Two-dimensional Photonic Bandgap Research Articles

Complete two-dimensional photonic bandgap in refractive-index ratio 2.1 photonic crystals due to high-order bands.

We find that in a suitably designed photonic crystal (PC) certain high-order photonic bands are less affected by the refractive-index ratio (RIR) than low-order bands, enabling the realization of a robust and complete two-dimensional (2D) photonic bandgap in a moderate refractive-index-ratio PC. A detailed theoretical investigation of low- and high-order bandgaps in a series of PCs with different configurations is performed that shows that high-order bands may favor substantial complete photonic bandgaps (CPBGs) for systems with a moderate RIR. Furthermore, the importance of the geometry and structural parameters on achieving a high-order CPBG is found. Specifically, a hexagonal lattice PC of annular-hole-peripheral connecting rods is proposed, which can support a CPBG with a refractive-index ratio (RIR) as low as nhigh:nlow=2.1; to the best of our knowledge, this is the lowest RIR used to obtain a 2D CPBG in a PC.

Topology optimization of 3D photonic crystals with complete bandgaps.

The design of photonic crystals with complete bandgaps has recently received considerable research focus for numerous reasons. This work leverages well-known nonlinear programming techniques to alleviate the non-smoothness caused by degenerate eigenvalues such that topology optimization problems can be solved with the open-source IPOPT software. A fully-vectorial plane wave expansion technique is used with an iterative eigensolver to efficiently predict dispersion properties of candidate structures. Nonlinear programming is employed to solve the inverse problem of designing three-dimensional periodic structures that exhibit complete two-dimensional (2D) and three-dimensional (3D) photonic bandgaps. Mesh refinement is performed to alleviate the large computational burden of designing and analyzing photonic crystals, and a periodic density filter is implemented to impose a minimum feature size for manufacturability considerations.

Compact Photonic Crystal Polarization Beam Splitter Based on the Self-Collimation Effect

We propose a new compact polarization beam splitter based on the self-collimation effect of two-dimensional photonic crystals and photonic bandgap characteristics. The device is composed of a rectangular air holes-based polarization beam splitting structure and circular air holes-based self-collimating structure. By inserting the polarization beam splitting structure into the self-collimating structure, the TE and TM polarized lights are orthogonally separated at their junction. When the number of rows in the hypotenuse of the inserted rectangular holes is 5, the transmittance of TE polarized light at 1550 nm is 95.4% and the corresponding polarization extinction ratio is 23 dB; on the other hand, the transmittance of TM polarized light is 88.5% and the corresponding polarization extinction ratio is 37 dB. For TE and TM polarized lights covering a 100 nm bandwidth, the TE and TM polarization extinction ratios are higher than 18 dB and 30 dB, respectively. Compared with the previous polarization beam splitters, our structure is simple, the size is small, and the extinction ratio is high, which meets the needs of modern optical communications, optical interconnection, and optical integrated systems.

Enhanced complete photonic bandgap in a moderate refractive index contrast chalcogenide-air system with connected-annular-rods photonic crystals

Connected-annular-rods photonic crystals (CARPCs) in both triangular and square lattices are proposed to enhance the two-dimensional complete photonic bandgap (CPBG) for chalcogenide material systems with moderate refractive index contrast. For the typical chalcogenide-glass–air system with an index contrast of 2.8:1, the optimized square lattice CARPC exhibits a significantly larger normalized CPBG of about 13.50%, though the use of triangular lattice CARPC is unable to enhance the CPBG. It is almost twice as large as our previously reported result [IEEE J. Sel. Top. Quantum Electron.22, 4900108 (2016)IJSQEN1077-260X10.1109/JSTQE.2015.2422997]. Moreover, the CPBG of the square-lattice CARPC could remain until an index contrast as low as 2.24:1. The result not only favors wideband CPBG applications for index contrast systems near 2.8:1, but also makes various optical applications that are dependent on CPBG possible for more widely refractive index contrast systems.

Photonic band gaps structure properties of two-dimensional function photonic crystals

The tunable two-dimensional photonic crystals band gap, absolute photonic band gap and semi-Dirac point are beneficial to designing the novel optical devices. In this paper, tunable photonic band gaps structure was realized by a new type two-dimensional function photonic crystals, which dielectric constants of medium columns are functions of space coordinates. However for the two-dimensional conventional photonic crystals the dielectric constant does not change with space coordinates. As the parameter adjustment, we found that the photonic band gaps structures are dielectric constant function coefficient, medium columns radius, dielectric constant function form period number and pump light intensity dependent, namely, the photonic band gaps position and width can be tuned. we also obtained absolute photonic band gaps and semi-Dirac point in the photonic band gaps structures of two-dimensional function photonic crystals. These results provide an important theoretical foundation for design novel optical devices.

