Integrated photonic device designs based on computational approaches

Nanofotonik, ışığın hareketinin dalga boyu mertebesinde veya daha küçük boyutlardaki yapılarda incelenmesidir. Fotonik cihazların tasarımı fiziksel bilgilere ve tahminlere dayalı olarak gelişmiştir. Bu sayede, geçmişten günümüze çok sayıda fotonik cihaz sunulmuştur. Yeni bir fotonik cihazın tasarlanması için bilinen bir fiziksel olgudan yararlanılır ve sonrasında fotonik cihaz üzerindeki az sayıda karakteristik parametre elle ayarlanarak istenilen optik özellik elde edilmeye çalışılır. Sonuç olarak, morötesinden orta-kızılötesine kadar farklı dalga boyu aralıklarında çalışan çeşitli fotonik cihazlar tasarlanmıştır. Nanofotoniğin gelişimi fotonik cihazların yoğun bir şekilde entegrasyonunu sağlamak ve çalışma bant aralıklarını genişletmek üzerine devam etmektedir. Öte yandan, fotonik cihazların karmaşıklığı arttıkça tasarım süreçlerinde zorluklar yaşanmaktadır. Örneğin; bir optik niteliği etkileyen çok sayıda karakteristik parametre olduğu durumlarda bu parametrelerin aynı anda ayarlanması gerekmektedir. Ancak, bilinen fotonik cihazlar üzerinde elle parametre ayarlamak istenilen optik özelliği elde edebilmek için yeterli olmamaktadır. Bu noktada şöyle bir yorum yapılabilir; belirtilen tasarım yaklaşımları nanofotoniğin geleceği için yeterli değildir. Karmaşık tasarım problemlerinin üstesinden gelebilmek için nanofotonikte tersine tasarım yöntemleri önerilmiştir. Tersine tasarım yöntemleri ile belirlenen bir tasarım alanı içerisinde istenilen optik özelliği veren bir fotonik cihaz tasarlanabilir. Bunun için bilinen bir fiziksel olgu kullanmak gerekmemektedir ve çok sayıda karakteristik parametre aynı anda eniyilenebilir. Karmaşık tasarımlarda, çeşitli eniyileme algoritmaları ve son yıllarda da makine öğrenmesi yöntemleri kullanılmaktadır. İstenilen optik özellikler maliyet fonksiyonu içerisinde tanımlanır ve algoritma bu maliyet fonksiyonunun değerini azaltacak şekilde karakteristik parametreleri belirler. Maliyet fonksiyonunun değerlerini hesaplamak için elektromanyetik alanları ve dalgaları modelleyen çeşitli nümerik yöntemler kullanılır. Çeşitli nümerik yöntemlerin ve algoritmaların birleştirilmesi sonucunda ise hesaplama tabanlı yaklaşımlar elde edilir. Tezin ilk bölümünde, nanofotonikte tersine tasarım yöntemlerinin tarihsel arkaplanı özetlenmiştir. İlk yapılan çalışmalardan günümüzde yapılan çalışmalara kadar sunulan önemli çalışmalar detaylıca sunulmuştur. Tezin ikinci bölümünde, tercih edilen algoritmalar ve nümerik yöntem detaylıca anlatılmıştır. Entegre fotonik cihazların tasarımında için evrimsel algoritmalar ve pekiştirmeli öğrenme algoritmaları kullanılmıştır. Evrimsel algoritmalar olarak Diferansiyel Evrim ve Genetik Algoritma kullanılmıştır. Ayrıca, pekiştirmeli öğrenme algoritmaları olarak toplamsal pekiştirmeli öğrenme algoritması ve çekici seçim algoritması kullanılmıştır. Nümerik yöntem olarak ise sonlu-fark zaman-boyutu yöntemi kullanılmıştır. Tezin üçüncü bölümünde, optik gizleyici, küçük boyutlu lens, optik bağlayıcılar, mod mertebe çevirici ve çok düzeyli difraktif lens gibi hüzme şekillendirici fotonik cihazlar sunulmuştur. Tezin dördüncü bölümünde, fotonik yasaklı bant yapıları, yani fotonik kristaller (FK'ler), üzerinde eniyileme algoritmaları uygulanmıştır. Sonuç olarak, mod mertebe çevirici FK dalga kılavuzu ve asimetrik ışık iletici FK tasarlanmıştır. Tezin beşinci bölümünde, asimetrik ışık iletici (AIİ), dalga boyu ayırıcılar, polarizasyon ayırıcı, dalga kılavuzu geçiş aracı, optik güç zayıflatıcı ve yansıtıcı yapıları sunulmuştur ki bu yapılar optik nitelik ayırıcı olarak sınıflandırılabilirler. Tezin altıncı bölümünde ise tez kapsamında yapılan çalışmalar özetlenmiştir ve nanofotonikte tersine tasarım yöntemlerine dair son sözler paylaşılmıştır. Özetle, tezdeki çalışmalar sonucunda, hüzme şekillendirici fotonik cihazlar, fotonik yasaklı bant tabanlı yapılar ve optik nitelik ayırıcı entegre