Metamateryal katkılı dalga kılavuzu uygulamaları
Waveguide applications with metamaterial additives
Yazar: İSA TOKGÖZ
Danışman: PROF. DR. ALİ YAPAR
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Elektronik ve Haberleşme Mühendisliği Ana Bilim Dalı / Telekomünikasyon Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2022
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering
Dizin: Dalga kılavuzları = Waveguides ; Metamalzemeler = Metamaterials ; Rezonatör = Resonator ; İletim yöntemi = Transmission method

Özet:
Bu çalışmanın temel motivasyonu metamalzeme özellik gösteren materyallerin özelliklerinin incelenmesi ve devamında bu özelliğin kullanıldığı bir sistem tasarımı analizi ortaya koymaktır. Normal şartlar altında doğada bulunan malzemelerden farklı olarak bazı olağanüstü özellikler gösteren metamalzemeler, belirli geometrik şekil ve büyüklükte tasarlanmış metalik rezonatörlerin belirli bir düzende (genelde periyodik) bir araya getirilmesi ile oluşturulan yapılardır. Bu yapıların literatürde en sık kullanılanı bölünmüş halka rezonatör yapılarıdır (SRR). Rezonatörlerin belirli doğrultularda periyodik olarak dizilimi ile hem dielektrik sabiti ε, hemde magnetik geçirgenlik μ'nün negatif değerler alabildiği, efektif olarak negatif kırılma indisine sahip ortamların oluşturulması mümkün hale gelir. Burada dielektrik sabiti ε ve magnetik geçirgenlik μ'nün gerçekte negatif değerler almadığı ancak sentetik yollarla oluşturulmuş bu tür bir yapının efektif olarak bu şekilde davranan bir malzeme haline geldiği unutulmamalıdır. Bu tür yapıların genel kullanım alanları; performans artırımı için çeşitli anten yapıları [1], kırınım sınırının ötesinde görüntüleme sistemleri için süperlens tasarımları [2], radar kesit alanı (RCS) azaltma için kullanılabilecek yutucu (absorber) malzemeler[3] ve tıp alanında kullanılabilecek çeşitli temassız ve hasarsız tespit sistemleridir[4].
Bu tezde dalga kılavuzları içerisine yerleştirilen metamalzeme özellikteki yapıların genel bir analizi ile birlikte bu tür yapıların özellikle mikrodalga görüntülemedeki bazı kullanım olanakları incelenmiştir. Bu kapsamda öncelikle basit bir rezonatör dizisi tasarlanmış ve dikdörtgen dalga kılavuzu içerisine yerleştirilmiştir. CST simülasyon programı kullanılarak frekans modunda yapılan analiz sonucunda saçılma parametreleri elde edilmiştir. Yansıma parametresi S11 dağılımı incelendiğinde kılavuz içerisindeki yapının etkisiyle, kılavuzun kesim frekansı olan 9.48 GHz'den düşük olan 6 GHz seviyelerinde iletim yaptığı görülmüştür. Metamalzeme özelliğinin bir sonucu olan bu durumun matematiksel analizi İletim-Yansıma (T-R) Metodu [5] kullanılarak yapılmıştır. Metod ile yapılan işlemler sonucunda yapının 6 GHz seviyesinde negatif dielektrik sabiti ve magnetik geçirgenlik değerlerine sahip bir özellik gösterdiği görülmüştür.
İkinci uygulama kısmında ise çalışmanın odağı kılavuz ve rezonatör içeren farklı sensör konseptlerinin analizi olmuştur. Bu analizde açık uçlu kılavuzda açık uç sınırına eklenecek rezonatör dizisi ile bir sensör sistemi kurgulanmıştır. Bu sensör sisteminin amacı belirli metal yüzeylerde var olabilecek hasarların (delik, çatlak, pürüz vb) tespitidir[6]. Burada ilk olarak rezonatör tasarımı, boyut ve geometrik şekil değişecek şekilde tasarlanarak sonuçlar incelenmiştir. Sonrasında metal yüzeydeki hasarın sensöre göre değişen konumunun ölçüm sonucuna etkisi, devamında artarak değişen levha dielektrik sabitinin sonuçları analiz edilmiştir. Son olarak ölçülecek olan yüzey hasarı genişliği alt sınırı ve çalışılan frekans seviyesi arasındaki ilişki analizleri yapılmıştır.
