Enhanced self-collimation effect by low rotational symmetry in hexagonal lattice photonic crystals

In this study, we present the design of a photonic crystal (PC) structure with a hexagonal lattice, where adjustments to the PC unit cell symmetry reveal an all-angle self-collimation (SC) effect. By optimizing opto-geometric parameters, such as the rotational angle of auxiliary rods and adjacent distances, we analyze the SC property in detail, leveraging group velocity dispersion (GVD) and third-order dispersion (TOD) characteristics. We also investigate the relationship between symmetry properties and their influence on dispersion characteristics. Through symmetry manipulation, we gain a comprehensive understanding of the underlying mechanisms governing light collimation and confinement in the proposed configurations. The PC structure with a $C_1$ symmetry group exhibits all-angle SC effect within the range of $a/\lambda=0.652$ and $a/\lambda=0.668$ normalized frequencies, with a bandwidth of $\Delta \omega/\omega_c = 2.4\%$. Further breaking the symmetry, transforming from $C_1$ to $C_2$ group symmetry, enhances the SC bandwidth to $\Delta \omega/\omega_c =6.5\%$ and reveals the perfect linear equi-frequency contours (EFC) at two different frequency bands: all angle SC between $a/\lambda = 0.616$ and $a/\lambda = 0.656$ normalized frequencies in the 4th transverse magnetic (TM) band and between $a/\lambda=0.712$ and $a/\lambda=0.760$ in the 5th TM band. Additionally, we propose a composite/hybrid PC structure resembling $C_2$ group symmetry, where two auxiliary rods are replaced by rectangular photonic wires with the same refractive index and width equal to the diameter of auxiliary rods. This hybrid structure exhibits an all-angle SC effect with an operating bandwidth of $\Delta \omega/\omega_c =11.7\%$, displays near-zero GVD and TOD performance and offers enhanced robustness against potential fabrication precision issues

Fotonik kristal mühendisliği ile ışığın kontrolü: Düşük simetri, derecelendirilmiş kırılma indisi ve parite zaman simetrisi

Tarihsel olarak, iki ve üç boyutlu Fotonik Kristaller (FK) olarak bilinen periyodik yapılara olan ilgi, E. Yablonovitch ve S. John ismindeki bilim adamlarının periyodik dielektrik yapılar üzerinde yaptıkları ilk çalışmalarıyla başladı. Çalışmalarında, elektromanyetik dalgaların yayılımının, yarıiletken yapılardaki elektronların hareketinde olduğu gibi, kontrol edilebileceğini savundular. FK'ların en önemli optiksel özelliklerinden biri, elektronik yasaklı bant aralığına benzer şekilde iletim spektrumunda Fotonik Yasaklı Bant (FYB) aralığına sahip olmalarıdır. Böylece, FK'lar belirli frekans bölgelerinde yönden bağımsız olarak ışığın yapı boyunca yayılmasını engeller. FYB bölgesinde, ne herhangi bir optiksel mod ne de fotonun anlık ışıması oluşmaz. Bu özellikler sayesinde FK'lar pek çok fotonik devre tasarımında kilit rol oynamaktadır. FK birim hücresindeki dönme ve ayna simetrisinin kırılması, eğilmiş öz-kolimasyon ve dalga boyuna göre ayırıcı gibi özelliklerin oluşmasını sağlar. FK devre dizaynında bir başka önemli konu da FK'ların pozisyonlarının düzenlenmesiyle ortamın kırılma indis profilinin ayarlanabilmesidir. Derecelendirilmiş kırılma indisli FK'lar sayesinde kuplör, odaklayıcı lens ve mod mertebesi değiştirici gibi fotonik entegre devre parçaları oluşturulabilir. Uzun mesafeler için herhangi bir kayıp olmaksızın optik sinyalinin iletimini sağlamak önemli bir sorundur. Bu durumda ışığın saçılımı problem teşkil etmektedir. Bu tez çalışmasında iki boyutlu aksikon şeklindeki halka tipi fotonik yapısı kullanarak ışık dağılımına alternatif çözüm sunmaya çalışılmıştır. Geleneksel fotonik dielektrik yapılarına ek olarak, kırılma indisi kazanç-kayıplı olacak şekilde modüle edilen Parite-Zaman simetrisine sahip iki boyutlu fotonik yapı incelenmiştir. Tasarlanan Parite-Zaman simetrik yapısı kullanılarak kristalografik rezonansların yakınında veya yüksek-simetri noktalarında asimetrik ışık iletimi elde edilmiştir.The great interest to the two and three dimensionally periodic structures, called photonic crystals (PCs), has begun with the pioneer works of Yablonovitch and John as one can efficiently control the propagation of the electromagnetic (EM) waves in the same manner with semiconductors that affect the electron conduction. One of the main peculiar properties of PCs is that they have photonic band gap in the transmission spectrum similar to electronic band gap and hence, they are able to prevent the light to propagate in certain frequency regions irrespective of the propagation direction in space. Inside the band gaps, neither optical modes nor spontaneous emissions exist. Breaking the rotational and mirror symmetries of PC unit cells provides rich dispersive features such as tilted self-collimation, and wavelength de-multiplexing effects. Another important issue in PC designs is that it is feasible to design graded index medium if the parameters of the two dimensional PCs is intentionally rearranged. That type of configuration is known as Graded index photonic crystals (GRIN PCs). The implementations of GRIN via periodic structures provide great flexibilities in terms of designing different index gradient and photonic integrated circuit components such as couplers, lenses, and mode order converters. It is crucial to deliver optical signal without any loss for the long distances where light diffraction plays an important role. Hence, dealing with the alternative solution to light diffraction phenomena using 2D axicon shape annular type photonic structure is another topic of this thesis. In addition to conventional photonic all dielectric structures, we have proposed gain-loss modulated parity-time (PT-) symmetric photonic structures to obtain strong asymmetric light transmission close to the crystallographic resonances or, equivalently, close to high-symmetry points