fotonik cihazlar tasarlanmıştır. Elde edilen sonuçlar nanofotoniğin geleceği için umut vericidir.Nanophotonics is a field of science which investigates the behavior of light at the scale of wavelength or smaller dimensions. The design of photonic devices have been developed based on physical knowledge and intuition. Thus, many photonic devices have been introduced from past to present. In order to design a new photonic devices, a known physical phenomena is utilized which is followed by tuning small number of characteristic parameters on it. As a result, ranging from ultraviolet to mid-infrared, various photonic devices have been designed to operate at different wavelength regimes. The development of nanophotonics is being pursued by dense integration of photonic devices and increasing their bandwidth. However, as the complexity of photonic devices increase, problemshave been faced in design processes. For example, when an optical property depends on large number of characteristic parameters, it is required to optimize these parameters simultaneously. In this case, manual adjustment of parameters is not a decent approach to obtain desired optical properties in photonic devices. It can be concluded that these design approaches are not efficient enough for the future of nanophotonics. In order to overcome these design problems, in nanophotonics, inverse design approaches have been introduced. A photonic device with desired optical property can be designed in a defined design space by using inver desing approaches. Here, a known physical phenomena is not required; and large number of characteristic parameters can be optimized simultaneously. In these designs, various optimization algorithms and, recently, machine learning methods have been applied. The desired optical properties are defined as a cost function and algorithms adjust characteristic parameters by minimizing the value of cost function. In order to calculate cost function values, several numerical methods are utilized which simulate electromagnetic fields and waves. The computational approaches are obtained by combining numerical methods with algorithms. In the first part of this thesis, the histroical background of inverse design approaches in nanophotonics are summarized. From very first studies to recently introduced ones, the most important studies are briefly presented. In the second part of this thesis, the selected algorithms and numerical method is explained in details. In this dissertation, evolutionary algorithms and reinforcement learning algrotihms are applied to design integrated photonic devices. As evolutrionary algorithms, Differential Evolution and Genetic Algorithm are applied. Also, as reinforcement learning algorithms, additive reinforcement learning algorithm and attractor selection algorithm are utilized. In addition, as a numerical method, finite-difference time-domain method is utilized. In the third part of this thesis, beam shaping photonic devices such as an optical cloak, a lens, optical couplers, a mode order converter and a multilevel diffractive lens are presented. In the fourth part of this thesis, optimization algorithms are applied on photonic bandgap structures, namely photonic crystals (PCs). As a result, a mode order converter PC waveguide and an asymmetric light transmitter (ALT) PC are designed. In the fifth part of this thesis, an ALT, wavelength demultiplexers, a polarization beamsplitter, a waveguide crossing, an optical attenuator are introduced which can be classified as optical splitters. In the sixth part of this thesis, the studies in this thesis are summarized and concluding remarks on inverse design in nanophotonics are shared. To conclude, As a result of the studies in this dissertation, beam shaping photonic devices, photonic bandgap structures and integrated optical splitter photonic devices are designed. The obtained results are promising for the future of nanophotonics

