Genetic optimization of two-dimensional photonic crystals for large absolute band-gap

A genetic algorithm (GA) is used for the design of two-dimensional photonic crystals with large stop-bands. In this procedure, the unit cell of the crystal with square lattice is assumed to be composed of a number of Si round rods. And the key point to obtain maximum absolute band-gap is using the GA to optimize the radius and center position of each rod in unit cell. In the implementations of GA, the structure of each unit cell is represented by a binary string and the fitness (the absolute band-gap) for each unit cell is calculated by the plane-wave expansion (PWE) method. As numerical examples, we present several GA designs considering different number of round rods in the unit cell as well as the band-gap under the light line. The maximum absolute bandwidth of these optimized band-gaps is 0.1466(2πc/a).     

a-Si:H based two-dimensional photonic crystals

We describe the fabrication processes of silicon-based two-dimensional photonic crystals (2D-PCs) with a photonic band gap in the near-IR range. The procedures involve electron beam lithography followed by an anisotropic etching step of hydrogenated amorphous silicon thin films deposited by plasma enhanced chemical vapor deposition. Micrometric and submicrometric arrays of cylindrical holes are transferred using a poly-methylmethacrylate resist layer as a mask. A careful comparison between standard parallel plate reactive ion etching and inductively coupled plasma etching techniques is performed, aimed at obtaining periodic structures with high aspect ratio and good profile sharpness.     

Novel optical modulator using silicon photonic crystals

We propose a novel compact and integrated optical modulator, which consists of p–i–n silicon photonic crystals with triangular lattice and a line defect waveguide. The device operation is based on a dynamic shift of the photonic band gap (PBG), which induced change in the silicon refractive index by the free carrier injection. We have numerically analyzed and investigated its light modulation performance by using plane wave expansion (PWE) method and finite-difference time-domain method. With small size, rapid response time and high extinct ratio, the designed optical modulator can be used in photonic integrated circuits.     

Topology optimization of two-dimensional asymmetrical phononic crystals

The multiple elitist genetic algorithm with the adaptive fuzzy fitness granulation (AFFG) is used to design the phononic crystals with large relative bandgap width (BGW) for combined out-of-plane and in-plane wave modes. Without assumption on the symmetry of the unit-cell, we obtain an asymmetrical phononic crystal with the relative BGW which is quite larger than that of the optimized symmetrical structure. With the help of AFFG, the number of the fitness function evaluations is reduced by over 50% and the procedure converges 5 times faster than the conventional evolutionary algorithm to reach the same final fitness values.     

Properties of defect modes in one-dimensional symmetric defective photonic crystals

We theoretically investigate the properties of defect modes in one-dimensional symmetric defective photonic crystals. We consider three defective photonic crystal structures, air/[(AB)^NsA^α(BA)^Ns]^Np/air, air/[(AB)^NsAB^βA(BA)^Ns]^Np/air, and air/{[(AB)^NsAB^βA(BA)^Ns]B^γ}^Np−1[(AB)^NsAB^βA(BA)^Ns]/air, where A and B are respectively taken to be the high- and low-index dielectric materials. The first has a defect layer of A^α, the second has a composite defect, AB^βA, and the third has a interleaving defect B^γ. The effect of thickness on the defect mode is studied by varying the parameters α, β, and γ, respectively, for the above model structures. It is found that the positions and the number of defect modes can be significantly changed due to the change in the defect thickness. In addition, by increasing the repeated number N_p, we can have multiple defect modes, leading to a possible design of tunable multichannel filter.     

Band gap studies of 2D photonic crystals with hybrid scatterers

Two-dimensional (2D) photonic crystals (PCs) of a square lattice with dielectric hybrid rods in air are proposed; these PCs consist of a square rod at the center of the unit cell and additional circular rods with their outermost edges against the middle of each side of the lattice unit cell. The band gap structures of PCs can be tailored and optimized by rotating the square rods and adding circular rods to the lattice unit cell. The variation of bands near the complete photonic band gap boundaries, due to some specific modes, is sensitive to certain structural parameters of the system. The results can be understood by analyzing the spatial energy distribution of the electromagnetic fields. Based on such a field analysis, a novel interpretative model is proposed. The PC can be fabricated easily and operated in the microwave region and, hence, should be suitable for applications in new microwave devices.     

Comparison of photonic bandgaps of two-dimensional periodic and quasi-periodic photonic crystals with different relative permittivity dielectric

Photonic bandgaps (PBGs) of two-dimensional (2D) triangular-lattice and square-lattice and decagonal quasi-periodic photonic crystals (PCs) have been analyzed, with a given scatterer radius and dielectric relative permittivity changing from 1 to 30 within air-cylinders-in-dielectric and dielectric-cylinders-in-air constructions. The results have shown that 2D quasi-periodic PC is more likely to generate PBG and complete PBG than 2D periodic PC. For the given scatterer radius and two constructions, PBG widths of the two types of 2D PCs vary little, whereas the corresponding center frequencies decrease in smooth “hyperbola-like” curves with dielectric relative permittivity increasing monotonically. The present results will guide the design of PBG-type microstructure photonic devices.     

Fabrication and characterization of three-dimensional metallodielectric photonic crystals for infrared spectral region

We propose a technique for the realization of three-dimensional metallodielectric photonic crystals based on fabricating polymeric structures using the interference lithography followed by the magnetron deposition of a gold nanolayer. The infrared reflectance spectra of the fabricated photonic crystals are studied. The spectrometry and finite-difference time-domain modeling data show that there is a photonic band gap centered at the wavelength approximately equal to the photonic crystal period.     

