Photonic band structures of two-dimensional photonic crystals with deformed lattices

Using the plane-wave expansion method, we have calculated and analysed the changes of photonic band structures arising from two kinds of deformed lattices, including the stretching and shrinking of lattices. The square lattice with square air holes and the triangular lattice with circular air holes are both studied. Calculated results show that the change of lattice size in some special ranges can enlarge the band gap, which depends strongly on the filling factor of air holes in photonic crystals; and besides, the asymmetric band edges will appear with the broken symmetry of lattices.

The single-longitudinal-mode operation of a ridge waveguide laser based on two-dimensional photonic crystals

An electrically driven, single-longitudinal-mode GaAs based photonic crystal （PC） ridge waveguide （RWG） laser emitting at around 850 nm is demonstrated. The single-longitudinal-mode lasing characteristic is achieved by introducing the PC to the RWG laser. The triangle PC is etched on both sides of the ridge by photolithography and inductive coupled plasma （ICP） etching. The lasing spectra of the RWG lasers with and without the PC are studied, and the result shows that the PC purifies the longitudinal mode. The power per facet versus current and current-voltage characteristics have also been studied and compared.

Application of Fourier Series Expansion Method with PMLs to the Microcavities on Two-Dimensional Photonic Crystals

By using a Fourier series expansion method combined with Chew＇s perfectly matched layers （PMLs）, we analyze the frequency and quality factor of a micro-cavity on a two-dimensional photonic crystal is analyzed. Compared with the results by the method without PML and finite-difference time-domain （FDTD） based on supercell approximation, it can be shown that by the present method with PMLs, the resonant frequency and the quality factor values can be calculated satisfyingly and the characteristics of the micro-cavity can be obtained by changing the size and permittivity of the point defect in the micro-cavity.

Germanium Based Two-Dimensional Photonic Crystals: The Hexagonal and Honeycomb Lattices

The properties of two-dimensional (2D) photonic crystals (PCs) composed of germanium (Ge) are discussed. We investigate polarization-dependent photonic band diagrams (transverse electric and transverse magnetic polarizations), gap maps, surface plots, contour maps, etc. for 2D PCs with Ge rods in air and vice versa for two different lattices geometries, namely hexagonal and honeycomb lattices. The obtained graphs for the four possible combinations are presented in this paper. All the graphs depict clear photonic band gaps. The conditions for the largest TE and TM band gaps are described. The honeycomb lattice of Ge rods in air background offers a large complete photonic band gap Δω/ωm greater than 8% (for rod radius of r = 0.2 μm). Using these data, new Ge based photonic devices can be fabricated to confine, control and manipulate light in a more useful way.

Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals

Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.

A compact T-branch beam splitter based on anomalous reflection in two-dimensional photonic crystals

We project a compact T-branch beam splitter with a micron scale using a two-dimensional （2D） photonic crystal （PC）. For TE polarization, one light beam can be split into two sub-beams along opposite directions. The propagating directions of the two splitting beams remain unchanged when the incident angle varies in a certain range. Coupled-mode theory is used to analyze the truncating interface structure in order to investigate the energy loss of the splitter. Simulation results and theoretical analysis show that choosing an appropriate location of the truncating interface （PC-air interface） is very important for obtaining high efficiency due to the effect of defect modes. The most advantage of this kind of beam splitter is being fabricated and integrated easily.

Comment on “Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals” by Si-Qi Zhang et al.

Recently, Zhang et al. （Chin. Phys. B 26 024208 （2017）） investigated the band gap structures and semi-Dirac point of two-dimensional function photonic crystals, and the equations for the plane wave expansion method were induced to obtain the band structures. That report shows the band diagrams with the effects of function coefficient k and medium column ra under TE and TM waves. The proposed results look correct at first glance, but the authors made some mistakes in their report. Thus, the calculated results in their paper are incorrect. According to our calculations, the errors in their report are corrected, and the correct band structures also are presented in this paper.

Numerical study on characteristic of two-dimensional metal/dielectric photonic crystals

An improved plan-wave expansion method is adopted to theoretically study the photonic band diagrams of twodimensional（2D） metal/dielectric photonic crystals.Based on the photonic band structures,the dependence of flat bands and photonic bandgaps on two parameters（dielectric constant and filling factor） are investigated for two types of 2D metal/dielectric（M/D） photonic crystals,hole and cylinder photonic crystals.The simulation results show that band structures are affected greatly by these two parameters.Flat bands and bandgaps can be easily obtained by tuning these parameters and the bandgap width may reach to the maximum at certain parameters.It is worth noting that the hole-type photonic crystals show more bandgaps than the corresponding cylinder ones,and the frequency ranges of bandgaps also depend strongly on these parameters.Besides,the photonic crystals containing metallic medium can obtain more modulation of photonic bands,band gaps,and large effective refractive index,etc.than the dielectric/dielectric ones.According to the numerical results,the needs of optical devices for flat bands and bandgaps can be met by selecting the suitable geometry and material parameters.