Designing photonic structures by using an optimization algorithm

Doğada bulunan malzemelerin farklı karakteristik özellikleri bulunmaktadır. Bu özelliklerden biri de maddenin ışık ile etkileşimine sebep olan kırıcılık indisidir. Farklı kırıcılık indislerine sahip dielektrik malzemelerin bir araya gelmesi ile fotonik kristaller oluşur. Fotonik kristaller bir, iki veya üç boyutlu periyodik ve dielektrik malzemelerden oluşan yapılardır. Fotonik kristaller ile ışığın hareketini farklı şekillerde kontrol etmek mümkündür. Fotonik kristallerin ortaya çıkışında etkili olan en büyük özellikleri fotonik yasaklı band aralıklarına sahip olmalarıdır. Bunun anlamı, bir fotonik kristal üzerine gelen ışığın frekansı bu fotonik yasaklı bant aralığında bulunuyor ise gelen ışık fotonik kristal içerisinde ilerleyemez. Fotonik yasaklı bant aralığı özelliğinden faydalanarak farklı fotonik kristal yapılar tasarlanabilmektedir. Örneğin; fotonik kristaller üzerinde nokta kusur oluşturulduğunda fotonik kristal kavite yapıları tasarlanabilir. Bir başka örnek; fotonik kristal üzerinde bir çizgi kusur oluşturulursa fotonik kristal dalgakılavuzu yapısı elde edilebilir. Fotonik kristaller ile tasarlanabilen yapılar sadece fotonik yasaklı bant aralığı esasına göre tasarlanmazlar. Örneğin bir fotonik kristal yapısı ile gelen ışığı odaklayabilen lens yapısı elde edilebilir. Fotonik kristallerde özkolimasyon, süper prizma, negatif kırılma ve yavaş ışık gibi alışılmadık ışık hareketlerini gözlemlemek de mümkündür. Ayrıca, fotonik kristaller ile biyokimyasal algılayıcı yapılar da tasarlanabilir. Fotonik kristaller genellikle elle tasarlanan basit yapılardır. Karmaşık fotonik kristallerin daha iyi sonuçlar verebildiği bilinmektedir. Ancak yüksek performansa sahip karmaşık fotonik kristalleri analitik teori ve tahminler ile tasarlamak oldukça sınırlıdır. Bu sebeple, yüksek performansa sahip karmaşık fotonik kristalleri tasarlarken bir eniyileme algoritması kullanmak iyi bir çözüm olabilir. Eniyileme algoritmaları, bir sistemin istenilen özelliklerini artırırken istenmeyen özelliklerini azaltmak için tasarım aşamasında kullanılan yöntemlerdir. Eniyileme algoritmaları genellikle doğadan veya evrim teorisinden esinlenilerek oluşturulan algoritmalardır. Eniyileme algoritmaları karmaşık tasarım problemleri için iyi birer aday sonuç verebilmektedir. Fotonik kristal tasarımı da karmaşık bir problem olduğu için eniyileme algoritmaları kullanarak fotonik kristal tasarlama fikri son yıllarda oldukça dikkat çekmiştir. Çünkü eniyileme algoritması ile tasarlanan fotonik kristaller oldukça iyi özelliklere sahip olabilmektedirler. Bu tez kapsamında eniyileme algoritması kullanılarak çeşitli fotonik kristal yapıları tasarlanmıştır. Eniyileme algoritması olarak bir çeşit evrimsel algoritma olan Diferansiyel Evrim algoritması kullanılmıştır. Diferansiyel Evrim algoritmasının yaygın olarak kullanılan diğer eniyileme algoritmalarına kıyasla daha iyi sonuçlar üretebildiği gösterilmiştir. Diferansiyel Evrim algoritması kullanılarak dalgaboyu altında odaklayan fotonik kristal lens yapıları tasarlanmıştır. Fotonik kristallerin birim hücrelerinde eniyileme yapılarak fotonik yasaklı band aralığı genişletilmiş ve bir fotonik kristal dalgakılavuzu yapısı tasarlanmıştır. Fotonik kristal kavite yapısının kavite bölgesi eniyileme algoritması ile değiştirilerek yüksek kalite faktörü elde edilmiştir. Bu tez kapsamında yapılan çalışmalar sonucunda tasarlanan yapılar literatüre bir katkı yapmıştır. Ayrıca, Diferansiyel Evrim algoritmasının fotonik kristal tasarımlarında uygulanabilir olduğu gösterilmiştir ve literatüre yeni bir tasarım yöntemi kazandırılmıştır. Elde edilen sonuçlar ileride tasarlanacak fotonik kristal