Temperature-dependent spontaneous emission of PbS quantum dots inside photonic nanostructures at telecommunication wavelength

Spontaneous emission of PbS quantum dots (QDs) in different photonic nanostructures has been studied. We use the temperature-dependent exciton photoluminescence and the classic dipole near interface models to understand the spontaneous emission control at various temperatures. Then, we demonstrate that the enhancement and the inhibition of PbS QDs due to the local density of states (LDOS) inside nanostructures are more efficient at temperature as low as 77K than the inhibition at 300K. Largest emission rate enhancement at 77K of 1.67±0.10 and inhibition factors at 100K of 2.27±0.15 are reported for the gold (Au) planar mirror and silicon (Si) two-dimensional photonic crystal bandgap, respectively. We attribute those enhancement and inhibition to the large quantum yields Qe at low temperatures, which is much larger than that at 300K. These results are relevant for application and optimization of PbS QDs in nanophotonics at telecommunication wavelength.

Calculation and fabrication of two-dimensional complete photonic bandgap structures composed of rutile TiO2 single crystals in air/liquid

Photoelectrochemical applications of photonic crystals are gathering great interests both from physicists and chemists. Here, we theoretically and experimentally present two-dimensional photonic bandgap (2D-PBG) structures based on rutile titanium dioxide (TiO2) single crystal that is a famous material because of the photoelectrochemical ability. The structures were the arrays of hollow hexagonal rutile TiO2 pillars in contact with air or a typical nonaqueous electrolyte solution, acetonitrile. Since the TiO2 refractive indices exhibit a strong dispersive behavior, the bandgap width was discussed from the viewpoint of the refractive index map that would be helpful for the real application of this structure. The 2D-PBG structures for both infrared light and visible light were fabricated by our established lithography technique for rutile TiO2 with and without Nb doping, i.e., photocatalytic TiO2 and high electron conductive TiO2, respectively. These structures show characteristic absorbance peaks or reflectance dips at wavelengths predicted by our theoretical calculations.

Highly directed emission from self-assembled quantum dots into guided modes in disordered photonic-crystal waveguides

We explore the dynamics and directionality of spontaneous emission from self-assembled In(Ga)As quantum dots into TE-polarised guided modes in GaAs two-dimensional photonic crystal waveguides. The local group velocity of the guided waveguide mode is probed, with values as low as $\sim 1.5\%\times c$ measured close to the slow-light band edge. By performing complementary continuous wave and time-resolved measurements with detection along, and perpendicular to the waveguide axis we probe the fraction of emission into the waveguide mode ($\beta$-factor). For dots randomly positioned within the unit cell of the photonic crystal waveguide our results show that the emission rate varies from $\geq 1.55$ $ns^{-1}$ close to the slow-light band edge to $\leq 0.25$ $ns^{-1}$ within the two-dimensional photonic bandgap. We measure an average Purcell-factor of $\sim 2\times$ for dots randomly distributed within the waveguide and maximum values of $\beta\sim 90 \%$ close to the slow light band edge. Spatially resolved measurements performed by exciting dots at a well controlled distance $0-45$ {\mu}m from the waveguide facet highlight the impact of disorder on the slow-light dispersion. Although disorder broadens the spectral width of the slow light region of the waveguide dispersion from $\delta E_{d}\leq 0.5$ meV to $>6$ meV, we find that emission is nevertheless primarily directed into propagating waveguide modes. The ability to control the rate and directionality of emission from isolated quantum emitters by placing them in a tailored photonic environment provides much promise for the use of slow-light phenomena to realise efficient single photon sources for quantum optics in a highly integrated setting.

Thermal properties and two-dimensional photonic band gaps

The effect of temperature on a two-dimensional square lattice photonic crystal composed of Si rods arranged in an air background was investigated theoretically using the plane-wave expansion method. Both the thermal expansion effect and thermo-optical effect are considered simultaneously. We have discussed the role of temperature in creating the complete photonic band gap as a function of temperature. Two different shapes of rods, i.e. square and circular, are considered in the presence of the two polarization states, i.e. TE and TM waves. The numerical results show that the photonic band gap can be significantly enlarged compared to the photonic band gap at room temperature. The effect of temperature on the complete photonic band width in the cylindrical rods case is more significant. Cylindrical and square Si rods may work as a temperature sensor or filter, among many other potential applications.