The Photonic Band Gaps in the Two-Dimensional Plasma Photonic Crystals with Rhombus Lattice

In this paper,under two different electromagnetic modes,the photonic band gaps（PBGs） in the two-dimensional plasma photonic crystals（PPCs） are theoretically investigated based on the plane wave expansion method.The proposed PPCs are arranged in rhombus lattices,in which the homogeneous unmagnetized plasma rods are immersed in the isotropic dielectric background.The computed results showed that PBGs can be easily tuned by the angle of rhombus lattices,and a cutoff frequency and a flatbands region can be observed under the TM and TE polarized waves,respectively.The relationships between the relative bandwidths of first PBGs and the parameters of PPCs in two such cases also are discussed.The numerical simulations showed that the PBGs can be manipulated obviously by the parameters as mentioned above.The proposed results can be used to design the waveguide and filter based on the PPCs.

Low Frequency Dispersion Law for Two-Dimensional Metallic Photonic Crystals

Using the rigorous multiple-scattering theory, we study the dispersion relation of electromagnetic （EM） waves in two dimensional dielectric photonic crystals （PCs） and metallic photonic crystals （MPCs） in the low-frequency limit. Analytic formula for the effective velocity of EM waves in PCs and MPCs is obtained. Accuracy of our formula is checked by comparing the results with rigorous calculations. For PCs, our result is exactly the same as the coherent potential approximation （CPA）, which is accurate even when the filling fraction is high. But for MPCs, our approach demonstrates special advantages, while the CPA theory fails, in predicting the effective velocity of EM waves in MPCs at low frequency.

Tunability of Photonic Band Gaps in One- and Two-dimensional Photonic Crystals Based on ZnS Particles Embedded in TiO2 Matrix

Using the Maxwell-GarneR theory, the evolution of the refractive index of titanium dioxide （TiO2） doped with zinc sulfide （ZnS） particles is presented. The presence of the nano-objects in the host matrix allows us to obtain a new composite material with tunable optical properties. We find that the filling factor of ZnS nanoparticles greatly alters photonic band gaps （PBGs）. We have calculated also the photonic band structure for electromagnetic waves propagating in a structure consisting of ZnS rods covered with the air shell layer in 2D hexagonal and square lattices by the finite difference time domain （FDTD） method. The rods are embedded in the TiO2 background medium with a high dielectric constant. Such photonic lattices present complete photonic band gaps （CPBGs）. Our results show that the existence of the air shell layer leads to larger complete photonic gaps. We believe that the present results are significant to increase the possibilities for experimentalists to realize a sizeable and larger CPBG.

The Absorbing Properties of Two-Dimensional Plasma Photonic Crystals

Plasma photonic crystals composed of periodic plasma and dielectric materials have attracted considerable attention because of their tunable photonic band gaps,but only their band structures or negative refractive index properties have been addressed in previous works.In this paper,through studying the transmission and reflection characteristics of two types of twodimensional plasma photonic crystals,it is found that plasma photonic crystals play an important role in absorbing waves,and they show broader band and higher amplitude absorption characteristics than bulk plasmas.Also,the absorption of plasma photonic crystals can be tuned via plasma parameters;varying the collision frequency can make the bandwidth and amplitude tunable,but cannot change the central frequency,whereas varying the plasma frequency would control both the location and the amplitude of the absorbers.These features of plasma photonic crystals have potential for terahertz tunable absorber applications.

Reconfigurable(4, 6^(2)) and(4, 8^(2)) Archimedean plasma photonic crystals in dielectric barrier discharge

Archimedean photonic crystal has become a research area of great interest due to its various unique properties. Here, we experimentally demonstrate the realization of reconfigurable(4, 6^(2))and(4, 8^(2)) Archimedean plasma photonic crystals(APPCs) by use of dielectric barrier discharges in air. Dynamical control on both the macrostructures including the lattice symmetry and the crystal orientation, and the microstructures including the fine structures of scattering elements has been achieved. The formation mechanisms of APPCs are studied by time-resolved measurements together with numerical simulations. Large omnidirectional band gaps of APPCs have been obtained. The tunable topology of APPCs may offer new opportunities for fabricating multi-functional and highly-integrated microwave devices.