yapıları için umut vericidir.Materials in nature have different characteristical properties. One of these properties is refractive index which lead to light-matter interaction. Photonic crystals consist of dielectric materials with different refractive index values. Photonic crystals are periodically designed dielectric structures and their periodicity can be one, two, or three dimensional. One can achieve different light manipulation scenarios by using photonic crystals. The main phenomena behind the revelation of photonic crystal is the photonic band gap which means that if a frequency of an incident wave is in the frequency interval of a photonic band gap, the incident wave cannot propagate through the photonic crystal structure. Taking advantage of photonic band gaps, various photonic crystal structures can be designed. For instance, by introducing a point defect in a photonic crystal, a photonic crystal cavity structure can be designed. Another example is that by introducing a line defect in a photonic crystal, one can design a waveguide structure. Photonic crystal structures are not only designed based on photonic band gap phenomena. For example, a photonic crystal lens structure can be designed to focus an incident wave. Also, anomalous light behaviors such as self-collimation, superprism, negative refraction and slow light phenomena can be observed in photonic crystals. Besides, a bio-chemical sensor structure can be designed by using photonic crystals. In general, photonic crystals are simple and designed by hand. And it is known that complex photonic crystal structures can have high performance. However, designing complex structures with high performance based on analytical theory and an intuition approach is limited. For this reason, using an optimization algorithm to design a photonic crystal with high performance can be a good solution. Optimization algorithms are used to increase the desired property and decrease the undesired property of a system during the design process of that system. In general, optimization algorithms are created as algorithms which are inspired by nature or theory of evolution. Optimization algorithms can produce good candidate solutions for complex design problems. Since designing a photonic crystals can be a complex problem, idea of using an optimization algorithm to design a photonic crystal structures has taken great attention in recent years because a photonic crystal that is designed by using an optimization algorithm can possess very good properties. In this dissertation, various photonic crystal structures are designed by using an optimization algorithm. Differential Evolution, which is an evolutionary algorithm, is selected as an optimization algorithm in this dissertation. It is shown that Differential Evolution can produce better solutions than the other well known optimization algorithms can. By using Differential Evolution, subwavelength focusing photonic crystal lens structures are designed. And by optimizing the unit cell of a photonic crystal, photonic band gap is widened and a waveguide structure is designed. Also, cavity region of a photonic crystal cavity structure is optimized to obtain a high quality factor value. As a result of the studies in this dissertation, the designed structures are brought to the literature. Also, it is shown that Differential Evolution can be used to design photonic crystal structures and a new approach to design a photonic crystal is introduced. The obtained results are promising for the photonic crystals that will be designed in the future

Metaheuristic approach enabled mode order conversion in photonic crystals: numerical design and experimental realization

