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The 90° waveguide bend is an important component of optical circuit applications. We propose several models for such a bend, some of them assisted by a two-dimensional photonic crystal with a bandgap in the desired range of operating frequencies. We show that a photonic crystal assisted bend reduces bending loss by several orders of magnitude for transverse electric modes. © 2011 World Scientific Publishing Company., Scientific and Technological Research Council of Turkey (107T569)

We propose a polarization-independent single-mode waveguide, using a two-dimensional square photonic crystal with a complete band gap. The waveguide is tuned such that both TE and TM modes have the same group velocity and zero group velocity dispersion at the centergap frequency. We also present results for a 90° bend with transmission values of 98% for both modes.

Photonic crystals are artificially engineered materials where the dielectric constantis varying periodically. A photonic band gap can be created by scattering at the dielectricinterfaces, which forbids propagation of light in a certain frequency range of light. Thisproperty ensure us to control light, which is normally impossible with conventional optics.Moreover, by placing a linear defect into the photonic crystal one can construct a waveguide,which can be considered as same as the wires, which keep the currents inside, a photoniccrystal waveguide keep light travel in the waveguide, thence in the desired direction. By thisway thanks to photonic crystal waveguides one can control light propagation in the integratedcircuit devices.The goal of this work is to provide a comprehensive understanding of photonic crystalwaveguides to bend light. The purpose is to create a 90 bend for line defect photoniccrystal assisted waveguides and present fully three-dimensional calculations with optimizedgeometrical parameters that minimize the bending loss.The scheme uses one-dimensional photonic crystal slab waveguides for straight sections'and a corner element made consisting a square photonic crystal slab.The two different structures, with either silicon-silica or with silicon-air are used inthe guiding photonic crystal layer. Furthermore, the guiding layer is sandwiched betweeneither air on both top and bottom, or between air on top and silica substrate at the bottom,to serve as the `cladding` medium. Calculations are presented for the transmission valuesof TE-like modes where the electric field is strongly transverse to the direction of propagation,with and without the photonic crystal corner element for comparison. We find that thebending loss can be reduced to under 2%. Fotonik kristaller, dielektrik sabitinin periyodik olarak değiştiği, yapay olarak düzenlenmis malzemelerdir. Fotonik bant aralığı ise fotonik kristale gönderilen ışığın, belli bir bantaralığındaki frekanslarda yayılımının yasaklanması anlamına gelir. Bu özellik yardımıyla,geleneksel optik ile normalde mümkün olmayan ışığın kontrol altına alınmasını sağlayabiliriz.Ayrıca, fotonik kristalin içine doğrusal bir kusur koyarak dalga kılavuzu elde edilebilinir,böylece bir tel nasıl içinde akımı saklıyor ve onu taşıyorsa, fotonik kristal dalga kılavuzudadalga kılavuzunun içinde ışığı saklar ve onu istenilen yöne taşır. Bu yol ile, fotonik kristaldalga kılavuzları sayesinde ışık iletimini entegre devre cihazlarda kontrol edebiliriz.Bu çalışmanın amacı, fotonik kristal dalga kılavuzlarında ışığın bükülmesi konusunukapsamlı bir şekilde incelemektir. Amaç fotonik kristal destekli cizgisel kusurlu dalga klavuzunu90 derecelik açı ile bükmek ve üç boyutlu hesaplamalarla bükmeden kaynaklı kayıpları parametrelerioptimize ederek minimuma indirmektir.Önerilen yöntem ile ışık düz ilerlerken bir boyutta periyodik dalga kılavuzu kullanılır,ışık döneceği zaman iki boyutta periyodik kare örgülü fotonik kristal içine girer, dönüşünütamamlar ve tekrar düz ilerlemek ¨uzere bir boyutta periyodik dalga kılavuzunun içine girer.Çalışmamızda kılavuz katmanı olarak iki farklı yapı ¨uzerinde çalışılmıştır. Bu yapılardanbiri silika-silikon kullanılarak diğeri ise hava-silikon kullanılarak elde edilmiştir. Ayrıca,kılavuz katmanını iki farklı şekilde çalışılmıştır. Birincisinde, kılavuz katmanını üstten vealttan hava arasına alınmıştır, ikincisinde ise kılavuz katmanını üstten hava ve alttan silikaarasına alınmıştır.Hesaplamalar TE-benzeri modları için verilmiştir, TE-benzeri modlar tanım olarakelektrik alanın ışığın yayılım yönünde bileşeninin değerinin 0'a yakın olduğu durumdur.Işığın virajı dönmeden önce ve döndükten sonra enerji değerleri oranlanmış, iletimbu orana göre hesaplanmıştır. İletim değeri grafiklerinde fotonik kristal dalga kılavuzukullanılarak tasarlanan yapılarla sadece dalga kılavuzu kullanılarak tasarlanmıs¸ yapılara aitsonuçlar karşılaştırmalı olarak verilmiştir. Dönmeden kaynaklanan kayıpların 2%'nin dealtına indirilebiliniceği gösterilmiştir. 117