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

Novel properties of Maxwell’s fish eye as an optical microresonator

Whispering gallery modes (WGMs) in Maxwell`s fish eye (MFE) as a graded index medium have interesting spectral and optical transport properties. We employ the finite-difference time-domain (FDTD) method to numerically study of these properties. In comparison to conventional microdisc, mode splitting and high quality factor have been achieved. Due to rapid advances in nanofabrication methods, it seems that MFE can be one of the key optical elements in the future photonic circuits

Active beam steering and afocal zooming by nematic liquid crystal-infiltrated graded index photonic structures

This study presents active beam steering and afocal zooming of light by incorporating liquid crystals (LCs) with graded index photonic crystals (GRIN PCs). The GRIN PC structures are composed of low refractive index polymer annular rods with holes of gradually varying radii. To actively manipulate incident light, the annular rods are infiltrated with nematic LCs. By applying an external voltage to the infiltrated LCs, the effective index profile of the low-index GRIN PC structure is modulated without introducing any mechanical movement. The incident beam deflection and corresponding focal distance modulation are tuned only by controlling the applied bias voltage. In the present work, the hyperbolic secant refractive index profile is chosen to design GRIN PC structures. To design a GRIN PC structure with annular PCs, the Maxwell-Garnett effective medium approximation is employed. We analytically express the relation between infiltrated LCs and the gradient parameter to show the physical background of the tuning ability of the proposed devices. Beam steering and afocal zooming devices are analytically investigated via geometrical optics, and numerically realized with the help of a finite-difference time-domain method. A beam deflection with an angle change of Delta theta(out) = 44 degrees and a light magnification with maximum x2.15 are obtained within operating frequencies of a/lambda = [0.10-0.15] and a/lambda = [0.15-0.25], respectively, where 'a' is the lattice constant and lambda is the incident wavelength. The corresponding operating frequency bandwidths are calculated as 40% and 50% for the beam steering and afocal zooming applications, respectively. LCs are inexpensive materials and work under low voltage/power conditions. This feature can be used for designing an electro-optic GRIN PC device that has the potential for use in a wide variety of optical applications

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