二维光子晶体在液体浓度测量方面的应用研究

利用平面波展开法(Plane Wave Expansion Method)分析了电磁波在二维周期性光子晶体中的传输特性，提出了采用光子晶体平面波展开法测定氯化钾浓度的新方案。并且利用计算机数值模拟了二维光子晶体的带隙变化规律，给出了光子晶体带隙随待测溶液浓度的变化规律和百分浓度测量方面的模拟计算，为二维光子晶体带隙法在液体百分浓度测量方面的实际应用奠定了理论基础。Based on the plane wave expansion method, the propagation of electromagnetic wave in the two- dimensional photonic crystal is analyzed and a new method to measure the concentration of po-tassium chloride using two-dimensional photonic crystal plane wave expansion method is proposed. The transformation law of defective two-dimensional photonic band gap is shown by computer simulation. The simulation calculation of concentration transformation law and percent concentration measurement of photonic band gap (PBG) along with solution under test are given. This provides a theoretical basis for the practical application of two-dimensional photonic crystal band gap method in liquid percent concentration measurement.

增强光子晶体谐振腔模式选择性的方法分析

Based on analyzing the dispersion characteristics and the global band gaps for general two-dimensional photonic band gap structures formed by triangular arrays of metal posts, we select TE04 at 140 GHz as the operational mode and present the modes distribution diagram in different band gaps. By optimizing the operational point, the number of modes competing with TE04 reduces from 5 to 2. On the other hand, the lattice constant and the radius of metal columns are expanded, thus it can bear more thermal loading. Finally, comparisons are made between electric field distributions of TE04 in different band gaps.

The properties of two-dimensional photonic crystals bandgap structure with rhombus lattice

The relative bandgap ωR of photonic crystals structure with rhombus lattice for both TE and TM modes is studied by the plane wave expansion method. Based on the analysis, a bending waveguide of U type can be easily obtained. The steady-state distribution of the electric field with ω=0.4765(a/λ) of TM mode is given by FDTD method and the transmission is obtained by FFT of the time domain field. All of the sufficient analysis shows the conceptual framework of the proposed rhombus lattice PCs and its great potential application in photonic integration circuit.

填充比和格点方向对二维三角晶格光子晶体带隙的影响

填充比和格点方向对二维三角晶格光子晶体带隙的影响

Controlled Spontaneous Emission of Single Molecules in a Two-Dimensional Photonic Band Gap

We have established a new platform to control the rate of spontaneous emission (SE) of organic molecules in the visible-light region using a combination of a two-dimensional (2D) photonic crystal (PC) slab made of TiO(2) and a single-molecule measurement method. The SE from single molecules of a perylenediimide derivative was effectively inhibited via a radiation field controlled by the 2D PC slab, which has a photonic band gap (PBG) for transverse-electric (TE)-polarized light. The fluorescence lifetimes of the single molecules were extended up to 5.5 times (28.6 ns) by the PBG effect. This result appears to be the first demonstration of drastic lifetime elongation for single molecules due to a PBG effect.

Higher-order core-guided modes in two-dimensional photonic bandgap fibers

We numerically and theoretically investigate the core modes of two-dimensional solid-core photonic bandgap (PBG) fibers based on hexagonal arrays of high-index circular rods. Such fibers guide light in discrete bandgaps, and the number of core-guided modes depends on the order of the bandgap as well as the position within the bandgap. We first classify the different core-guided modes in such fibers and we discuss the links among band structure, losses, and number and type of modes. We demonstrate that, similar to the case of bandgapless Kagome and ring-based fibers, solid-core bandgap fibers can have core-guided modes that are within photonic bands of the cladding. We discuss the classification of core modes in such fibers, and highlight analogies and differences with that of index-guiding fibers. Through an asymptotic expansion of an analytic model of a fiber’s photonic bands, we show that, in the limit of higher-order gaps (i.e., short wavelengths), the number of modes in the middle of gaps tends to a constant that is independent of refractive index contrast, as is the case for index-guiding photonic crystal fibers. We also discuss the evolution of the effectively single-mode propagation regime with geometrical parameters of structures having constant or variable band diagrams. For small- and large-core PBG fibers, we compute the exact number of core-guided modes within the center of the transmission band. We discuss their evolution with gap orders and coupling strength between high-index inclusions in the cladding. We find good agreement of the core-guided mode number in the center of the gaps computed with our theoretical model and with a numerical method for short wavelengths.

