Band Structure Of Photonic Crystals Research Articles

FDTD Based Simulation of Light Extraction in OLED using Triangular Band Structure

ABSTRACT In OLED, external light extraction shows very low efficiency due to total internal reflection, metal surface absorption and surface Plasmon coupling. The photonic crystal is a unique platform for controlling or modifying the light propagation and its properties such as transmission and absorption. The band structure of photonic crystal is mainly proposed for suppressing the spontaneous emission of light. In this work, the Finite Difference Time Domain (FDTD) mathematical modelling has been used to analyse the light extraction efficiency in the triangular band structure of OLED displays by measuring the Purcell factor. Due to the rectangular nature of FDTD solver region, it may be necessary to include multiple unit cells in the solver region for the triangular band structure. There is an improvement in the far-field intensity in OLED by optimizing the angular distribution of light through the substrate with the triangular band structure. Hence it can be widely used in ultra-compact optical devices.

Finite element modeling of electromagnetic properties in photonic bianisotropic structures.

Given a constitutive relation of the bianisotropic medium, it is not trivial to study how light interacts with the photonic bianisotropic structure due to the limited available means of studying electromagnetic properties in bianisotropic media. In this paper, we study the electromagnetic properties of photonic bianisotropic structures using the finite element method. We prove that the vector wave equation with the presence of bianisotropic is self-adjoint under scalar inner product. we propose a balanced formulation of weak form in the practical implementation, which outperforms the standard formulation in finite element modeling. Furthermore, we benchmark our numerical results obtained from finite element simulation in three different scenarios. These are bianisotropy-dependent reflection and transmission of plane waves incident onto a bianisotropic slab, band structure of bianisotropic photonic crystals with valley-dependent phenomena, and the modal properties of bianisotropic ring resonators. The first two simulated results obtained from our modified weak form yield excellent agreements either with theoretical predictions or available data from the literature, and the modal properties in the last example, i.e., bianisotropic ring resonators as a polarization-dependent optical insulator, are also consistent with the theoretical analyses.

Non-Hermitian effective medium theory and complex Dirac-like cones.

In this work, we propose a non-Hermitian effective medium theory to interpret the spawning rings of exceptional points out of the Dirac cones in the band structures of photonic crystals with loss/gain. Based on this theory, we predict and demonstrate two unique types of band dispersions of fully passive photonic crystals. In one type, the exceptional ring shrinks into a complex Dirac point associated with a complex Dirac-like cone. In the other type, a point of quadratic degeneracy is realized in the imaginary frequency spectrum. Our theory provides a unified picture for the exceptional points in effective media and gives rise to novel concepts like complex Dirac-like cones in non-Hermitian photonics.

A finite element method for the band structure computation of photonic crystals with complex scatterer geometry

In this paper, a Petrov–Galerkin finite element interface method (PGFEIM) is proposed to compute the band structures of 2D photonic crystals (PtCs) with complex scatterer geometry, which is formulated as a generalized eigenvalue problem (GEP) for given wave vectors. The key idea of this method is to choose a piecewise linear function satisfying the jump conditions across the interface to be the solution basis, and choose a special finite element basis independent of the interface to be the test function basis to remove the boundary term upon the assertion of Bloch boundary conditions. Non-body-fitting projected grid is employed to implement this approach. Both isotropic and anisotropic materials are considered and discussed for two- and three-component PtCs with square or triangular lattice. Taking advantage of the PGFEIM in dealing with sharp-edged interfaces, PtCs with various peculiar scatterer geometries are studied. Particularly, some distinctive three-component structures with triple-junction points between different materials are fabricated, and the middle frequencies of its absolute photonic band gaps are higher than conventional three-component structures. Numerical examples demonstrate that the bands move to higher or lower frequency regions, which is determined by the component materials, with the increase of number of sharp corners on the surface of entire scatterer.

Design Method of Notch Filter Based on One-dimensional Photonic Crystal Band Structure

Design Method of Notch Filter Based on One-dimensional Photonic Crystal Band Structure

A high sensitivity hydrostatic pressure and temperature based on a defective 1D photonic crystal

We study the transmission spectrum and the band structure of a one-dimensional photonic crystal, made of alternating layers of SiO2 and TiO2 with a GaAs defect layer. The relative permittivity of the GaAs depends on the hydrostatic pressure and the temperature, while its thickness depends only on the pressure. The objective of this work is to apply an external pressure and temperature on the GaAs and study the behavior of the defect mode. The insertion of the GaAs layer inside the perfect structure creates defect mode in the gaps with higher quality factor and important transmission rate . The results show that our structure is sensitive to pressure and temperature variations of approximately P = 50 bar and Θ = 5°K, with a frequency shift of 0.05THz and 0.108THz, respectively. So, our proposed structure is a good candidate for the hydrostatic pressure and temperature sensor design.