Elde edilen bulgular eşliğinde hasar olmayan yüzey ve hasar olan yüzeyler karşılaştırıldığında manyetik alan şiddeti ve yüzey akımı değerlerinin hasarlı yüzeyde arttığı ve saçılma parametrelerinden yansıma katsayısı S11'in frekans bandı dağılımında faz kayması ile sonuçlandığı görülmüştür. Bu çalışmada tasarımı çalışılan sensör sistemi, VNA kullanılan sistemde deneysel çalışmalarda kullanılabilir.

Abstract:
Metamaterials are artificially constructed materials that exhibit extraordinary electromagnetic properties that are not readily available or easily obtained in nature. It has been suggested that the refractive index may be negative in the study titled "The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ" by Victor Veselago in 1968 for the first time [2]. Waves with a negative index of refraction are considered backward waves and are waves with group and phase velocities in opposite directions. In the case of negative material constants, namely negative dielectric coefficient and negative permeability, it can be said that negative refraction will occur, and materials in this situation are called 'left handed' [7]. In a different terminological nomenclature, if both material constants are negative; named as DNG, named as ENG if only ε is negative, named as MNG if only μ is negative, and finally named as DPS materials if both constants are positive. Since 1999 [8], with the emergence of the metamaterials field, metamaterials have received great attention from the scientific community all over the world and offer applications in antenna and waveguide engineering, imaging, microscopy, sensing and light manipulation [1],[2],[3],[4].
The main motivation of this study is to examine the functionality of materials with metamaterial properties and then to present a system design analysis in which this property is used. Microwave waveguide will be used in the system to be designed. Waveguides are the most efficient ways to transmit electromagnetic energy [9]. While the most common type of material is copper, it can also be found in very valuable materials such as brass, silver or even gold[3]. While the waveguide can be designed in various shapes such as rectangular, circular or elliptical cross section, the most commonly used design concept is rectangular[3]. They are mostly used for power transmission in the microwave frequency band [10]. Electromagnetic signal transmission takes place in different modes, namely TEM, TE and TM [11]. The main factor that determines the guide size is the frequency of the signal to be transmitted [3]. Common uses vary, such as radar installations, microwave filter designs and power dividers of various test systems.
Metal structures designed in certain geometric shapes and sizes are called resonators. The most commonly used of these structures in the literature are split-ring resonator structures (SRR). In the historical process, the definition of SRR was first used by Wardy and Whitehead in the literature [7]. A single-celled SRR consists of a pair of closed loops with compartments inside them at opposite ends. The loops are made of a non-magnetic metal such as copper and are spaced a few tens of micrometers apart. A magnetic flux penetrating the metal rings will induce currents that rotate in the rings and produce their own flux, increasing or decreasing the charge field depending on the resonance characteristics of the SRRs.
Small gaps between the rings produce large capacitance values that lower the resonant frequency. Therefore, the dimensions of the structure are small compared to the resonant wavelength.
Metamaterials, whose general usage areas are various antenna structures for performance enhancement, superlens designs for imaging systems beyond the diffraction limit, absorber materials that can be used for radar cross-sectional area (RCS) reduction, and various non-contact and non-destructive detection systems that can be used in medicine, also have many opportunities in surface detection [7],[12]. The ultimate goal of the studies in this thesis is to present a sensor system approach for the detection of micrometer cracks that may occur on metal surfaces. Before proceeding to the metamaterial doped waveguide analysis, which is necessary for the analysis of this system, some basic information about the structure was obtained by working on the guide and resonator. In the light of the information obtained, the design of the sensor system and its analysis in different situations were made in the second part.