Buckled colloidal crystals with nonspherical bases for two-dimensional slab photonic band gaps

Theoretical modeling of the photonic band gap forming properties is reported for the buckled phase of anisotropic particles. These exist between the first and second particulate layers of confined colloidal suspensions. Inspired by the range of non-spherical mushroom-cap building blocks for self-assembly that have been synthesized using seeded emulsion-polymerization, we explore in particular the band structures as a function of toroid shape parameter. The parameter is adjusted to incrementally transform hemispheres to spheres. Additionally, corrugation heights that systematically modulate the slab photonic crystal unit cell from rectangular monolayer to square bilayer are investigated. Polarization independent gaps in the guided modes are determined for direct and inverted structures that exhibit bifurcation in the particle orientation perpendicular to the slab plane. Gaps in the guided modes are observed between the fourth and fifth, twelfth and thirteenth, as well as higher band locales as the particle morphology and lattice aspect ratio vary.

Analysis of two-dimensional photonic band gaps of any rod shape and conductivity using a conical-integral-equation method

The conical-boundary-integral-equation method has been proposed for calculation of the sensitive optical response of two-dimensional photonic band gaps (PBGs), including dielectric, absorbing, and high-conductive rods of various shapes working in any wavelength range. It is possible to determine the diffracted field by computing the scattering matrices separately for any grating boundary profile. The computation of the matrices is based on the solution of a 2×2 system of singular integral equations at each interface between two different materials. The advantage of our integral formulation is that the discretization of the integral equation system and the factorization of the discrete matrices, which takes the majority of the computing time, are carried out only once for a boundary. It turns out that a small number of collocation points per boundary combined with a high convergence rate can provide an adequate description of the dependence on diffracted energy of very different PBGs illuminated at arbitrary incident and polarization angles. The numerical results presented describe the significant impact of rod shape on diffraction in PBGs supporting polariton-plasmon excitation, particularly in the vicinity of resonances and at high filling ratios. The diffracted energy response calculated vs the array cell geometry parameters was found to vary from a few up to a few hundred percent. The influence of other types of anomalies (i.e., waveguide anomalies, cavity modes, Fabry-Perot and Bragg resonances, Rayleigh orders, etc.), conductivity, and polarization states on the optical response is demonstrated.

一种光子晶体谐振腔的TM模特性

A model of two-dimensional photonic band gap structures resonant cavity is proposed made by GaAs pillars in air with graphite lattice.Its TMy mode formant wavelength changing with stress and temperature is calculated by finite difference time domain method.The results show that no mater what direction for the stress acting on the resonant cavity,there will be a good linear characteristic between the formant wavelength and the stress,the sensitivity responding to stress is 0.013 69 nm/Mpa.Meanwhile,it is found that the sensitivities responding to stress along x and y direction are the same.There is a sectional linear characteristic between the main formant wavelength and temperature for this kind of photonic crystal resonant cavity,and the biggest sensitivity responding to temperature is 1.4 nm/℃.Furthermore,the results show that there is a make-and break key characteristic for the proposed resonant cavity.

Compact hollow-core photonic band gap resonator with optimised metallic cavity at microwave frequencies

A report is presented on the improvement by an optimised hexagonal metallic cavity of the electromagnetic field confinement in a hollow-core resonator based on out-of-plane two-dimensional photonic band-gap crystal cladding. A resonator was constructed with silica rods to prove the concept at frequencies around 30 GHz. It is shown that the technique can reduce the resonator size by 8.1 times without loss in quality.

Two-dimensional photonic crystal band gap characteristics

The plane wave expansion method is used to calculate the band gap of two-dimensional photonic crystal in the E and H polarization, with Taking into account the effects of filling ratio, lattice structure, and relative dielectric constant ratio on the maximum absolute band gap. The results show that either square or triangular array arrangement, it is easier for the dielectric cylinder type photonic crystal to form TM-polarized mode band gap; while, in the air-hole photonic crystal it is much easier to form TE-polarized-mode band gap. For a given filling ratio, with the increase of relative dielectric constant, the maximum gap width does not always increase, but it is peaked. Similarly, for a given relative dielectric constant, with the increase of filling ratio, it is also peaked for the maximum gap width. Moreover, no matter the erystal is air hole type or dielectric cylinder type in structure, the triangular lattice structure is much easier to form bands gap.