In the presented study, we proposed a design approach based on optimization algorithm to obtain mode order conversion in photonic crystal (PC) structures and experimentally verify the numerical result of the corresponding approach. The finite-difference time-domain method is integrated with an evolutionary algorithm to develop the introduced design method. Here, we designed two different mode order converter PCs with ultra-compact sizes that transform a fundamental mode to a higher order mode. The first designed structure realizes a mode order conversion in free-space host medium, and the second structure performs the same operation in a PC waveguide with optimized region. Also, asymmetric light transmission effect in PC waveguide structure is investigated. Additionally, we performed microwave experiments to confirm the numerical results of mode order conversion. In conclusion, we demonstrated a novel design approach to obtain mode order conversion, which can be feasible to design diverse photonic structures in the future applications of nanophotonics

Photonic crystal rectangular hole based nanobeam cavity refractive index sensor

21st International Conference on Transparent Optical Networks, ICTON ( 2019: Angers, France )In this study, we propose the design of a one-dimensional photonic crystal rectangular hole based nanobeam cavity structure for refractive index sensing. The designed sensor structure consists of periodic air slots on a thin substrate which is made of a dielectric thermoplastic material. Here, three-dimensional finite-difference time-domain method is used to evaluate resonator and refractive index sensing characteristic of the designed sensor structure. The light localization in the cavity region is numerically investigated for various refractive index values at microwave wavelengths. The sensitivity of 5.739 mm/RIU is calculated for a liquid analyte with refractive index value at around 1.33. The possible experimental validation of numerical results can be demonstrated at microwave wavelengths by 3D-printing the designed sensor structure. © 2019 IEEE

Genetically optimized design of ultra-compact and highly efficient waveguide crossing, optical attenuator and reflector

21st International Conference on Transparent Optical Networks, ICTON ( 2019: Angers, France )In this study, we present the design of ultra-compact and highly efficient photonic integrated devices by applying a meta-heuristic approach. Here, we integrated the three-dimensional finite-difference time-domain method into an evolutionary optimization algorithm to specifically design waveguide crossing, optical attenuator and reflector. The proposed devices have ultra-compact footprints of 2×2 ?m2 with slab thickness of 220 nm and consist of 100×100 nm2 silicon or air cells on a SiO2 substrate. We demonstrate an ultra-compact waveguide cross on silicon photonic platform with transmission efficiency greater than 80% and with a negligible crosstalk. Also designed attenuator and reflector devices are providing 3 dB signal reduction and over 85% reflectivity, respectively. All of the devices are excited by a fundamental transverse-electric mode guided in a silicon waveguide with a width of 500 nm. Throughout the optimization process, fabrication constraints are taken into account to enable the realization of the designed devices in applications. The introduced design method can be further expanded to form either diverse photonic integrated devices or even plasmonic devices. © 2019 IEEE

Transmission enhanced wavelength demultiplexer design based on photonic crystal waveguide with gradually varied width

21st International Conference on Transparent Optical Networks, ICTON ( 2019: Angers, France )In this study, we propose the design of photonic crystals with linearly tapered waveguide such that waveguide width is gradually varied. Four drop-channels are included to implement wavelength demultiplexing applications. Here, a tapering of the waveguide has been chosen to localize propagating light within the desired positions. Afterwards, the corresponding drop-channels have been opened to confine the light with the targeted wavelengths. The designed structure consists of cylindrical alumina (Al2O3) dielectric rods and operates at microwave frequencies between 13.2 GHz and 15.3 GHz. An optimization algorithm is applied to enhance transmission efficiencies of the drop-channels and to minimize possible cross-talks between the channels by optimally modulating the position of the dielectric rods inside the channels which form cavity-coupling regions. The optimization algorithm is incorporated with the finite-difference time-domain method to evaluate the transmission efficiencies of the drop-channels for the instant designed structure. The physical mechanism of wavelength demultiplexing is related to slowing down and trapping of light in the tapered waveguide and its coupling to drop-channels for selected microwave wavelengths at different positions. Moreover, an experimental verification of the numerical analyses is demonstrated in the microwave regime and corresponding results will be shared in the conference. © 2019 IEEE

