Two-dimensional Photonic Crystals Research Articles

Design and simulation of all-optical logic gates based on two-dimensional photonic crystals

Design and simulation of all-optical logic gates based on two-dimensional photonic crystals

Design of an ultra-compact and high-contrast ratio all-optical NOR gate

In this research, an all-optical NOR gate is designed and simulated based on two-dimensional photonic crystals. A square lattice has been used to design this structure. This logic gate has two main inputs, a bias input, and an output. Because the output of the NOR gate must be “1” for zero inputs, a bias input is required. One of the characteristics of this structure is its small size for use in optical integrated circuits. Also, in order to reduce the detection error in the output, it has been tried that the outputs have a suitable difference in two “0” and “1” logical states. The use of a small number and simple point defects makes the design of this gate easier. The simulation results show that the proposed structure is suitable for working at a wavelength of 1.55 µm. Also, the amount of optical power at the output is high in the “1” logical mode and low in the “0” logical mode. In the proposed gate, the normalized output power in low logic mode is reduced to 0.05 by changing the defect rods.

Exciton–polaritons in GaAs-based slab waveguide photonic crystals

We report the observation of bandgaps for low loss exciton–polaritons propagating outside the light cone in GaAs-based planar waveguides patterned into two-dimensional photonic crystals. By etching square lattice arrays of shallow holes into the uppermost layer of our structure, we open gaps on the order of 10 meV in the photonic mode dispersion, whose size and light–matter composition can be tuned by proximity to the strongly coupled exciton resonance. We demonstrate gaps ranging from almost fully photonic to highly excitonic. Opening a gap in the exciton-dominated part of the polariton spectrum is a promising first step toward the realization of quantum-Hall-like states arising from topologically nontrivial hybridization of excitons and photons.

A reversible bistate joint nimply optical logic gate using photonic crystals

In this work an optical reversible bistate joint NIMPLY (BJN) logic gate was designed using two-dimensional photonic crystals. The gate was designed using an asymmetrical waveguide with reference to a point defect introduced at the center of the structure. The desired logic functions were obtained in the forward and reverse state using the principle of interference of light. The defect rod radius and length of the waveguide using a line defect were chosen to introduce constructive and destructive interference of light. The BJN gate has a low footprint of 40.83 µm2 and the resonant wavelength was designed to be 1550 nm. The finite-difference time-domain method was used to attain the wave propagation and photonic bandgap for the proposed structure. The maximum contrast ratio of the reversible optical BJN gate in the forward and reverse states was found to be 25.11 dB and 24.86 dB, respectively.

A general method for calculation of Faraday rotation and transmittance in two-dimensional magneto-optic photonic crystals by solving vector-Helmholtz equation in anisotropic media

We propose a general method based on the plane wave expansion method for the calculation of the Faraday rotation and transmittance spectrum of the two-dimensional magneto-optic photonic crystal. The method is an extension of the conventional plane wave expansion method by and taking into account all the three components of the electromagnetic fields and considering the permittivity tensor with off-diagonal imaginary components representing the Faraday effect and then solving the vector Helmholtz equation. The formulation is explained in detail from the implementation points of view and the computation cost of the method. In the end, numerical results are presented to verify the accuracy and convergence of the method.

Band gap of two-dimensional layered cylindrical photonic crystal slab and slow light of W1 waveguide

In this paper, we apply the scatterers of cylindrical rings to a two-dimensional photonic crystals slab. The effects of the number of layers, the thickness, the index, and the height of the cylindrical layers on the photonic band gaps (PBGs) of such slab with different lattice arrangements are studied. It turns out that our new structure helps to obtain a large range of the PBGs. The maximum bandwidth is obtained with the value of 0.117 (2πc/a). The PBGs are moved to the lower frequencies with the augment of thickness, refractive index, and height. The choice of height, refractive index, and thickness is a trade-off, and adding the number of dielectric layers is not always positively correlated with the area of PBGs. In addition, in the W1 waveguide with a triangular lattice layout, we obtain a slow light of 0.026 × c. Compared with the square lattice, the triangular lattice is more suitable for slowing down the speed of light.

