Two-dimensional Triangular Lattice Photonic Crystals Research Articles

BP neural network model for reverse design of two-dimensional triangular lattice photonic crystals

By learning the related properties of photonic crystals, two-dimensional photonic crystals with triangular lattice are selected for study. The point defects are set up and the photon band calculation is carried out by using MPB. The calculated sample data is imported into MATLAB, and the relationship between point defects and photonic energy bands is found by building Bp neural network model, which provides a new method to solve the reverse design of photonic crystals.

Numerical optimization design for waveguide bends with low-loss and wide-bandwidth in two-dimensional photonic crystal slabs

In this paper, we demonstrate some optimization designs for waveguide bends in two-dimensional photonic crystal slabs based on the effective index approximation. Four different types of waveguide bends with low-loss and wide-bandwidth are designed, which involve 60°, Z-shaped, Y-shaped and 120° waveguide bends in the two-dimensional triangular lattice photonic crystals. In all numerical experiments, the electromagnetic fields in the photonic crystal slab waveguides are solved by the finite element method in COMSOL software. Several strategies are applied to design slab waveguide bends with low-loss and wide-bandwidth, for example, adding some elliptical air-holes near the corner or adjusting the radii of some air-holes. For four optimized structures, the transmission efficiencies at 1550 nm are all more than 92%. As we show, this is achieved over a −0.915 dB bandwidth of more than 65 nm in all waveguide bends. The numerical results indicate that the design scheme we applied to optimize waveguide bends in photonic crystal slabs is simple and efficient, which can provide some useful guidance for further three-dimensional design.

Polarization-independent and super broadband flat lens composed of graded index annular photonic crystals

Abstract In this paper, we propose two types of all-dielectric polarization-independent graded index annular flat lens with a wide operating frequency range. The lenses are composed of two-dimensional triangular and square lattice photonic crystals with circular silica ( S i O 2 ) rods in the air. We assume in both square and triangular structures, the lenses are obtained by making air holes within each dielectric rod and we consider that the outer radius of the created annular rods is maintained constant while the size of the inner air holes varies along the transverse direction whose the air holes variation follow two types of linear and parabolic function. The graded structures are made in such a way that the modulus of the refractive index is biggest at the centre and decreases towards the edges. The optical properties and the physical background of the polarization-independent focusing mechanism are studied in frequency and spatial domains, using plane wave expansion and finite-difference time-domain methods. Our numerical results show that, through an appropriate set of design, the designed lenses are able to focus the light regardless of polarization for a wide frequency range into approximately same focal length in which difference between the focal distance of TE and TM polarization modes stays below λ 4 . Compared to previously polarization-independent designed photonic crystal based lenses, our proposed structures work under much wider frequency range. Also, in contrast with most of the graded structures, our graded lens are made without altering the lattice constant along the optical axis or transverse to the optical axis. Moreover, the design approach is restricted to the use of silica and non-use of more complicate materials such as liquid crystals, plasma, and the like. Thus, the designed systems can be constructed easier relative to the previously designed lenses.

Photonic crystal frequency band selecting and power splitting devices based on the energy coupling effect between waveguides

The photonic crystal power splitter based on the energy coupling effect between waveguides has the advantages of compact structure, wide bandwidth, low bending loss, large angle of separation, and no external electromagnetic interference. In this paper, the power splitting characteristics of two-dimensional triangular-lattice photonic crystal coupled waveguide are theoretically studied by using the finite-difference time-domain method, and a functional device is designed in order to achieve different output power ratios within different frequency ranges.In the two-dimensional photonic crystal structure with triangular lattice, we set two adjacent straight waveguides and the light beam is introduced from one of them. Because of the energy coupling effect between the two line defects, the light energy propagates alternately in them. Based on this principle, structures of different coupling lengths are simulated and the interference effect of each surface is considered. The device with the best coupling length is achieved for three different output energy propagating characteristics at different frequencies, which include three-division, two-division and single output cases. That is to say, the incident light beam within a frequency band travels through a particular waveguide; light in another frequency band only flows through the other two output waveguides; light in the third frequency band is assigned to all the three output waveguides equally. However, the frequency band width for the high-quality light beam splitting area as well as the transmittance contrast of the other two functional band areas are not very ideal.Based on the above numerical results, two transmission modes in the coupling waveguides are achieved by changing the cross section shape of the dielectric column in the coupling region and also by changing the connecting position between the output branch waveguide and the energy-coupling waveguide. Through the above change, the splitting performance is further optimized.By detecting and analyzing the relative intensity of the three output waveguides, we can determine the range of the incident light beam. Furthermore, the frequency ranges of the three different light output characteristics can be adjusted flexibly by changing the cross section shape of the dielectric column in the coupling region or by changing the connecting position of output waveguides. The functional device proposed in this paper has a high transmittance contrast ratio and a compact structure, which will promote the practical application of the all-optical functional devices in the fields of large-scale all-optical complex integration.