Analysis in reciprocal space of the band-pass filter effect in uniform and non-uniform grating couplers

A detailed study on the origin of the bandwidth reduction in the Coupling- Efficiency (CE) spectrum for non-uniform grating couplers (nu-GCs) due to a band-pass filter effect is reported. This effect is deeply investigated through Finite Difference Time Domain simulations (FDTD) in order to look at the spatial Fourier Transform (sFT) of the nu-GC’s emission, which gives the energies and the wavevectors sustained by the overall structure. We show: how to evaluate the bandwidth from the sFT and how the band-pass filter effect arises from the sFT affecting the CE spectrum giving a physical insight on the bandwidth’s reduction. Moreover, we also point out how the concept of photonic crystal bandstructure can be applied for such nu-GCs and used as a powerful tool to describe the dispersion of the light inside these non periodic structures. Finally, both the sFT and the bandstructure approaches are shown to give the same outcomes in terms of the bandwidth evaluation and to be in agreement with the CE spectra’s behaviours. The entire analysis is proposed also for uniform-GC in order to directly compare the two different types of structures.

Design and Numerical Analysis of an All-optical 4-channel Power Splitter in E, S, C, L, and U Bands via Nano-line Defects in Photonic Crystal

AbstractIn the present study, the propagation of electromagnetic waves in a square-lattice photonic crystal waveguide (PCW) is investigated using the finite-difference time-domain (FDTD) method. Then, the plane wave expansion (PWE) method is utilized to calculate the 2D photonic crystal band structure. To realize the desired waveguide, nano-line defects are introduced. The results of the numerical simulations and optimization scanning indicate that for the proposed photonic crystal structure consisting of silicon circular dielectric rods with a radius of 84 nm, a band gap can be achieved in the wavelength range of 1.34 μm<λ<1.93 μm. This wavelength range covers E, S, C, L, and U communication bands. Subsequently, by eliminating the rods in four parts of the structure, an all-optical 4-channel splitter can be designed. The numerical simulation results indicate that by coupling a light source to the main path of the structure and propagating it through each channel, the powers of the 4 output facets become approximately the same. The output power of channels 1 and 2 equals to 24.5 % of the input power, and the output power of channels 3 and 4 is 21 % of the input power and the remaining 9 % is lost in the structure as the leakage power. Since the 1.55 μm wavelength is within the band gap, that is the telecommunication band C, this device can be used as a power splitter.

Coupling between plasmonic and photonic crystal modes in suspended three-dimensional meta-films.

A complementary metal oxide semiconductor (CMOS) compatible fabrication method for creating three-dimensional (3D) meta-films is presented. In contrast to metasurfaces, meta-films possess structural variation throughout the thickness of the film and can possess a sub-wavelength scale structure in all three dimensions. Here we use this approach to create 2D arrays of cubic silicon nitride unit cells with plasmonic inclusions of elliptical metallic disks in horizontal and vertical orientations with lateral array-dimensions on the order of millimeters. Fourier transform infrared (FTIR) spectroscopy is used to measure the infrared transmission of meta-films with either horizontally or vertically oriented ellipses with varying eccentricity. Shape effects due to the ellipse eccentricity, as well as localized surface plasmon resonance (LSPR) effects due to the effective plasmonic wavelength are observed in the scattering response. The structures were modeled using rigorous coupled wave analysis (RCWA), finite difference time domain (Lumerical), and frequency domain finite element (COMSOL). The silicon nitride support structure possesses a complex in-plane photonic crystal slab band structure due to the periodicity of the unit cells. We show that adjustments to the physical dimensions of the ellipses can be used to control the coupling to this band structure. The horizontally oriented ellipses show narrow, distinct plasmonic resonances while the vertically oriented ellipses possess broader resonances, with lower overall transmission amplitude for a given ellipse geometry. We attribute this difference in resonance behavior to retardation effects. The ability to couple photonic slab modes with plasmonic inclusions enables a richer space of optical functionality for design of metamaterial-inspired optical components.