Band structure analysis of two-dimensional photonic crystals using the wavelet-based boundary element method

By adopting the scaling functions of the B-spline wavelet on the interval (BSWI) as interpolation functions, a wavelet-based boundary element method (BEM) model is constructed to compute the band structures of two-dimensional photonic crystals (2D PCs), which are composed of square or triangular lattices with arbitrarily shaped inclusions. The boundary integral equations of both the matrix and inclusion are developed in a unit cell because of the structural periodicity. In order to make the curve boundary be compatible well, geometric boundaries are interpolated by employing second order BSWI scaling functions while arbitrary order scaling functions are used to approximate boundary variables. For any given angular frequency, an effective technique is provided to generate matrix values related to the boundary shape. Moreover, singular integral problem involved in the presented wavelet-based BEM is considered. Then, combining the Bloch theorem and the interface conditions, a linear eigenvalue equation related to the Bloch wave vector is obtained. Numerical examples are given to verify the performance of the wavelet-based BEM developed herein compared with the conventional BEM.

Strong coupling between hybrid plasmonic–photonic resonances and excitons in metallic photonic crystal–monolayer WS2 nanostructures

Nanostructures, supporting hybrid plasmonic–photonic modes that combine the advantages of the electromagnetic field enhancement of the localized plasmon resonances (LSPRs) and the higher quality factor of the photonic resonances, have served as flexible and efficient platforms for engineering strong light–matter interactions. Here, we demonstrate theoretically that the two-dimensional metallic photonic crystals (PhCs) as a class of hybrid plasmonic–photonic lattices play an active role in light–matter interaction. The metallic PhCs are composed of optical waveguides strongly coupled to periodically arranged metallic nanodisks, and this coupling gives rise to the formation of waveguide–plasmon polaritons. By combining two-dimensional semiconducting materials (WS2) and the metallic PhCs, we prove strong coupling between waveguide–plasmon modes and excitons at room temperature. The strong coupling includes three types of resonances: guided modes excited by diffractive gratings, LSPRs on individual nanodisks, and WS2 excitons. Using coupled oscillator models, we show that the mode composition and coupling strength between polaritons can be controlled effectively by tuning the geometrical factor of the lattice, and thus reveal the LSPR-mediated energy transfer process. Our reports are not only of fundamental interest but could also be useful for practical applications based on monolayer semiconductors.

Topological edge state bandwidth tuned by multiple parameters in two-dimensional terahertz photonic crystals with metallic cross structures.

Originating from the study of topological photonic crystals (TPCs), analogues of the quantum spin Hall effect have been used as a potential way to control the propagation of electromagnetic waves. Due to the topological robustness of the spin TPCs, the edge states along the interface between the trivial and topological areas are topologically protected and not reflected from structural defects and disorders. Here, on the basis of the time-spatial reversal symmetry and topological defect theory, we demonstrate broadening of the edge state bandwidth in spin TPCs made of regular metallic cross structures by simultaneously deforming the hexagonal honeycomb lattice and adjusting the rotation angle. Due to the simultaneous tuning of the two parameters, the designed spin TPCs possess more flexibility. Topologically protected one-way propagating edge states are observed in the terahertz regime, where electromagnetic waves propagate along sharp corners without backscattering. Our findings offer the potential application for topological devices in terahertz technology and are beneficial for the development of 6G mobile communications.

Effective medium theory for photonic crystals with quadrupole resonances.

An effective medium theory is proposed to characterize two-dimensional dielectric photonic crystals (PCs) exhibiting quadrupole resonances. In addition to the effective permittivity and permeability associated with electric and magnetic dipoles, we obtain a local effective parameter to describe the contributions of quadrupole resonances by taking the low frequency limit of multiple-scattering theory. These effective parameters can be used to predict the characteristics of double-Dirac-cone PCs, showing good agreement with the numerical results. Moreover, we show that, after introducing the new effective parameter, the double-Dirac-cone PCs can be regarded as a generalization of the traditional double-zero-index metamaterials.

Nontrivial point-gap topology and non-Hermitian skin effect in photonic crystals

We show that two-dimensional non-Hermitian photonic crystals made of lossy material can exhibit non-trivial point gap topology in terms of topological winding in its complex frequency band structure. Such crystals can be either made of lossy isotropic media which is reciprocal, or lossy magneto-optical media which is non-reciprocal. We discuss the effects of reciprocity on the properties of the point gap topology. We also show that such a non-trivial point gap topology leads to non-Hermitian skin effect when the photonic crystal is truncated. In contrast to most previous studies on point gap topology which used tight-binding models, our work indicates that such non-Hermitian topology can studied in photonic crystals, which represent a more realistic system that has technological significance.

Photon Hall effect in two-dimensional photonic crystal waveguide

The finding of Photon Hall effect (PHE) on metal surface is an important progress in photonics, but it will be more practical if PHE can be realized in line-type waveguide. In this paper, we suggested a way to realize PHE in two-dimensional photonic crystal (PC) waveguide. Numerical simulation results show that the propagating direction and strength of light in the PC waveguide can be controlled by the polarization state of incident light. Different from the PHE on metal surface, the PHE in PC waveguide can be driven not only by circularly polarized light, but also by linearly polarized light. The PHE in PC waveguide can be attributed to the interference of the two component waves excited by the incident light.

