Low group velocity in a photonic crystal coupled-cavity waveguide

A two-dimensional photonic crystal coupled-cavity waveguide is designed and optimized, the transmission spectrum is calculated by using the finite-difference time-domain method, and the group velocity of c/1856 is obtained. To our knowledge, this value of group velocity is the lowest group velocity in a photonic crystal waveguide calculated from its transmission spectrum so far. The result is confirmed by the photonic band structure calculated by using the plane wave expansion method, and it is found that the photonic crystal waveguide modes in a photonic band structure are in accordance with those in the transmission spectrum by using the finite-difference time-domain method. The mechanism of slow light in the coupled-cavity waveguide of photonic crystal is analysed.     

Obtaining the band structure of a complicated photonic crystal by linear operations

Absolute band gaps can be created by lifting the degeneracy in the bands of a photonic crystal.To calculate the band structure of a complicated photoinc crystal generated by e.g.symmetry breaking ,general forms of all possible linear operations are presented in terms of matrices and procedure to combine these operations in given.Other forms of linear operations (Such as the addition,subtraction,and translation transforms)are also presented to obtain an explicit expression for the Fourier coefficient of the dielectric function in the plane-wave expansion method.With the present method,band structures for various complicated photoinc crystals(related through these linear operations)can be obtained easily and quickly.As a numerical example,a large absolute and gap for a complicated photonic crystal structure of GaAs is found in the high reglon of normalized frequency.     

A method of designing photonic crystal grating slow-wave circuit for Ribbon--Beam microwave travelling wave amplifiers

A method of designing a photonic crystal grating slow-wave circuit in which the cylinders of the 2D photonic crystals dot on a cross-sectional plane is established by calculating the band structures of the 2D photonic crystals, and the eigenfrequency of the equivalent waveguide grating. For calculating the band structures, the eigenvalue equations of the photonic crystals in the system of photonic crystal grating slow-wave circuit are derived in a special polarization mode. Two examples are taken to show the method. The design result is validated by the scattering parameters of the same circuit. The result indicates that there exists no photonic band gap if the metal gratings do not extend into the photonic crystals; the design of the circuit without the metal gratings extending into the photonic crystals is less flexible than that with the metal gratings extending into the photonic crystals.     

Tunable negative-index photonic crystals using colloidal magnetic fluids

The model of using colloidal magnetic fluid to build tunable negative-index photonic crystal is established. The effective permittivity εe and permeability μe of the two-dimensional photonic crystal are investigated in detail. For transverse magnetic polarization, both εe and μe exhibit a Lorentz-type anomalous dispersion, leading to a region where εe and μe are simultaneously negative. Then, considering a practical case, in which the thickness of photonic crystal is finite, the band structures for odd modes are calculated by the plane wave expansion method and the finite-difference time-domain method. The results suggest that reducing the external magnetic field strength or slab thickness will weaken the periodic modulation strength of the photonic crystal. Simulation results prove that the negative-index can be tuned by varying the external magnetic field strength or the slab thickness. The work presented in this paper gives a guideline for realizing the flat photonic crystal lens with tunable properties at optical frequencies, which may have potential applications in tunable near-field imaging systems.     

Analysis of two-dimensional photonic band gap structure with a rhombus lattice

The relative band gap for a rhombus lattice photonic crystal is studied by plane wave expansion method and high frequency structure simulator(HFSS)simulation.General wave vectors in the first Briliouin zone are derived.The relative band gap as a function of air-filling factor and background material is investigated,respectively,and the nature of photonic band gap for different lattice angles is analyzed by the distribution of electric energy.These results would provide theoretical instruction for designing optical integrated devices using photonic crystal with a rhombus lattice.     

Analysis of two-dimensional photonic band gap structure with a rhombus lattice

The relative band gap for a rhombus lattice photonic crystal is studied by plane wave expansion method and high frequency structure simulator (HFSS) simulation. General wave vectors in the first Briliouin zone are derived. The relative band gap as a function of air-filling factor and background material is investigated, respectively, and the nature of photonic band gap for different lattice angles is analyzed by the distribution of electric energy. These results would provide theoretical instruction for designing optical integrated devices using photonic crystal with a rhombus lattice.     