Half-disordered photonic crystal slabs.

Optical transmission spectra of finite-thickness slabs of two-dimensional triangular-lattice photonic crystals of air holes in a dielectric matrix with various concentrations of randomly located vacancies (absent air holes) are studied. We focus on structures in which only one half of the structure-the incidence or transmission side-is disordered. We find vacancy-induced scattering gives rise to a strong difference in the two cases; for light incident on the disordered side, high transmission within the photonic pseudogap at normal incidence is predicted, in strong contrast to the opposite case, where low transmission is predicted throughout the pseudogap, as is observed in the case of an ideal structure with no defects.

All-optical AND, XOR, and NOT logic gates based on Y -branch photonic crystal waveguide

This paper presents all-optical AND, XOR, and NOT logic gates based on the light beam interference effect. Each logic gate is simply composed of a Y-branch waveguide with two input ports and one output port in the two-dimensional triangular-lattice photonic crystals. The designed logic gates are analyzed and simulated by the plane wave expansion and finite difference time-domain method. Simulation results show that the proposed all-optical structures really function as AND, XOR, and NOT logic gates, possess a small size of less than 11.6 μm×13.8 μm and low power consumption. The contrast ratio of the proposed devices reaches 5.4 dB for the AND gate, 33 dB for the XOR and NOT gates, respectively, by precisely controlling the phase differences and properly choosing the size of the scattering rods.

Mode division multiplexing of two-dimensional triangular lattice photonic crystal based on magneto-optical effect

With the rapid development of all-optical communication, the wavelength division multiplexing transmission system cannot meet the requirements of high capacity in optical networks, while mode division multiplexing uses the limited stability modes as independent channels to transmit information, improving the system capacity and spectrum efficiency, which is one of the key technologies in the construction of future optical network. In this paper, a mode division multiplexer of two-dimensional triangular lattice photonic crystal in 1.55 μm band based on the magneto-optic effect of Bi-doped compound rare earth iron garnet bulk single crystal is proposed. The defects of TbYbBiIG medium are introduced as mode splitting waveguides in photonic crystal, of which the permeability changes with the applied magnetic field in different polarization modes. Therefore, mode division multiplexing in 1.55 μm band can be achieved by controlling the propagations of TE and TM mode. The band and transmission characteristics of this device can be analyzed by using the plane wave expansion and finite difference time domain method. The results show that the transmission rates of TE and TM modes both exceed 92% and channel segregation degrees reach 19.7 dB and 42.1 dB respectively. These features indicate the important application prospect in the future high-capacity optical transmission system.

光子晶体理论应用于二元溶液浓度测量的研究

The application of photonic crystal in the solution concentration detection is investigated by using plane wave expansion method. A two-dimensional triangular lattice photonic crystal(Si and Ge) is chosen as the substrate,filling the air hole with different percentage concentration of mixed binary solution materials which will be measured,and the photonic band gap of the photonic crystal filled with binary solution under different polarization modes is obtained. The results show that when the binary solution is used as the dielectric material in the air hole, the photonic band gap(PBG) changes with the different percentage concentrations of the solution quality. This has a certain guiding function in solution mass percentage concentration detection applications.