Thesis (Doctoral)--Izmir Institute of Technology, Mathematics, Izmir, 2014, Includes bibliographical references (leaves: 100-103), Text in English; Abstract: Turkish and English, xiii, 103 leaves, Photonic crystals are artificially engineered materials where the dielectric constant varies periodically. A photonic band gap can be created by scattering at the dielectric interfaces, which forbids propagation of light in a certain frequency range of light. This property enables us to control light, which is normally impossible with conventional optics. Moreover, by placing a linear defect into the photonic crystal, one can construct a waveguide, which keeps light inside the waveguide in the desired direction. Thus, by using photonic crystal waveguides one can control light propagation in integrated circuit devices. The goal of this work is to provide a comprehensive understanding of how to bend light using photonic crystal waveguides. The purpose is to create a 90◦ bend for line defect photonic crystal assisted waveguides and present fully three-dimensional calculations with optimized geometrical parameters that minimize the bending loss. The scheme uses one-dimensional photonic crystal slab waveguides for straight sections, and a corner element that employs a square photonic crystal with a band gap at the operating frequency.. The two different structures, with either silicon-silica or with silicon-air are used in the guiding photonic crystal layer. Furthermore, the guiding layer is sandwiched between either air on both top and bottom, or between air on top and silica substrate at the bottom, to serve as the ”cladding” medium. Calculations are presented for the transmission values of TE-like modes where the electric field is strongly transverse to the direction of propagation, with and without the photonic crystal corner element for comparison. We find that the bending loss can be reduced to under 2%.

Thesis (Master)--Izmir Institute of Technology, Physics, Izmir, 2012, Includes bibliographical references (leaves: 163-164), Text in English; Abstract: Turkish and English, xxii, 164 leaves, Photonic crystal waveguides (PhCWGs), designed by removing one or more slabs from a perfectly periodic structures, are possibly future optoelectronic circuit elements that promising a good ability to confine light in a direction and allowing it to propagate in other direction. One of the problem in their application is the coupling from a PhCWG to a completely different structure. This difficulty arrives from sudden change in structure's geometry. In this thesis, to over come this difficulty we used a transition region between two photonic crystal structures that have completely different geometrical parameters. According to our simulation results we find that by using transition region, coupling can be achieved almost without any loss.

Kusursuz bir periyodik yapıdan bir veya daha fazla plaka kaldırılarak tasarlanmış Fotonik Kristal Dalga Kılavuzları (FKDK), ışığın belli yönlerde ilerlemesine engel olup diğer yönlerde klavuzlanmasına olanak sağlayan özelliği sayesinde optoelektronik devre elemanları olarak kullanılabilmeleri yönunde gelecek vaat eden bir uygulama olarak ortaya çıkmıştır. Bu uygulamalar sırasında karşılaşılan problemlerden biri, bir fotonik kristal (FK) yapıdan başka bir yapıya geçişte yaşanan kayıplardır. Bu problem,bir FK yapıdan diğer yapıya geçişlarin ani bir şekilde olmasından kaynaklanmaktadır. Bu tezde farklı yapılar arasındaki geçiler sırasında yaşanan bu kayıpları azaltmak için geçişlerin daha yavaş olduğu birgeçiş geometrisi kullandık. Yaptığımız similasyon sonuçlarına göre bu geçişler hemen hemen hiçbir kayıp olmadan gerçekleşmektedir. Photonic crystal waveguides (PhCWGs), designed by removing one or more slabs from a perfectly periodic structures, are possibly future optoelectronic circuit elements that promising a good ability to confine light in a direction and allowing it to propagate in other direction. One of the problem in their application is the coupling from a PhCWG to a completely different structure. This difficulty arrives from sudden change in structure's geometry. In this thesis, to over come this difficulty we used a transition region between two photonic crystal structures that have completely different geometrical parameters. According to our simulation results we find that by using transition region,coupling can be achieved almost without any loss. 186