A novel method of rapidly modeling optical properties of actual photonic crystal fibres

<正>The flexible structure of photonic crystal fibre not only offers novel optical properties but also brings some difficulties in keeping the fibre structure in the fabrication process which inevitably cause the optical properties of the resulting fibre to deviate from the designed properties.Therefore,a method of evaluating the optical properties of the actual fibre is necessary for the purpose of application.Up to now,the methods employed to measure the properties of the actual photonic crystal fibre often require long fibre samples or complex expensive equipments.To our knowledge, there are few studies of modeling an actual photonic crystal fibre and evaluating its properties rapidly.In this paper,a novel method,based on the combination model of digital image processing and the finite element method,is proposed to rapidly model the optical properties of the actual photonic crystal fibre.Two kinds of photonic crystal fibres made by Crystal Fiber A/S are modeled.It is confirmed from numerical results that the proposed method is simple,rapid and accurate for evaluating the optical properties of the actual photonic crystal fibre without requiring complex equipment.     

Broadband Frequency Down-Conversion Using Coupled Cavity Structures in One-Dimensional Photonic Crystals

The frequency down-conversion of one-dimensional photonic crystals with the coupled cavity structure is investigated by the nonlinear finite-difference time-domain method. The efficient frequency conversion is obtained by utilizing the advantages of the broad eigenfrequency band, the strong localization and the Bloch phase matching of the coupled cavity structure. More importantly, the signal frequency could be tuned continuously within the whole band of the coupled cavity structure （with a bandwidth to central frequency ratio of 5.4%）, and the gains are homogeneous in the band.     

Broad Omnidirectional Reflection Band Forming using the Combination of Fibonacci Quasi－Periodic and Periodic One－Dimensional Photonic Crystals

By combining two Fibonacci quasi-periodic structures and a periodic structure to form a heterostructure, abroad omnidirectional reflection band is obtained. From the numerical results performed by the transfer matrixmethod, it is found that the reflection bands of the two Fibonacci quasi-periodic sub-structures and the periodicsub-structure can be compensated for each other. This method is expected to be useful in constructing a one-dimensional quasi-periodic photonic crystal structure with a broad omnidirectional reflection band.     

Degeneracy and Split of Defect States in Photonic Crystals

One-dimensional photonic crystals with two or more structural defects are studied. We observed an interesting characteristic of transmission band structure of photonic crystals with defects using the transmission-matrix-method simulation. The transmission states in the wide photonlc band gap caused by defects reveal degeneracy and split in certain conditions. Every split state is contributed by coupling of all defects in a photonic crystal.Using the tight-binding method, we obtain an approximate analytic expression for the split frequency of photonic crystals with two structural defects.     

Near-field imaging of a square-lattice metallic photonic-crystal slab at the second band

Imaging properties of a two-dimensional photonic crystal slab lens are investigated through the finite-difference time-domain method. In this paper, we consider the photonic crystal slab consisting of a square lattice of square metallic rods immersed in a dielectric background. Through the analysis of the equifrequency-surface contours and the field patterns of a point source placed in the vicinity of the photonic crystal slab, we find that a good-quality image can form at the frequencies in the second TM-polarized photonic band. Comparing the images formed at different frequencies, we can clearly see that an excellent-quality image is formed by the mechanisms of simultaneous action of the self-collimation effect and the negative-refraction effect.     

Photonic Crystal Polarizing and Non-Polarizing Beam Splitters

A polarizing beam splitter （PBS） and a non-polarizing beam splitter （NPBS） based on a photonic crystal （PC） directional coupler are demonstrated. The photonic crystal directional coupler consists of a hexagonal lattice of dielectric pillars in air and has a complete photonic band gap. The photonic band structure and the band gap map are calculated using the plane wave expansion （PWE） method. The splitting properties of the splitter are investigated numerically using the finite difference time domain （FDTD） method.     

Fabrication of High Quality Three-Dimensional Photonic Crystals

High quality colloidal photonic crystals made from polystyrene spheres with diameter 24Ohm are fabricated by the vertical deposition method. The scanning electron microscopy (SEM) and the transmittance spectrum are used to characterize the properties of the photonic crystal. The SEM images show that there are few lattice defects. The transmittance of the photonic crystal is above 75% in the pass band at 700nm and is lower than 5% at the centre of the band gap, respectively. It is found that proper concentration is a very important factor to fabricate the photonic crystal when the diameter of the spheres is lower than 30Onm.     

