Improving unrestricted imaging quality of a triangular lattice photonic crystal slab by modifying surface configuration

We propose a photonic crystal (PC) structure only by replacing square lattice [Luo et al. (2002) [12]] with triangular lattice to obtain an unrestricted imaging. Equal-frequency contours (EFCs) analysis shows that this triangular lattice two-dimensional PC exhibits an effective isotropic refractive index n_eff=−1 at a normalized frequency ω=0.291×2πc/a. Imaging quality of this triangular lattice PC slab involving both power intensity and full-width at half-maximum intensity of the image is studied using the finite-difference time-domain (FDTD) simulation. In order to achieve a high-quality image, an appropriate surface termination is chosen. In addition, by adjusting the surface air-hole radius of the PC slab, the imaging quality can be further improved. Coupled-mode theory analysis shows that the optimized surface termination and the adjusted surface air-hole can excite two kinds of surface modes that can couple with the Bloch wave in the PC. With the help of these surface modes, both the intensity of image and the super-resolution capacity of this triangular lattice PC slab can be improved greatly.     

Improving the imaging intensity of a photonic crystal flat lens by an antireflection method

In this paper, a two-dimensional photonic crystal (PC) consisting of a triangular lattice of silicon rods in air is studied theoretically. Equal-frequency contours (EFCs) analysis shows that this PC structure exhibits an effective refractive index n_eff = −1 at a normalized frequency ω=0.30×2πc/a$\omega =0.30\times 2\pi c/a$. A superlens effect is demonstrated using this PC structure by the finite-difference time-domain (FDTD) simulation. An antireflection layer (ARL) is introduced into the PC slab surface in order to achieve a high-intensity image. Two point sources imaging process is also simulated both in the case of a perfect PC structure and in the case of a PC structure with an ARL. The results show that the method of introducing the ARL into the PC surface is effectual for improving both the intensity of the image and the capability of the super-resolution of two sources, which are in accord with the coupled-mode theory analysis. Theoretical study implies that the surface defect modes play an important role in enhancing the transmitted intensity of energy flow.     

Design of photonic crystal superlens with improved image resolution

In this paper, we theoretically investigate the spatial resolution of a triangular two-dimensional photonic crystal superlens. We prove that this resolution can be improved by optimizing the air hole radius as well as the air hole shape. First, it is found that by decreasing the radius of the air holes, the spatial resolution is improved significantly. Next, we demonstrate that using elliptic air holes instead of circular air holes in a triangular two-dimensional photonic crystal can leads to good-quality images and focusing, with effective refractive index n_eff=−1 and enhanced image resolution. It is also shown that for the case of two sources, the resolution of such a photonic crystal lens can be made indeed better than the radiation wavelength.     

Negative refraction and imaging beyond the diffraction limit by a two-dimensional left-handed metamaterial

We report our experimental results on two-dimensional left-handed metamaterials (LHM) exhibiting negative refraction and subwavelength imaging. Transmission and reflection spectra of LHM are studied and a left-handed transmission band is observed at the frequencies where both dielectric permittivity and magnetic permeability are negative. Impedance matching is verified both with the experiments and simulations. The two-dimensional LHM structure is verified to have a negative refractive index. We employed three different methods to observe negative refraction; refraction through prism-shaped LHM, beam shifting method, and phase shift experiments. We further demonstrated subwavelength imaging and resolution using LHM superlenses. The effect of thickness on the resolving power is investigated experimentally.     

The beam splitting in the photonic crystal at a degenerate state

In this paper, using the plane-wave expansion and finite difference time-domain methods, the photons behavior in the photonic crystal is investigated. Theoretically, when a polarized wave is incident from the background medium to the photonic crystal, the beam propagation directions in the photonic crystal determined by two methods are approximately same. But in this paper, the results exhibit that there is an additional direction obtained by the finite difference time-domain method compared with the plane-wave expansion. Considering basic physical mechanism of the photon behavior, the present work circumvents the electromagnetic field distribution in the photonic crystal at a degenerate state, which can reasonably explain the phenomenon. Finally, it shows that a photonic crystal can be properly designed to achieve double refraction simultaneously at one frequency, which can also offer new thoughts and foundation for the novel beam splitter that applied to many optical systems.     

Physics and applications of photonic crystals

In this article, we investigate how the photonic band gaps and the variety of band dispersions of photonic crystals can be utilized for various applications and how they further give rise to completely novel optical phenomena. The enhancement of spontaneous emission through coupled cavity waveguides in a one-dimensional silicon nitride photonic microcrystal is investigated. We then present the highly directive radiation from sources embedded in two-dimensional photonic crystals. The manifestation of novel and intriguing optical properties of photonic crystals are exemplified experimentally by the negative refraction and the focusing of electromagnetic waves through a photonic crystal slab with subwavelength resolution.     