Topological edge and corner states of valley photonic crystals with zipper-like boundary conditions

We present a stable valley photonic crystal(VPC)unit cell with C_(3v)symmetric quasi-ring-shaped dielectric columns and realize its topological phase transition by breaking mirror symmetry.Based on this unit cell structure,topological edge states(TESs)and topological corner states(TCSs)are realized.We obtain a new type of wave transmission mode based on photonic crystal zipper-like boundaries and apply it to a beam splitter assembled from rectangular photonic crystals(PCs).The constructed beam splitter structure is compact and possesses frequency separation functions.In addition,we construct a box-shaped triangular PC structures with zipper-like boundaries and discover phenomena of TCSs in the corners,comparing its corner states with those formed by other boundaries.Based on this,we explore the regularities of the electric field patterns of TESs and TCSs,explain the connection between the characteristic frequencies and locality of TCSs,which helps better control photons and ensures low power consumption of the system.

Characteristics of local photonic state density in an infinite two-dimensional photonic crystal

The local density of photonic states （LDPS） of an infinite two-dimensional （2D） photonic crystal （PC） composed of rotated square-pillars in a 2D square lattice is calculated in terms of the plane-wave expansion method in a combination with the point group theory. The calculation results show that the LDPS strongly depends on the spatial positions. The variations of the LDPS as functions of the radial coordinate and frequency exhibit “mountain chain” structures with sharp peaks. The LDPS with large value spans a finite area and falls abruptly down to small value at the position corresponding to the interfaces between two different refractive index materials. The larger/lower LDPS occurs inward the lower/larger dielectric-constant medium. This feature can be well interpreted by the continuity of electricdisplacement vector at the interface. In the frequency range of the pseudo-PBG （photonic band gap）, the LDPS keeps very low value over the whole Wiger-Seitz cell. It indicates that the spontaneous emission in 2D PCs cannot be prohibited completely, but it can be inhibited intensively when the resonate frequency falls into the pseudo-PBG.

Photonic Band Modulation in a Two-Dimensional Photonic Crystal with a One-Dimensional Periodic Dielectric Background

A two-dimensional photonic crystal with a one-dimensional periodic dielectric background is proposed. The photonic band modulation effects due to the periodic background are investigated based on the plane wave expansion method. We find that periodic modulation of the dielectric background greatly alters photonic band structures, especially for the E-polarization modes. The number, width and position of the photonic band gaps （PBGs） sensitively depend on the structure parameters （the layer thicknesses and dielectric constants） of the one-dimensional periodic background,

Dispersion characteristics of two-dimensional unmagnetized dielectric plasma photonic crystal

This paper studies dispersion characteristics of the transverse magnetic （TM） mode for two-dimensional unmagnetized dielectric plasma photonic crystal by a modified plane wave method. First, the cutoff behaviour is made clear by using the Maxwell-Garnett effective medium theory, and the influences of dielectric filling factor and dielectric constant on effective plasma frequency are analysed. Moreover, the occurence of large gaps in dielectric plasma photonic crystal is demonstrated by comparing the skin depth with the lattice constant, and the influence of plasma frequency on the first three gaps is also studied. Finally, by using the particle-in-cell simulation method, a transmission curve in the Г - X direction is obtained in dielectric plasma photonic crystal, which is in accordance with the dispersion curves calculated by the modified plane wave method, and the large gap between the transmission points of 27 GHz and 47 GHz is explained by comparing the electric field patterns in particle-in-cell simulation.

Influence of disorder and deformation on the optical properties of a two-dimensional photonic crystal waveguide

We investigate the effect of disorder and mechanical deformation on a two-dimensional photonic crystal waveguide. The dispersion characteristics and transmittance of the waveguide are studied using the finite element method. Results show that the geometric change of the dielectric material perpendicular to the light propagation direction has a larger influence on the waveguide characteristics than that parallel to the light propagation direction. Mechanical deformation has an obvious influence on the performance of the waveguide. In particular, longitudinal deformed structure exhibits distinct optical characteristics from the ideal one. Studies on this work will provide useful guideline to the fabrication and practical applications based on photonic crystal waveguides.

Influence of line defects on focusing in a two-dimensional photonic-crystal flat lens

We investigate in detail the influence of line defects on focusing of electromagnetic waves in a two-dimensional photonic-crystal flat lens. Through simulations, we find that a focusing can always be observed when a line defect in the lens is introduced along the light transmission direction and the width of the line defect is less than λ/2. However, there appear two focusings when the width of the line defect is more than λ/2. When the line defect is introduced along the direction perpendicular to the transmission, there is always one focusing.

Momentum-space polarization fields in two-dimensional photonic-crystal slabs:Physics and applications

In addition to non-radiative guided modes, two-dimensional photonic-crystal slabs support guided resonant ones which can radiate into free space. From the polarization states of these guided resonances, a polarization field on a photonic band can be constructed in momentum space. Momentum-space polarization fields display complicated configurations and patterns with different types of polarization singularities inside, shedding new light on the manipulations of light flows.In this review, we summarize the recent research progress on momentum-space polarization fields and singularities in two-dimensional photonic-crystal slabs, focusing on their unique optical properties and potential applications as well.