Polarization Beam Splitter Based on Self-Collimation Effect in Two-Dimensional Photonics Crystal

A photonic crystal polarization beam splitter based on the self-collimation effect is proposed. By means of the plane wave expansion method and the finite-difference time-domain method, we analyse the splitting mechanism in two alternative ways： performing a band gap structure analysis and simulating the field distribution. The results indicate that two beams of different polarizations can be split with an extinction ratio of nearly 20 dB in a wavelength range of POnm. The splitter may have practical applications in integrated photonic circuits.     

Fabrication of a Two-Dimensional Organic Photonic Crystal

A high-quality two-dimensional polystyrene photonic crystal is fabricated by the method of focused ion beam etching. The scanning electron microscopy (SEM) and the transmittance spectrum are used to characterize the properties of the photonic crystal. The measured transmittance spectrum is in agreement with the theoretical one. The influences of the disorders caused by the random perturbations in the diameter or the position of the air holes on the photonic band structure are analysed. It is found that the phtonic bandgap can tolerate less than 10% degree of disorder.     

Positive-negative birefraction phenomenon for TM polarization in annular photonic crystal

We propose a two-dimensional (2D) annular photonic crystal (APC) with dual equi-frequency contours (EFCs) in one band. The refractive behaviors of a Gaussian beam incident from air to the APC are analyzed by the EFC analysis and finite-diflerence time-domain (FDTD) method. The results show the positive-negative birefraction phenomenon for the transverse magnetic (TM) polarization in the same band occurs at the interface between air and the APC, and the surface termination of the APC has a large effect on the strength of the negatively refracted beam.     

Symmetric and Anti-Symmetric Lamb Waves in a Two-Dimensional Phononic Crystal Plate

It is weft known that Lamb waves in a plate with a mirror plane can be separated into two uncoupled sets： symmetric and anti-symmetric modes. Based on this property, we present a revised plane wave expansion method （PWE） to calculate the band structure of a phononie crystal （PC） plate with a mirror plane. The developed PWE method can be used to calculate the band structure of symmetric and anti-symmetric modes separately, by which the depending relationship between the partial acoustic band gap （PABG）, which belongs to the symmetric and anti-symmetric modes alternatively, and the position of the scatterers can be determined. As an example of its application, the band structure of the Lamb modes in a two-dimensional PC plate with two layers of void circular inclusions is investigated. The results show that the band structure for the symmetric and anti-symmetric modes can be changed by the position of the scatterers drastically, and larger PABGs will be opened when the scatterers are inserted into the area of the plate, where the elastic potential energy is concentrated.     

Absolute band gaps in two-dimensional graphite photonic crystal

The off-plane propagation of electromagnetic (EM) waves in a two-dimensional (2D) graphite photonic crystal structure was studied using transfer matrix method. Transmission spectra calculations indicate that such a 2D structure has a common band gap from 0.202 to 0.2035 c/a for both H and E polarizations and for all off-plane angles form 0° up to 90°. The presence of such an absolute band gap implies that 2D graphite photonic crystal, which is much easier and more feasible to fabricate, can exhibit some properties of a three-dimensional (3D) photonic crystal.     

Negative Refraction and Near-Field Imaging of an Elliptical-Rod Photonic Crystal Slab in the Second Band

Negative refraction and imaging properties of the electromagnetic wave through a two-dimensional photonic crystal （PC） slab, which consists of a square lattice of elliptical dielectric rods immersed in the air background, is studied by the plane-wave expansion method and the finite-difference time-domain method. A point source placed in the vicinity of the PC slab can form a good-quality image spot through the PC slab for the incident frequencies within the second photonic band. The calculated result also shows that negative refraction occurs in this kind of PC slab.     

Bragg reflection in a quantum periodic structure

We investigate the reflected field for few-cycle ultra-short laser pulses propagating through resonant media embedded within wavelength-scale structures. Full-wave Maxwell–Bloch equations are solved numerically by using the finite-difference time-domain method. The results show that the spectral feature of the reflected spectrum is determined by the Bragg reflection condition, and that the periodic structure of a dense atomic system can be regarded as a one-dimensional photonic crystal and even as a highly reflective multilayer film. Our study explains the suppression of the frequency shifts in the reflected spectrum based on the Bragg reflection theory and provides a method to control the frequency and frequency intervals of the spectral spikes in the reflected spectrum.