Study and Simulation of a Sensor Based on 2D Photonic Crystals for the Detection of Aromatic Compounds: C6H5I, C6H5F and C6H5Cl

A new study was presented on a new sensor based on two-dimensional photonic crystals (Phc's) to detect the following three organic materials: iodobenzene (C6H5I), fluorobenzene (C6H5F), chlorobenzene (C6H5Cl). These materials have dielectric constants (εr) equal to 2.623; 2.140; 2.318, respectively. The proposed sensor is a structure made of silicon rods submerged in air plus a ring resonator. The ring resonator is stuck between two horizontal waveguides. At the end of the ends of the structure there are four ports where port 1 and 2 belong to the top guide and port (3) and (4) the bottom one. In order to analyze the behavior of the sensor, a plane wave expansion approach (PWE) and the finite element method (FEM) are applied. Thanks to the MATLAB and COMSOL simulation software, we were able to obtain the following numerical results: the norm of the electric field, the total energy density and this last magnitude according to the refractive indices of the different organic materials used. We could observe variations in energy density for each material. So, this change is due to their refractive index which varies from one material to another. In this study, we have fixed the other parameters like the constant of the lattice "a" and the radius "r" and we are interested in the dielectric constants (εr) or more precisely the refractive index (n), the latter proves that it is one of the important parameters for detection.

Two-dimensional photonic crystals with insertion of circular and triangular defects

In this work, we calculate photonic band structure for a defective two-dimensional photonic crystal using plane wave expansion method and supercell technique. The photonic crystal comprises circular GaAs cylinders arranged in a two-dimensional hexagonal lattice embedded in an air background in which circular and triangular GaAs defects are inserted. Within the photonic band gap, we can observe a defect mode, whose electric field intensity exhibits a bipolar pattern confined around the defect. If we increase pressure while keeping the GaAs dielectric constant at a constant temperature, we observe that the defective modes shift toward higher frequencies without changing the width of the photonic band gap. Moreover, increasing the radius of the circular GaAs defect favors the appearance of a new defective mode within the photonic band gap. However, if we increase the length of the triangular defect, only a single defect mode may be observed at frequencies close to the air band. We hope that these findings can be considered for the development of new photonic devices.

Transmission and reflection cloaking by using a zero-refractive-index photonic crystal in the microwave region.

We propose a rectangular column two-dimensional square lattice photonic crystal to realize zero refractive index. Through analysis of the energy band structure of the photonic crystal structure, the lattice constant and side length of the rectangular columns can be optimized, and the Dirac cone dispersion appears at the center of the Brillouin zone. The Dirac cone is formed by the interaction of a monopolar eigenstate and a dipolar eigenstate to form a triple accidental degenerate state. The effective medium theory is used to invert the effective electromagnetic parameters of the photonic crystal with a double zero refractive index. The zero-phase change and the focusing characteristic of the concave lens of this kind of zero-refractive-index material are verified. Importantly, we have achieved transmission and reflection cloaking with this zero-index medium. Through the analysis of the amplitude and phase distribution characteristics of the electromagnetic field, it is proved that the designed cloaking devices have obvious cloaking effect.

Photonic band structure in a two-dimensional photonic crystal with a Sierpinski triangle structure

The plane wave expansion method was used to calculate the photonic band structure of a hexagonal lattice in which the triangular GaAs scatterers have a Sierpinski structure. In triangles with lengths of less than 0.6 a, in the photonic band structure for low frequencies, the photonic band gaps appear mainly in the transverse-magnetic polarization, as shown by the results. Nevertheless, when the size of triangles increases above 0.8 a, an overlap of the photonic band gap in the transverse-electric and transverse-magnetic polarizations occurs. Hence, a complete photonic band gap is produced, where the photonic modes cannot propagate in either direction. In addition, we detected that another optimal condition for creating a complete photonic band gap is that the dielectric contrast should be greater than 12. Likewise, the pressure and temperature dependence of the GaAs dielectric constant are considered, detecting a higher frequency shift of the photonic band structure, when the temperature remains constant at 4 K and the pressure increases from 0 to 70 kbar.

Photonic Crystal Polymeric Thin-Film Dye-Lasers for Attachable Strain Sensors.