Analysis on the efficiency of parallel FDTD method and its application in two-dimensional photonic crystal

A new kind of parallel finite-difference time-domain (FDTD) method is used to calculate and analyze the transmission properties of photonic crystal. The effectiveness and the accuracy of parallel FDTD method were proved by the typical two-dimensional sine wave. The result shows that parallel FDTD method, which can save time effectively in electromagnetic problems with large size and long time, performs as accurate as the series one. This method, whose results shows that the photonic band gap normalized frequency moves to the low-frequency direction with the enlargement of the section area of the square cylinder and that the band gap gets thinner, is applied to simulate and analyze the two-dimensional photonic crystal and gives calculating method and analyzing accordance to calculate and analyze large-sized photonic crystal structure.     

FDTD simulation of time varying optical vortex phenomena in SOI photonic crystal structures

In this paper we analyze the time varying optical vortex phenomena in the gain photonic crystals built on the silicon-on-insulator (SOI) wafer by using the finite difference time domain (FDTD) method. With launching the optical waves in 1.55 μm wavelength to the SOI rib waveguide, optical vortices are generated and the spinning details are observed at various time steps. The analysis results are helpful to understand the progress of optical vortices which may be utilized for the development of future nonlinear optical switches.     

Complete analysis of photonic crystal fibers by full-vectorial 2D-FDTD method

In this paper, an extended finite difference time domain (FDTD) algorithm for the full-vectorial analysis of photonic crystal fibers has been derived. For achieving a good convergence and high accuracy, a kind of modified conformal FDTD method has been applied. An anisotropic perfectly matched layer for truncation of boundary conditions has been introduced. Material and chromatic dispersions are numerically investigated for the photonic crystal fibers with different dimensions and geometrical parameters and different dispersion behaviors are exhibited.     

Ternary photonic crystal with left-handed material layer for refractometric application

A ternary photonic crystal with left-handed material (LHM) layer is examined for refractometric applications. One of the layers is assumed to be air and treated as an analyte. The transmittance from the ternary photonic crystal is studied in details and the wavelength shift due to the change in the refractive index of the analyte is investigated. The transmittance is investigated with the parameters of the LHM. It is found that the wavelength shift can be significantly enhanced with the decrease of both real part of the LHM permittivity and thickness.     

Contra-directional coupling between two-dimensional photonic crystal waveguides

The contra-directional coupling between two photonic crystal (PC) waveguides is studied, using the finite-difference time-domain (FDTD) method. A design of contra-directional coupler is presented and its transmission properties are investigated. The device can be used as an add/drop filter. It is also shown that the coupled mode theory is suitable to study the photonic crystal waveguide coupler.     

Application of fast Pade approximation in simulating photonic crystal nanocavities by FDTD technology

The exact calculation of mode quality factor Q is a key problem in the design of high-Q photonic crystal nanocavity. On the basis of further investigation on conventional Pade approximation, FDM and DFT, Pade approximation with Baker’s algorithm is enhanced through introducing multiple frequency search and parabola interpolation. Though Pade approximation is a nonlinear signal processing method and only short time sequence is needed, we find the different length of sequence requirements for 2D and 3D FDTD, which is very important to obtain convergent and accurate results. By using the modified Pade approximation method and 3D FDTD, the 2D slab photonic crystal nanocavity is analyzed and high-Q multimode can be solved quickly instead of large range high-resolution scanning. Monitor position has also been investigated. These results are very helpful to the design of photonic crystal nanocavity devices.     

Cloaking and imaging effects in plasmonic checkerboards of negative and and dielectric photonic crystal checkerboards

Negative refractive index materials are known to be able to support a host of surface plasmon states for both polarizations of light. This makes possible unique effects such as a perfect lens. Checkerboards consisting of alternating cells of positive and negative refractive index represent a very singular situation in which the density of modes diverges at the corners. This raises the question as to whether such effects will still be observed in a real dissipative system of finite size. We have considered several aspects of such structures including these and symmetry aspects (rectangular against triangular checkerboards). We have also studied silver checkerboards whose transverse extent is finite. Negative refractive index checkerboards bring new electromagnetic paradigms both through the intriguing possibilities they appear to offer, and the challenges they present to our understanding of the diffraction process. Most intriguing of all is the possibility of a triangular checkerboard lens whose resolution is limited not by wavelength, but only by the losses in the constituent materials, while a ray picture suggests it behaves as a perfect mirror. The resolution of this lens increases without limit as the losses tend to zero as shown by the generalized lens theorem. We finally show that light confinement can be achieved to certain extent using dielectric triangular photonic crystal (PC) checkerboards displaying the all-angle-negative-refraction (AANR) within the Bragg regime in p polarization. Effectively even a single rectangular or triangular PC can act as an open resonator that confines light in its neighborhood. This cloaking effect has been previously observed in PC slabs displaying the AANR effect. We show that the cloaking is enhanced for three triangular PC wedges sharing a vertex and further improved for 12 triangular PC wedges arranged in a checkerboard fashion.     