Demonstration of carpet cloaking by an anisotropic zero refractive index medium

In this Letter, we numerically and experimentally demonstrate the carpet cloaking effect by a rectangular lattice two-dimensional photonic crystal (PC) exhibiting a semi- Dirac cone (SDC) dispersion phenomenon. The proposed SDC PC with an anisotropic zero refractive index medium operates as an optical carpet cloak for a perfect electric conductor surface bump. The experimental verification of the cloak is realized at microwave frequencies at around 12.1 GHz via dielectric rods. A good agreement between experimental measurements and numerical calculations is observed. Finally, features such as rendering larger objects invisible are possible with the proposed idea. © 2020 Optical Society of America

Subspace methods for three-parameter eigenvalue problems

© 2019 John Wiley & Sons, Ltd. We propose subspace methods for three-parameter eigenvalue problems. Such problems arise when separation of variables is applied to separable boundary value problems; a particular example is the Helmholtz equation in ellipsoidal and paraboloidal coordinates. While several subspace methods for two-parameter eigenvalue problems exist, their extensions to a three-parameter setting seem challenging. An inherent difficulty is that, while for two-parameter eigenvalue problems, we can exploit a relation to Sylvester equations to obtain a fast Arnoldi-type method, such a relation does not seem to exist when there are three or more parameters. Instead, we introduce a subspace iteration method with projections onto generalized Krylov subspaces that are constructed from scratch at every iteration using certain Ritz vectors as the initial vectors. Another possibility is a Jacobi–Davidson-type method for three or more parameters, which we generalize from its two-parameter counterpart. For both approaches, we introduce a selection criterion for deflation that is based on the angles between left and right eigenvectors. The Jacobi–Davidson approach is devised to locate eigenvalues close to a prescribed target; yet, it often also performs well when eigenvalues are sought based on the proximity of one of the components to a prescribed target. The subspace iteration method is devised specifically for the latter task. The proposed approaches are suitable especially for problems where the computation of several eigenvalues is required with high accuracy. MATLAB implementations of both methods have been made available in the package MultiParEig (see http://www.mathworks.com/matlabcentral/fileexchange/47844-multipareig).status: publishe

Zones optimized multilevel diffractive lens for polarization-insensitive light focusing

In this study, we present the numerical design and experimental demonstration of an all-dielectric low refractive index polarization-insensitive multilevel diffractive lens (MDL) at microwave frequencies. The proposed MDL structure is composed of concentric rings (zones) having different widths and heights. Here, the heights and widths of each dielectric concentric rings of lens structure are optimized by using the differential evolution (DE) algorithm to obtain the desired polarization-insensitive focusing performance. The DE method is incorporated with the three-dimensional finite-difference time-domain method to design an MDL structure and evaluate its wave focusing ability. The design frequency is fixed to 10 GHz and, at the design frequency, the DE method is applied to achieve light focusing with the full-width at half-maximum (FWHM) values of 0.654 lambda and 0.731 lambda for transverse-magnetic (TM) and transverse-electric (TE) polarizations, respectively, where lambda is the wavelength of incident light in free space. Moreover, focusing efficiencies and numerical apertures are calculated as 60.3% and 0.853 at the design frequency, respectively, for both polarizations. Besides, experimental verifications of the numerical results are carried out in microwave regime where the MDL design is fabricated by 3D printing technology by using a polylactic acid material. In the microwave experiments, MDL focuses the TM and TE polarized waves at the focal distances of 71.82 mm and 69.3 mm with the FWHM values of 0.701 lambda and 0.887 lambda, respectively. We believe that the proposed design approach can be further expanded to design low refractive index lenses for visible and near-infrared wavelengths