二维三角晶格光子晶体波导的辐射特性

A photonic crystal waveguide structure with two-dimensional triangular lattice photonic crystals is proposed,in which emission efficiency can be enhanced. The composite structure is composed by cascading a coupled waveguide arrays to a single waveguide. The emission characteristics of light are analyzed via the finite-difference time-domain( FDTD) method. The results show that the emission efficiency of the cascading composite structure is improved. The device has been optimized further. When the distance between the single waveguide and the waveguide arrays is 1. 8a,the horizontal and vertical period number of the waveguide arrays are 6 and 5,the emission efficiency is the best. The emission efficiency is over 20%,when the distance is 100 a between the waveguide output and detector. This type structure of photonic crystal has potential applications in near-field optics and integrated optics.

一种新型高透射率高品质因子光子晶体耦合腔波导结构

A novel coupled-cavity waveguide based on two-dimensional triangular lattice photonic crystals was proposed.This structure was composed of the line-defect waveguides,resonant microcavity,and ellipse-holes which are located between line-defect waveguide and resonant micro-cavity.The band structure of line-defect waveguide was simulated by the method of the plane-wave expansion.The transmission characteristics and quality factor of the coupled-cavity waveguides were investigated by the finite-difference time-domain(FDTD) method.By optimizing the structural parameters such as amount,size,and arrangement of ellipse-holes between the resonant micro-cavity and the line-defect waveguide,a 90% transmission efficiency was obtained with a Q-factor of 104.Then,appropriate parameters were selected,a high Q-factor of 107was achieved,the transmission efficiency corresponding to the resonance frequency was still above 60%.

Transmission properties of a two-dimensional photonic crystal in a dielectric constant supercell

The photonic band gap of a two-dimensional triangular-lattice photonic crystal has been studied using the finite-difference time-domain method. The structure consists of two types of supercells: one with uniform dielectric rods and another with composite rods. Our results show that in both cases an enlarged band gap is present. The central frequency shifts to lower positions with a rise in the rod dielectric constant, but for the supercell with uniform dielectric rods, there are three smaller band gaps that cannot be formed into the enlarged one even when the dielectric constant reaches 57.5. For the photonic crystal of composite medium rods, the largest band gap appears when the dielectric constant reaches 36. Furthermore, the enlarged band gap is present when the dielectric constant decareases to 28. Our results show that the supercells play an important role in the formation of the enlarged photonic band gap. This work will be of significance in fabricating photonic crystal devices.

1 × 2 Beam splitter with high efficiency based on nonreciprocal photonic crystal waveguide

This paper presents a new method for designing efficient 1 × 2 beam splitter in two-dimensional triangular lattice photonic crystals (PhCs). The proposed splitter is based on the one-way edge mode of gyromagnetic PhC, thus can prevent scattering losses even when there are defects or obstacles in its channels. The incident electromagnetic wave can be evenly split into two output channels as long as structural symmetry is kept in a small area around the -junction. The loss effect of gyromagnetic material on the splitting behavior is examined. Moreover, power ratio between the two outputs can be tuned by introducing a defect at a proper position in the splitter. The advantages of the proposed splitter have been validated through numerical simulations.

New design of channel drop filters based on photonic crystal ring resonators

In this paper, a new design of channel drop filters (CDFs) based on photonic crystals ring resonators (PCRRs) is presented. The filter characteristics for single-ring and dual-ring configurations based on two-dimensional (2D) triangular lattice photonic crystal (PC) silicon rods have been investigated by using the two-dimensional (2D) finite-difference time-domain (FDTD) method. Backward dropping efficiency of 96% and forward dropping efficiency up to 98% can be achieved in third communication window. Moreover, we investigate the dependence of resonant frequency on dielectric constant of whole rods of the structure as well as radius of the coupling rods. This device can be used as an optical channel drop filter (OCDF) in future communication applications.

Slow light propagating characteristics through a two-dimensional silicon-based coupled-resonator optical waveguide

The light propagating characteristics of the coupled-resonator optical waveguides (CROWs) are studied by the finite-difference time-domain method. The circular CROWs are constructed by arranging the micro-cavities at a certain distance, which is constructed by removing the air holes along the edge of a circle from a two-dimensional (2D) triangular-lattice photonic crystal (PC). With the increasing of distance between the adjacent cavities, the group velocities of the guiding modes reduce significantly. The circular CROW studied in the paper have much minibands within the band gap, and their respective group velocities can be quite different from each other. This kind of CROW structure can provide different group velocities for the light signals with different frequencies, and avails to the separating and controlling the light signals in the all optic integrated circuits.