Influence of bias magnetic field direction on band structure of magnetic photonic crystal and its role in constructing topological edge states

The topological transitions in two-dimensional photonic crystals (PCs) originate from the opening-closing-reopening of the bandgap, accompanied with the band order inversion. The topological bandgap in magnetic PC can be created by applying a bias magnetic field or deforming the geometry structure of the PC. In this paper, we demonstrate that the direction of the bias magnetic field also plays a key role in modifying the band structure in a two-dimensional magnetic PC. The results show that by reversing the direction of the bias magnetic field, the eigenstates with the same parity may exchange their orders in the band structure. We investigate this type of band order exchange in the applications of constructing topological edge states and its influence on the properties of edge states. We find, for example, reversing the direction of the bias magnetic field can create two almost degenerated topological edge modes, which propagate in the same direction but have opposite orbital angular momenta. The edge modes and their characteristics can be determined by the schematics of the band orders for the photonic crystals on the two sides of the boundary. The relative relationship of the band orders determines the emergence of the topological edge states, the number of edge states, and edge modes’ properties such as the orbital angular momentum and group velocity. Also, it affects the transmission efficiency of the electromagnetic wave on the boundary. The direction effect of the bias magnetic field on band order exchange presented in this paper provides us with a new way to change the feature of topological edge states and helps us to better understand the influence of band order on topological phases of photonic crystals. It may have potential applications, such as in pseudo-spin splitter and reflection-free one-way optical switch.

Photonic band structure of 2D photonic crystals—a comparative study

Photonic crystals (PhCs) are considered to be the backbone of future technology for terabit data transfer in which the photonic band gap (PBG) is an essential criterion. The PBG determines the range of the stop-band used for design. In this paper, the influence of design parameters, such as the refractive index contrast and the radius of the pillar or rod and lattice constant in 2D PhCs, on its stop-band are analyzed. The PBG for various material combinations is investigated, and the results are reported. Based on the results obtained from the simulation it is possible to choose a suitable material for designing the optical device.

Engineering fragile topology in photonic crystals: Topological quantum chemistry of light

In recent years, there have been rapid advances in the parallel fields of electronic and photonic topological crystals. Topological photonic crystals in particular show promise for coherent transport of light and quantum information at macroscopic scales. In this work, we apply for the first time the recently developed theory of "Topological quantum chemistry" to the study of band structures in photonic crystals. This method allows us to design and diagnose topological photonic band structures using only group theory and linear algebra. As an example, we focus on a family of crystals formed by elliptical rods in a triangular lattice. We show that the symmetry of Bloch states in the Brillouin zone can determine the position of the localized photonic wave packets describing groups of bands. By modifying the crystal structure and inverting bands, we show how the centers of these wave packets can be moved between different positions in the unit cell. Finally, we show that for shapes of dielectric rods, there exist isolated topological bands which do not admit a well-localized description, representing the first physical instance of "fragile" topology in a truly noninteracting system. Our work demonstrates how photonic crystals are the natural platform for the future experimental investigation of fragile topological bands.

Influence of optical Kerr coefficient on photonic band structures of hexagonal-lattice function photonic crystals

در این مقاله، بلورهای فوتونی تابعی را که در آنها ثابت دی‌الکتریک مراکز پراکندگی (میله‌ها) تابعی از مکان است، مورد مطالعه قرار داده‌ایم. شبکه مورد بررسی هگزاگونال بوده و سطح مقطع میله‌ها نیز دارای تقارن دایروی است که در زمینه هوا قرار گرفته‌اند. ساختار نوار فوتونی در هر دو قطبش الکتریکی و مغناطیسی برای امواج الکترومغناطیس محاسبه شده و نتایج به دست آمده وجود نواحی ممنوعه بسامدی (گاف نوار فوتونی) را نشان می‌دهند. فرض می‌شود که میله‌های دی‌الکتریک از مواد کر تشکیل یافته‌اند. بنابراین با در نظر گرفتن توزیع‌های متفاوت شدت نور، صورت‌های مختلفی برای تابعیت مکانی ثابت دی‌الکتریک میله‌ها حاصل خواهد شد. اثر ضریب تابع (متناسب با ضریب کر) بر روی ساختارهای نوار فوتونی به طور نظری بررسی شده است. نتایج به دست آمده نشان می‌دهند که پهنا و تعداد گاف‌های نوار فوتونی در بلورهای فوتونی تابعی نسبت به بلورهای فوتونی مرسوم قابلیت کنترل پذیری بیشتری دارند و می‌توانند در طراحی ابزارهای نوری بسیار مفید باشند.

Highly efficient GPU eigensolver for three-dimensional photonic crystal band structures with any Bravais lattice

A null-space free method with the FFT-based matrix–vector multiplications was proposed to solve the Maxwell equations that model the three-dimensional photonic crystals. The most time-consuming parts of this method were the FFT-based matrix–vector multiplications. In this article, we propose new mathematical formulas to compute the FFT-based matrix–vector multiplications and derive highly efficient algorithms on top of the NVIDIA GPU architecture. The resulting algorithms are approximately two- to threefold faster than the previous algorithms. We have successfully used a single NVIDIA Tesla P100 GPU to solve a set of generalized eigenvalue problems of 5,184,000 dimensions in 17 to 22 seconds for each problem. Furthermore, we ported the codes to a GPU cluster and achieved near linear scalability. To our knowledge, these GPU implementations of the proposed algorithms are the fastest implementations. The schemes can be applied to simulate a three-dimensional photonic crystal with all 14 Bravais lattices. These highly efficient schemes and codes raise possibilities for large-scale and near real-time numerical simulations for novel physical discoveries and engineering applications of photonic crystals.