In this report, using two-dimensional photonic crystals (PhC) and a one-dimensional PhC nano-beam cavity, we realized the development of all-polymeric dye-lasers on a dye-doped, suspended poly-methylmethacrylate film with a wavelength-scale thickness. In addition to the characterization of basic lasing properties, we also evaluated its capacity to serve as an attachable strain sensor. Through experimentation, we confirmed the stable lasing performances of the dye-laser attaching on a rough surface. Moreover, we also theoretically studied the wavelength responses of the utilized PhC resonators to stretching strain and further improved them via the concept of strain shaping. The attachability and high strain sensing response of the presented thin film PhC dye-lasers demonstrate their potential as attachable strain sensors.

Study on the PBGs of a two-dimensional photonic crystal with multilayer rings composite structure and its slow light in W1 waveguide

In this paper, we present a scatterer with a multilayer annular nested composite structure. The photonic band gaps (PBGs) characteristics of the two-dimensional photonic crystals and the slow light features of the W1 waveguide are studied by the plane-wave expansion method. The influences of the number and the thicknesses of hollow annular dielectrics on the PBGs are analyzed. Meanwhile, the impact of the refractive index of each dielectric column is also taken into account. Herein, the scatterers are placed in the square and triangular lattices, and the PBGs traits of the TE and the TM modes in different lattice arrangements are fully discussed. With five layers of dielectric, we get a wide range of complete PBGs. When the thickness and refractive index of the dielectric layer are constant, increasing the number of dielectric layers does not always contribute to boosting the PBG scope. With the aggrandizement in the number of dielectric layers, the PBGs of the TM mode are larger and larger, but the PBGs of the TE mode always aggrandize first and then reduce, or even die down. As the thickness of the dielectric layer is altered, the results depict that the PBGs appertain to the TE mode when the thickness is small, while the TM mode and absolute PBGs tend to occur with the condition that the thickness of the dielectric column is large. Besides, the width of the PBGs always aggrandizes to the accession in the refractive index, and when the refractive index adds to a certain value, the PBGs width degrades to the augment in the refractive index. Finally, the slow light phenomenon in the W1 waveguide with a diverse number of ring layers is analyzed by introducing line defects into the structure. In the GaAs waveguide, we obtain group velocities of ±0.23c.

The Behavior of Electromagnetic Wave Propagation in Photonic Crystals with or without a Defect

In this study, the electromagnetic wave propagation behavior of two-dimensional photonic crystal plates with a defect is investigated. For this purpose, the partial differential equation for the electromagnetic wave propagation in various photonic crystal plates containing a defect or not is obtained by using Maxwell’s equations. The defect is also defined in the electromagnetic wave propagation equation appropriately. In order to solve the electromagnetic wave propagation equation, the finite differences method is used. The material property parameters of the photonic crystal plates are determined with respect to the defects. Accordingly, the effects of material property parameters on electromagnetic wave propagation frequencies, phase velocities, and group velocities are examined. The effects of the size and position of the defects on the electromagnetic wave propagation frequencies are also discussed. The highest electromagnetic wave propagation fundamental frequency value obtained from the analyses performed is 1.198 Hz. This fundamental frequency value is obtained for the electromagnetic wave propagation in the t-shaped photonic crystal plate. Electromagnetic field distribution maps for the fundamental frequencies of the photonic crystal plates whose electromagnetic wave propagation behaviors are examined are obtained with the ANSYS package program based on the finite differences time-domain (FDTD) method.

A study of the origin of supercollimation in two-dimensional square-lattice photonic crystals

The origin of the supercollimation (SC) phenomenon in two-dimensional photonic crystals (PhCs), which is generated by a weak periodic modulation of the dielectric constant, is studied by the plane-wave expansion (PWE) method. We find that the smallest order of PWE required in order to obtain the SC phenomenon is the second order. The distance in k-space and the frequency difference between the SC point and the M point are proportional to the square of the periodic modulation strength. These results strongly imply that the SC phenomenon originates from second-order Bragg scattering. In addition, we rotate the coordinates and study the SC phenomenon using a model which is physically the same as the original model but has a unit cell two times larger and a folded Brillouin zone. In such a rotated model, the mathematical form of the eigenequation becomes much simpler and the SC phenomenon can be obtained with the first-order expansion alone. By neglecting the smaller off-diagonal terms, we can block diagonalize the matrix, which then corresponds to a layered model. Since the layered model is strictly solvable, we derive that a curvature-reversion (CR) point must exist for equi-frequency contours because of the robust asymptotic behavior in the small region. Theoretically and numerically, we also prove that the CR point of the layered model has similar properties to those of the SC point of a square-lattice PhC and infer that the physical origin of these properties is second-order Bragg scattering.