Photonic band gap in Ge-based two-dimensional triangular lattice photonic crystals

The relationship between the filling factor and the circumcircle radius of the regular polygon scatter is deduced in a two-dimensional triangular lattice photonic crystal.The photonic band gaps(PBGs) are calculated with the plane wave expansion method in Ge-based two-dimensional triangular lattice photonic crystals.When Ge cylinder is placed in air background,the TM band gaps and TE band gaps appear with the TM band gaps dominating.As Ge filling factor increases,the width of the photonic band gaps increase initially but then decrease and the center frequency decrease.The width of the first band gap of the TM band gaps reaches the maximum at the radius of 0.14a.On the contrary,when air cylinder is placed in Ge background,the TM band gaps and TE band gaps as well as the complete band gaps appear with the TE band gaps dominating.With the air filling factor increasing,the width of the photonic band gaps also increase initially then decrease,whereas the center frequency increase.The width of the first band gap of TE band gaps and the largest complete band gap reaches the maximum at the radius of 0.46a and 0.49a,respectively.

Intensity depending on object distance in a two-dimensional photonic crystal

The propagation of electromagnetic (EM) waves in two-dimensional triangular-lattice photonic crystals (PCs) is investigated through dispersion characteristics analysis and numerical simulation of field pattern. The designed PC structure can exhibit all angle negative refraction in the second band. A flat superlens formed from such a PC has been designed and its imaging properties have been investigated systematically. Good-quality images and focusing, with relative refractive index of −1, have been observed in this system for TE mode waves. In contrast to the images in near-field region for the lowest valence band, non-near-field images, explicitly following the well-known wave-beam negative refraction law, have been demonstrated. The relation between the intensity of the image and the object distance has also been discussed in this paper. The extensive applications of such a phenomenon to optical devices are anticipated.

高品质二维三角晶格光子晶体90°弧度弯曲波导

高品质二维三角晶格光子晶体90°弧度弯曲波导

Bends and splitters for self-collimated beams in two-dimensional triangular lattice photonic crystals

By introducing a line defect and a V-shaped defect into two-dimensional triangular lattice photonic crystals, a 60 deg beam bend, a Y-shaped beam slitter, and a one-to-three beam splitter are designed based on the self-collimation effect of photonic crystals (PCs). By analyzing the equi-frequency contours calculated with the plane wave expansion method, the frequency for self-collimation in the PC is determined. By using the finite-difference time-domain method, the beam bending efficiency and splitting ratios of the device as a function of the defect radius are calculated. These results are confirmed by computational simulations that provide field distributions of light propagating in the structures. The designed beam bend and splitters offer more choices for beam control in the design of photonic integrated circuits.

Imaging properties of triangular lattice photonic crystal at multi-bands

The propagation of electromagnetic (EM) waves in two-dimensional triangular-lattice photonic crystals (PCs) is investigated through dispersion characteristics analysis and numerical simulation of field pattern. The designed PC structure can exhibit all angle negative refraction in the second and the eighth band. A flat superlen formed from such a PC has been designed and its imaging properties have been investigated systematically. Both in band 2 and band 8, a quite high quality image in the opposite side of the slab can be found.

Absolute band gaps of a two-dimensional triangular-lattice dielectric photonic crystal with different shapes

Absolute band gaps of a two-dimensional triangular-lattice photonic crystal are calculated with the finite-difference time-domain method in this paper. Through calculating the photonic band structures of the triangular-lattice photonic crystal consisting of Ge rods immersed in air with different shapes, it is found that a large absolute band gap of 0.098 (2c/a) can be obtained for the structures with hollow triangular Ge rods immersed in air, corresponding to 19.8% of the middle frequency. The influence of the different factors on the width of the absolute band gaps is also discussed.