In the first part of the application studies of the thesis, the resonator array is designed and placed in a rectangular waveguide [7]. The waveguide used in the analysis is a square waveguide with a cross section size of 6mm x 6mm [7]. Ring resonators designed with an outer radius of 2.6 mm and an inner radius of 1.9 mm, with a distance between the inner and outer rings of 0.2 mm and a ring width of 0.5 mm [7]. 7 pairs of split double ring resonators are added to the waveguide [7]. When the waveguide was empty, that is, no material was added, it was simulated in the CST simulation program in frequency mode and the scattering parameters were obtained.Based on the frequency distribution graphs of the 𝑆11 and 𝑆21 parameters, it is understood that the
9.48 GHz level is the cutoff frequency. Then, the scattering parameters were obtained as a result of the analysis in frequency mode in the case of adding the resonator array. When the reflection parameter 𝑆11 distribution obtained as a result of the simulation in the 4-10 GHz frequency band is examined, it is seen that the guide transmits around 6 GHz, which is lower than the cutoff frequency of 9.48 GHz, with the effect of the structure in the guide. The mathematical approach of the situation, which is a result of the metamaterial property, was made using the Transmission-Reflection (T-R) method [5]. The outputs of the CST simulation results were calculated using MATLAB and a scatter plot was drawn in the frequency band. As a result of the graphs obtained, it was seen that it has negative dielectric constant and negative permittivity values at 6 Ghz level.
In the second application part, the focus of the study was the analysis of different design concepts including guide and resonator. The main purpose of this system is to make surface analysis. To be used in this analysis, the sensor system was designed with the resonator array to be added to the open-end boundary in the open-ended guide. In order for this sensor system to detect possible damage to metal surfaces, the distance to the target must be within certain limits. The waveguide used has cross-sectional values of 15.8mm x 7.9mm [6]. While constructing the structure in the design, 5x2 double resonator series were used, 5 on the open-end boundary and 5 on the plate adjacent to the open-end boundary [22]. Here, firstly, the resonator structure was designed to change in size and geometric shape, and the results were examined. In 5 different designs, first larger size circular split resonators, then more (10x2) circular split ring resonators, then circular double split ring resonators and finally square split resonators were used. The second analysis parameter was the changing position of the damage on the metal surface relative to the sensor, which had an effect on the measurement result. It has been observed that the result decreases as the angle of damage on the target surface and guide increases, that is, as the amount of damage area in the field of view decreases. The third analysis parameter was the dielectric constant of the plate placed at the open end boundary. The results obtained with increasing dielectric constant were analyzed and it was observed that the magnetic field strength and surface current values obtained as a result also increased. Finally, the damage width on the metal surface to be measured was reduced from the normal value of 300 micrometers and the measurement limit was examined. In the measurement made at 10 micrometers, the same result was obtained as in the undamaged condition and the dimensions of the waveguide used were reduced to a higher frequency, that is, a lower wave size. In the study made with the high frequency system, it was seen that the surface damage with a width of 10 micrometers could be detected.
When the non-damaged surfaces and damaged surfaces were compared, it was observed that the magnetic field strength and surface current values increased on the damaged surface, in the light of the findings obtained. In the case of using a series of square split resonators, the numerical results are different compared to circular resonator sensors in the other four designs. Likewise, when examining the effect of the direction of damage on the surface on the result, the values obtained converged to the values in the undamaged condition as the surface and the sensor approached the vertical position. In addition to the numerically obtained differences, it was observed that the reflection coefficient 𝑆11 resulted in a phase shift in the frequency band distribution. Although this phase shift varies in value according to the measurements, it was definitely observed for every case with damage.
In a system using VNA, results can be obtained physically by analyzing metal surfaces using a sensor. The most important parameters to be considered are to use the resonator array designed in the right size and shape and to be aware that the damages cannot be detected below the resolution level of the frequency value studied. In addition, since the sensor open-end boundary distance to the metal surface is of critical importance, measurements made farther than necessary will result in a negative change in the results.