Thesis (Master)--Izmir Institute of Technology, Physics, Izmir, 2009, Includes bibliographical references (leaves: 79-82), Text in English; Abstract: Turkish and English, xv, 88 leaves, Photonic crystals are periodic dielectric structures. This periodicity allow us to manipulate light in ways that have not been possible before. As a result, photonic crystal waveguide components play a significant role in integrated optical circuit design because waveguides allow only certain electromagnetic wave modes to propagate inside the structure. There are many corresponding applications that rely on total internal reflection. However, with total internal reflection, there is a problem in guiding light through sharp corners, large optical losses occur around tight curves with a small bending radius. A simple explanation for these losses is that the angle of the incident light too low for total internal reflection when wave turns through a sharp corner. Thus, an unacceptable fraction of the electromagnetic energy is radiated out of the waveguide. To overcome this difficulty, in this thesis, we demonstrate a novel method for guiding light through sharp corners, using a 1 photonic crystal slab waveguide for the straight sections, and assisted by 2D Line Defect Waveguide at the corners.Plane Wave Method and Supercell Method are used to Figure out parameters and obtain the guided mode for our proposed structure. Then, numerical simulations (FDTD) reveal nearly perfect transmission at certain frequency ranges. Also, in this thesis different corner elements are used to show highly efficient transmission of light through sharp corners. Thus, light can be guided through a 90. corner, almost without loss, by using different corner elements. "Crystals are like people, it is the defect in them which tend do make them interesting". Colin Humphreys.

Thesis (Master)--Izmir Institute of Technology, Physics, Izmir, 2009, Includes bibliographical references (leaves: 64-69), Text in English; Abstract: Turkish and English, x, 69 leaves, Photonic crystals are periodically arranged dielectric materials. If the periodicity is broken along a line, i.e. a line defect is formed, then the line defect can behave like a waveguide. In this thesis, a frequency splitting device for electromagnetic waves is designed and tested theoretically using line defect waveguides. The theoretical design of the waveguides is accomplished using the plane wave expansion and the supercell method. The testing is done by the finite difference time domain method. Frequency mixing and splitting, or multiplexers and demultiplexers as they are known in industry, for electromagnetic waves are important since they lead to a multiplication in capacity for optical communications. Multiplexers and demultiplexers have been in use for a long time. However, designing photonic crystal multiplexers has a history of about ten years. In this thesis, a new photonic crystal demultiplexer design is suggested using photonic crystal line defect waveguides.

The supercell method is used to study the variation of the photonic bandgaps in one-dimensional photonic crystals under random perturbations to thicknesses of the layers. The results of both plane wave and analytical band structure and density of states calculations are presented along with the transmission coefficient as the level of randomness and the supercell size is increased. It is found that with the supercell size fixed at 1024 unit cells, higher bandgaps disappear first as the randomness is gradually increased. The lowest bandgap is found to persist up to a randomness level of 55%. However, as the supercell size is increased all bandgaps are observed to approach pseudogaps but with very low density of states. It is shown that harmonics of a relatively small cluster of closely spaced defects largely account for the bulk of the modes that populate the photonic bandgaps., İYTE

Thesis (Master)--Izmir Institute of Technology, Physics, Izmir, 2004, Includes bibliographical references (leaves: 83-84), Text in English; Abstract: Turkish and English, xi,84 leaves, This thesis deals with the implementation of a numerical method to describe how electromagnetic waves propagate through a one-dimensional photonic crystal waveguide. The one-dimensional photonic crystal waveguide is a periodic arrangement of dielectric slabs of alternating dielectric constant with an impurity slab introduced as the guiding layer. This impurity guides, and connes light within a given range of frequencies by producing waveguide modes within the photonic band gap. These modes are different from those of conventional waveguides that use total internal reflection as the basic guiding mechanism. Photonic crystal waveguides are expected to lead to compact photonic integrated circuits.