Two-dimensional photonic crystals for engineering atom–light interactions

We present a 2D photonic crystal system for interacting with cold cesium (Cs) atoms. The band structures of the 2D photonic crystals are predicted to produce unconventional atom-light interaction behaviors, including anisotropic emission, suppressed spontaneous decay, and photon-mediated atom-atom interactions controlled by the position of the atomic array relative to the photonic crystal. An optical conveyor technique is presented for continuously loading atoms into the desired trapping positions with optimal coupling to the photonic crystal. The device configuration also enables application of optical tweezers for controlled placement of atoms. Devices can be fabricated reliably from a 200-nm silicon nitride device layer using a lithography-based process, producing predicted optical properties in transmission and reflection measurements. These 2D photonic crystal devices can be readily deployed to experiments for many-body physics with neutral atoms and engineering of exotic quantum matter.

Band structure and topological phase transition of photonic time crystals

We investigate the band structure and topological phase transition of photonic time crystals (PTC)-systems in which the physical parameter varies periodically in time. We find that the topological phase transition of the PTC system can be revealed by the wave vector gap (k-gap) size, which was induced by the temporal refraction and reflection. Interestingly, a temporal zero-averaged refractive index k-gap is obtained when the PTC system includes a dispersive medium. This special k-gap is invariant with modulation time scaling at a given modulation frequency.

Band structure of two-dimensional photonic crystals that include dispersive left-handed materials with rough surfaces in their lattice

In this work, we have calculated the photonic band structure in 2D photonic crystals composed of a dielectric and a dispersive metamaterial with cylindrical inclusions that present rough surfaces by using an integral equation method. We found that for purely dielectric photonic crystals with a relatively small roughness (compared to the wavelength), the band structures remain unperturbed compared to those associated with photonic crystals that have smooth surfaces. However, when a dispersive left-handed material is included in the lattice, band structures become strongly affected under TE and TM polarizations, since new photonic band gaps arise. Moreover, the band gaps that appear in the case of smooth surfaces change their position, becoming narrower or generating more band gaps in the same region.

A finite element based fast eigensolver for three dimensional anisotropic photonic crystals

The standard Yee's scheme for the Maxwell eigenvalue problem places the discrete electric field variable at the midpoints of the edges of the grid cells. It performs well when the permittivity is a scalar field. However, when the permittivity is a Hermitian full tensor field it would generate un-physical complex eigenvalues or frequencies. In this paper, we propose a finite element method which can be interpreted as a modified Yee's scheme to overcome this difficulty. This interpretation enables us to create a fast FFT eigensolver that can compute very effectively the band structure of the anisotropic photonic crystal with SC and FCC lattices. Furthermore, we overcome the usual large null space associated with the Maxwell eigenvalue problem by deriving a null-space free discrete eigenvalue problem which involves a crucial Hermitian positive definite linear system to be solved in each of the iteration steps. It is demonstrated that the CG method without preconditioning converges in 37 iterations even when the dimension of a matrix is as large as 5,184,000.

Band structure and spatial electromagnetic field distribution in the 2D photonic crystals with nontrivial elementary cell

Periodic systems with the silver-based waveguides are discussed. The elementary cell in such systems consists of several waveguides. We employ the multiple scattering formalism based on solving the Maxwell equations solution for a single cylinder. The method involving the lattice-sum transformation into a fast convergent series is implemented. This enables us not only to increase the computational accuracy but also to reduce the necessary time for performing the numerical simulation. It is shown that under condition of nonzero propagation constant, the guided modes located closely in the frequency region appear. The number of these modes equals the number of waveguides in the elementary cell of the system. As a quasi-wave vector approaches the edge of the Brillouin zone, the frequency of these modes decreases. Increasing the propagation constant affects the modes shifting them towards the high frequency region. It is also shown that it is possible to match simultaneously wave vector and frequency of guided modes in the zigzag shaped systems.

Peculiarities of band structure of one-dimensional photonic crystals

In this paper, the peculiarities of the band structure of one-dimensional photonic crystals are studied, when the periodic (quasiperiodic) medium is inhomogeneous in relation to both the dielectric and magnetic properties. It is shown that the photonic band gap does not appear at small angles of incidence, in the case when the modulation depths of the dielectric permittivity and magnetic permeability coincide. The possibilities of obtaining photonic bandgaps in the terahertz radiation region are considered. The features of the band structure of photonic crystal with different spatial periods of the dielectric permittivity and magnetic permeability are investigated. It is shown that in this case, four PBGs appear in each diffraction reflection order.