays together, we observed a transmission band where both permittivity and permeability are simultaneously negative, indicating a left-handed behavior. Reflection measurements reveal that the impedance is matched to the free space at a certain frequency range. The left-handed metamaterial is also shown to exhibit negative refractive index by using three different experimental methods namely, refraction from a wedge-shaped negative-index metamaterial (NIM), beam-shift from a slab-shaped NIM and phase shift from NIMs with different lengths. Flat-lens behavior is observed from a slab-shaped negative-index metamaterial based microwave lenses. Furthermore, we demonstrated subwavelength imaging and subwavelength resolution by using thin superlenses constructed from SRR-wire arrays with an effective negative index. We have been able to image a point source with a record-level resolution. SRR and wire arrays exhibit negative index provided that the wave propagates parallel to the plane of SRR structure which makes it hard to fabricate at higher frequencies. An alternative structure called fishnet metamaterial however could yield negative index with wave propagation normal to the structure. We observed left-handed transmission and negative phase velocity in fishnet type metamaterials. Finally, we studied enhanced transmission from a single subwavelength aperture by coupling incident electromagnetic wave to a single SRR placed at the near-field of the aperture. 136

Metamaterialien sind künstliche Materialien, die wie in einem Kristallgitter aus speziell geformten technischen Bausteinen zusammengesetzt sind, wobei die einzelnen Bausteine als "künstliche Atome" betrachtet werden können. Wenn die Wellenlänge elektromagnetischer Strahlung (z.B. Licht) wesentlich größer ist als die inneren Strukturen des Metamaterials, erscheint dieses wie ein homogenes Medium und kann daher als Werkstoff mit makroskopischen Eigenschaften beschrieben werden. Schon seit einigen Jahrzehnten wurden Metamaterialien theoretisch diskutiert, die in der Natur nicht vorkommende neuartige Eigenschaften aufweisen sollten. Seit wenigen Jahren können sie zunehmend besser hergestellt werden. Der Aufsatz gibt einen kurzen Überblick über den Stand der Technik, Anwendungsfelder und Entwicklungstendenzen.

Date of Conference: 22 June-2 July 2007 Conference Name: Advances in Nanophotonics II: International Summer School on Advances in Nanophotonics II We review experimental studies on left-handed metamaterials operating at microwave frequencies. Left-handed transmission is obtained from a composite metamaterial consisting of periodic split ring resonator and wire arrays. Phase measurements reveal that the left-handed metamaterial has a negative phase velocity and negative refraction. The negative index metamaterial is capable of imaging subwavelength features with a resolution of λ/8.

Metamaterialien sind künstliche Materialien, die wie in einem Kristallgitter aus speziell geformten technischen Bausteinen zusammengesetzt sind, wobei die einzelnen Bausteine als "künstliche Atome" betrachtet werden können. Wenn die Wellenlänge elektromagnetischer Strahlung (z.B. Licht) wesentlich größer ist als die inneren Strukturen des Metamaterials, erscheint dieses wie ein homogenes Medium und kann daher als Werkstoff mit makroskopischen Eigenschaften beschrieben werden. Schon seit einigen Jahrzehnten wurden Metamaterialien theoretisch diskutiert, die in der Natur nicht vorkommende neuartige Eigenschaften aufweisen sollten. Seit wenigen Jahren können sie zunehmend besser hergestellt werden. Der Aufsatz gibt einen kurzen Überblick über den Stand der Technik, Anwendungsfelder und Entwicklungstendenzen.

Wie maakt tegenwoordig geen gebruik van fotonica? Optische vezels in het wereldwijde Internet, streepjescodelezers in de supermarkt en plasmaschermen zijn maar enkele voorbeelden van fotonische toepassingen die de laatste jaren hun plaats op de markt hebben veroverd. Een van de drijvende krachten achter deze ontwikkelingen is ongetwijfeld de introductie van nieuwe - en betere - optische materialen. Recente doorbraken in het materiaalonderzoek hebben geleid tot materialen met negatieve brekingsindex. Het gebruik van deze materialen in fotonische componenten kan leiden tot verbeterde fotonische toepassingen met grensverleggende eigenschappen.