FDTD analysis of out-of-plane propagation in 12-fold photonic quasi-crystals

The out-of-plane propagation characteristics of an infinitely extended 12-fold photonic quasi-crystal structure is modeled using the FDTD technique. The quasi-crystal pattern is designed using the dual beam multiple exposure holographic lithography system previously reported. Simulations indicate that two types of mode families are possible; “bandgap guided” and; “index guided”. Results are presented showing mode profiles; effective index versus propagation constant and wavelength plots; and modal attenuation due to power leakage. Potential applications include a new novel micro-structured optical fiber.     

High-Q microcavities realized in a circular photonic crystal slab

A series of microcavities in circular photonic crystal slabs are studied in this paper. It is shown that high quality factors can be obtained for such microcavities. For a cavity with three inner layers of air holes missing, Q factor larger than 10⁵ can be obtained. It is also worth noting there exists resonant modes with high quality factors, even for the defect-free circular photonic crystal slab, due to gradual change of the average effective index.     

Electromagnetic field in a slab of photonic crystal by BPM

The finite-difference vector beam propagation method is used to simulate propagation of Gaussian light beam in a finite slab of photonic crystal. A possibility to control light flow by the change of symmetry and polarisation of the incident light beam is demonstrated.     

不对称左手介质平板波导模式特性分析

对不对称左手介质平板波导的几个低阶的TE模和TM模进行了数值计算,得到了模式特征方程,分析了归一化传播常数β/k_0随平板厚度d变化的色散关系,作出了模式的电场E_y(x)分布．在左手介质平板波导中,每一模式都有截止点, TE_0模和TM_0模不出现,在我们给出的特定的介质参数下,TE_1模和TM_1模不能和其他高阶模式共存,其归一化传播常数β/ k_0随k_0d的增加而减小．给出的结果对左手介质元器件的研究有实际的参考意义．     

Theoretical study on biosensing characteristics of heterostructure photonic crystal ring resonator

In this paper, we investigate the biosensing characteristics of two-dimensional heterostructure photonic crystals (PCs) ring resonator theoretically by using the finite difference time domain (FDTD). The coupling air holes and inner air holes of ring resonator are treated as coupled sensing area and internal sensing area. When both of the sensing areas are filled with the same biological samples solution, the resonant peak wavelength shift of the ring resonance is different. Both the resonant peak center wavelength and peak intensity are related to the positions of sensing holes. With the same refractive index change of the biological sample, the sensing sensitivity of the coupling sensing area is much higher than that of the inner sensing area. Meanwhile, through the analysis of resonant peak wavelength shift, the refractive index change of the sample filled in the sensor area can be derived, which can be monitored real-time.     

基于非分裂FDTD的左手介质电磁特性的研究

为验证左手介质的电磁特性,采用非分裂时域有限差分方法对左手介质的Drude模型进行建模.这种方法不需要对电场和磁场进行分裂,也不需要对PML空间进行特殊处理,吸收边界PML和工作空间可以通过参数转换来完成,并且构造的PML层为有耗介质,进入PML层的透射波将迅速衰减.它是一种准确而有效的分析色散和各向异性介质的方法,通过此方法有效地验证了左手介质的负折射效应、汇聚效应、相位补偿效应,充分验证了左手介质及其反常特性的存在性和此方法分析左手介质的有效性. 关键词： 左手介质 非分裂 时域有限差分 Drude     

Ultrahigh-Q of the L3 photonic crystal microcavity

In this paper, we theoretically investigate the L3 cavity with three missing holes in the center. They are of great interest for the realization of low threshold laser nanosources and for a strong interaction between the cavity and sources. In order to improve the transmission and Q factor simultaneously of these structure, by reducing unwanted reflection due to mismatch and through minimization of propagation losses, we modified L3 geometry: three missing holes in a line where both lateral displacement of the first hole adjacent to the cavity, d, and their radius, r, were changed. A photonic microcavity with a high Q factor of 1.8741 × 10⁷ and a modal volume V of 0.351 is demonstrated. We demonstrate that the calculated Q factor for the designed cavity increases by a factor of 49 relative to that for a cavity without displaced and reduced air holes, while the modal volume remains almost constant.