ÖzetGERÇEK SOLAK MATERYALLER KULLANARAKNEGATİF KIRILMA ELDE EDİLMESİKoray AydınFizik Yüksek LisansTez Yöneticisi: Prof. Dr. Ekmel ÖzbayEylül 2004Solak materyaller ve negatif kırılma kendilerine has fiziksel özellikleridolayısıyla günümüzde oldukça ilgi çeken konular haline gelmişlerdir. Yeni biryapay yapı olan yarıklı halka rezonatörleri ve ince tel yapıları kullanılarak solakmateryal elde etmek mümkündür. Bu çalışmada yarıklı halka rezonatörleri, telyapıları ve bu ikisinin bir araya getirilmesiyle oluşan karma ara-maddelerdegeçirgenlik ve yansıma özelliklerini inceledik. Gerçek solak davranış sergileyen veyüksek geçirgenliğe (-1.2 dB) sahip olan karma ara-maddeler başarıyla gösterildi.Bu geçirgenlik değeri bugüne kadar rapor edilmiş olan en yüksek değerdir. Solakgeçirgenlik bandı hem dielektrik permitivite hem de magnetik permeabilitenin eksideğerler aldığı frekans bölgesinde yer almaktadır. Yarıklı halka rezonatörlerininmagnetik rezonansını belirleyebilmek için yeni bir metod geliştirdik ve bu metodudeneysel olarak da doğruladık.iiiSolak geçirgenliğin olduğu frekans aralığında karma ara-maddenin eksi kırılmaindeksine sahip olduğunu deneysel olarak kanıtladık. İki farklı uzunluktaki karmaara-maddelerin faz farkı ölçülmek suretiyle, ilgili frekans aralıklarında bu yapılarıneksi faz hızına sahip oldukları gösterildi. Kırılma deneyinden elde edilen kırılmaindeksi (-1.87) ile faz farkından hesaplanan kırılma indeksi (-1.78) birbirlerineoldukça yakın değerlere sahiptirler.Anahtar Sözcükler: Solak Materyal, Karma Ara-Madde, Yarıklı HalkaRezonatörü, Negatif Permitivite, Negatif Permeabilite, Efektif Ortam Teorisi,Fotonik Bant Aralığı, Negatif Kırılma, Negatif Faz Hızı.iv AbstractNEGATIVE REFRACTION USING TRUELEFT-HANDED METAMATERIALSKoray AydınM. S. in PhysicsSupervisor: Prof. Dr. Ekmel ÖzbaySeptember 2004Left-handed materials and negative refraction attracted a great amount ofattention in recent years due to their unique physical properties. It is possible toobtain a left-handed material by combining a novel artificial structure (split ringresonator) and a wire structure periodically. We investigated the transmission andreflection properties of split ring resonators (SRR), wires and compositemetamaterials consisting of SRR and wire structures. We have successfullydemonstrated true left-handed behavior in free space with a high transmission peak(-1.2 dB). This is the highest transmission peak reported for a left-handed material.The left-handed transmission band coincides exactly with the region where bothdielectric permittivity and magnetic permeability have negative values. Weproposed and demonstrated a new method to distinguish the magnetic resonance ofthe SRR structures.iWe experimentally confirmed that composite metamaterial has a negativerefractive index, at the frequencies where left-handed transmission takes place.Phase shift between consecutive numbers of layers of CMM is measured andphase velocity is shown to be negative at the relevant frequency range. Refractiveindex values obtained from the refraction experiments (-1.87) and the phase shiftexperiments (-1.78) are in good agreement.Keywords: Left-Handed Material, Composite Metamaterial, Split Ring Resonator,Negative Permittivity, Negative Permeability, Effective Medium Theory, PhotonicBand Gap, Negative Refraction, Negative Phase Velocity.ii 97

Photonic crystals are three-dimensional periodic structures having the property of reflecting the electromagnetic (EM) waves in all directions, for a certain range of frequencies. Defects or cavities around the same geometry can also be built by means of adding or removing material. The EM fields in such cavities are usually enhanced, and by placing active devices in such cavities, one can make the device benefit from the wavelength selectivity and large enhancement of the resonant EM field within the cavity. In this work, we have demonstrated the resonant cavity enhanced (RCE) effect by placing microwave detectors in defect structures built around dielectric based photonic crystals. A power enhancement factor of 3450 was measured for planar cavity structures. The tuning bandwidth of the RCE detector extends from 10.5 to 12.8 GHz. We also used these defect structures to demonstrate waveguiding around layer-by-layer photonic crystals. An air gap introduced between two photonic crystal walls was used as waveguide. We observed full transmission of the EM waves through these planar waveguide structures within the frequency range of the photonic band gap. The dispersion relations obtained from the experiments were in good agreement with the predictions of our waveguide model. We also observed 35% transmission for the EM waves traveling through a sharp bend in an L-shaped waveguide carved inside the photonic crystal.

Photonic nanocrystals are periodic dielectric or metallic structures having photonic bands in analogy to electronic bands of semiconductors. The presence of photonic band-gaps, where the propagation of photons of certain frequencies is prohibited, and the variety of photon dispersions give rise to novel and unusual optical phenomena. Consequently, photonic crystals are now envisaged as an essential building block of future photonic devices. This paper aims to provide a review of contemporary developments on the physics and applications of photonic crystals with an emphasis on optical properties of coupled microcavity waveguides and on the negative refraction phenomenon. The enhancement of spontaneous emission in a silicon nitride photonic nanocrystal is investigated in detail. Both the negative refraction of a Gaussian beam and the focusing of a microwave point source through a photonic crystal slab with subwavelength resolution are studied experimentally.

Photonic nanocrystals are periodic dielectric or metallic structures having photonic bands in analogy to electronic bands of semiconductors. The presence of photonic band-gaps, where the propagation of photons of certain frequencies is prohibited, and the variety of photon dispersions give rise to novel and unusual optical phenomena. Consequently, photonic crystals are now envisaged as an essential building block of future photonic devices. This paper aims to provide a review of contemporary developments on the physics and applications of photonic crystals with an emphasis on optical properties of coupled microcavity waveguides and on the negative refraction phenomenon. The enhancement of spontaneous emission in a silicon nitride photonic nanocrystal is investigated in detail. Both the negative refraction of a Gaussian beam and the focusing of a microwave point source through a photonic crystal slab with subwavelength resolution are studied experimentally.

Recent introduction of artificial materials with simultaneously negative effective permittivity and negative effective permeability (Smith et. al., Phys. Rev. Lett. (18), 2000) have gained considerable attention. In such a &#8216 ; ; backward&#8217 ; ; (or &#8216 ; ; left-handed&#8217 ; ; ) material, direction of phase velocity (wave vector k) is opposite to the direction of energy flow (Poynting vector P). This unique property causes reversion of some basic electromagnetic phenomena such as Snell law and Doppler effect. Several ideas for application of new material, such as high resolution electromagnetic lens (Pendry, Phys. Rev. Lett., (18), 2000) and sub-wavelength resonator (Engheta, ICEA 2001 proc., 2001) have already been suggested. So far, the backward materials have been studied experimentally in free-space environment (or in scattering chamber which simulates free-space propagation). Experimental investigations of waveguide filled with backward material has not been reported yet. On the other hand, a waveguide offers possibility of testing meta-material within a small, closed space, loosing requirements on size of a sample. Some of the results of on-going research on rectangular waveguide filled with backward material will be presented in this talk. Since the electromagnetic field in dominant (TE01) mode of the rectangular waveguide can be thought of two planar waves, the previously reported artificial two-dimensional materials can be used for filling. In on-going experiments, negative permittivity is achieved using an array of parallel thin wires (Pendry, J. Phys. Cond. Matter., (12), 1998). Both the FDTD simulation and experiments show shift of the cut-off to the higher frequency (comparing with an empty waveguide), due to plasma-like behaviour of negative permittivity achieved by thin wires. Negative permeability is achieved by two-dimensional array of loaded loops (Hrabar et al, ICECOM 2001 proc., 2001) or split ring resonators (Pendry et al, IEEE Trans. MTT, (11), 1999). A waveguide with this structure exhibits very pronounced (>80 dB) stop-band associated with resonance behaviour of negative permeability. The waveguide which contains both thin wires and loaded loops exhibits a pass-band. The pass-band central frequency may be different of central frequency of the negative permeability stop-band. This shift of frequency is caused by interaction between wires and loops. The phase of S21 parameter has positive gradient within the pass-band, indicating negative differential group velocity associated with backward propagation. The waveguide T junction filled with prism shaped wire-loop material is simulated using FDTD method. Results verify anomalous reflection at the air-material boundary indicating reversion of Snell law. Future research efforts will be directed toward experimental investigation of different waveguide components filled with wire-loop structures. The optimisation of the waveguide backward structure, in order to minimise interaction between elements and improve matching, will be attempted. We also envisage to experimentally confirm reversion of Doppler effect in waveguide filled with backward material.

We study the coupling between negative diffraction and direct dispersion in a nonlinear ring cavity containing slabs of Kerr nonlinear right-handed and left-handed materials. Within the mean field approximation, we show that a portion of the homogeneous response curve is affected by a three-dimensional modulational instability. We show numerically that the light distribution evolves through a sequence of three-dimensional dissipative structures with different lattice symmetry. These structures are unstable with respect to the upswitching process, leading to a premature transition to the upper branch in the homogeneous hysteresis cycle.

We study Veselago's lens with arbitrary index of refraction and characteristic impedance. Using a full wave optics calculation, we show that this lens can be considered as an imaging system and we derive the appropriate lens formula. The lens with arbitrary index and impedance retains some of the properties of the matched lens, such as the invariance of its optical axis, three-dimensional imaging and easy manufacturing, but it loses the property of sub-wavelength resolution. We also show that identical results can be obtained for the impedance matched lens in the framework of paraxial geometrical optics, from which it can be inferred that optical systems containing such a lens can be studied and designed using traditional ray-tracing tools.

We study a ring cavity filled with a slab of a right-handed material and a slab of a left-handed material. Both layers are assumed to be nonlinear Kerr media. First, we derive a model for the propagation of light in a left-handed material. By constructing a mean-field model, we show that the sign of diffraction can be made either positive or negative in this resonator, depending on the thicknesses of the layers. Subsequently, we demonstrate that the dynamical behavior of the modulation instability is strongly affected by the sign of the diffraction coefficient. Finally, we study the dissipative structures in this resonator and reveal the predominance of a two-dimensional up-switching process over the formation of spatially periodic structures, leading to the truncation of the homogeneous hysteresis cycle., 8 pages, 5 figures