Band gap structure of disordered chiral photonic crystals

Based on the non-symmetric transmission-line method, the band gap structure of disordered chiral photonic crystals (CPC) has been investigated. The influence of the chiral parameters, the disorder, the periods and the refractive index on the band gap structure has been discussed. It is found that the photonic band gap (PBG) in CPC is more obvious than that in the conventional photonic crystals, and the PBG can be increased by increasing the periods or the contrast of the refractive index of the two media. It is also found that the existence of disorder will influence the band edge of the PBG, and such influence will increase with the increment of periods or the contrast of the refractive index of the two media.     

Phase response of omnidirectional reflection one-dimensional photonic crystals and defect modes

In this paper, we investigate the phase properties of light reflected from one-dimensional omnidirectional reflection photonic crystal. We observe that the phase changes drastically at large incident angles. This asymmetrical phase change should be considered at oblique incidence, and various phase compensators and retarders can be designed by this nonlinear curved surface of phase shift. Furthermore, for the coupled defect 1D PC, the phase change depends mainly on the top of the sharp peak of the weak undulation within the rectangular defect band, because the top of the peak of the undulation is very sharp, i.e. large phase change look like within almost a single frequency. This drastic phase change can be used to design phase controllers.     

A detailed derivation of eigenvalue equation in two dimensional and three dimensional photonic crystals

A detailed derivation of eigenvalue equation in two dimensional and three dimensional photonic crystals is given by the plane-wave expansion method. Some mathematical formulas such as the rotation of vector, the gradient of scalar, the divergence of the vector, the vector triple product and the conversion between scalar and vector are employed. The eigenvalue equation in photonic crystals has become the important base for obtaining the band structure and the distribution of eigenmode.     

Near-field probing of photonic crystals

Photonic crystals form an exciting new class of optical materials that can greatly affect optical propagation and light emission. As the relevant length scale is smaller than the wavelength of light, sub-wavelength detection forms an important ingredient to obtain full insight in the physical properties of photonic crystal structures. Spatially resolved near-field measurements allow the observation of phenomena that remain hidden to diffraction-limited far-field investigations. Here, we present near-field investigations in both collection and illumination modes that highlight the power of local studies. We show how propagation losses are unambiguously determined and that light detected in far-field transmission can actually contain contributions from different, sometimes unexpected, local scattering phenomena. Simulations are used to support our findings. Furthermore, it is shown that local coupling of light to a thick three-dimensional photonic crystal is position-dependent and that the spatial distribution of the coupling efficiency itself is frequency-dependent.     

Modification of photonic properties in porphyrin-infiltrated opal crystals

Structural, optical and magnetic properties of porphyrin-infiltrated opal hybrid structures were investigated. Bulk samples of synthetic opal were grown by sedimentation technique from colloidal solution of SiO₂ spheres of diameter 250 nm. The structure of the samples was examined by atomic force microscopy. The photonic properties of crystals were investigated by optical measurements in transmission and reflection modes. The stop band was observed in the region 510–550 nm. The photonic properties of synthetic opal crystals were modified by infiltration with aqueous basic solution of iron–porphyrin (FeTPPS) of concentration 1.0 mM. In hybrid samples the absorption bands typical of FeTPPS were observed in the vicinity of the opal stop band. Magnetic properties of FeTPPS-infiltrated opal samples have been studied at 5–300 K in magnetic fields up to 5 T. The FeTPPS-infiltrated opal crystals can be considered as the structures perspective for magnetophotonic devices.     

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用时域有限差分法研究了电磁波在等离子体光子晶体中的传播特性。数值模拟中使用完全匹配层吸收边界条件,计算了电磁波通过等离子体光子晶体的反射和透射系数。讨论了等离子体密度、等离子体温度、介电常数比和引入缺陷层对等离子体光子晶体光子带隙的影响。     

Modelling and design of complete photonic band gaps in two-dimensional photonic crystals

In this paper, we investigate the existence and variation of complete photonic band gap size with the introduction of asymmetry in the constituent dielectric rods with honeycomb lattices in two-dimensional photonic crystals (PhC) using the plane-wave expansion (PWE) method. Two examples, one consisting of elliptical rods and the other comprising of rectangular rods in honeycomb lattices are considered with a view to estimate the design parameters for maximizing the complete photonic band gap. Further, it has been shown that complete photonic band gap size changes with the variation in the orientation angle of the constituent dielectric rods.      

Design of photonic bands for opal-based photonic crystals

To make a device from an opal—or otherwise—the photonic bands and the optical properties derived from them are needed. Knowing the effects of different parameters defining the opal geometry and different possible modifications of its structure are needed, too. An accurate definition of the device will be required to obtain a good performance. With this aim, the optics of light with a wavevector in the vicinity of the L point in the Brillouin zone and its coupling to bare opals band structure are presented. An important aspect is the transition from finite to infinite crystal and the study of size effects on the bands. It is possible to substantially alter the photonic band structure of an opal-based system, while maintaining the lattice structure, simply by growing layers of other materials with an appropriate refractive index. Here, it is shown how, by the growth of accurately controlled thin layers of silicon and germanium, and further processing, one can induce the opening of two complete photonic band gaps (PBGs) in an opal structure. Finally, the possibility to fabricate a simple device consisting in a planar waveguide will be shown. By means of a very simple and inexpensive procedure, engineered planar defects acting as microcavities have been realized. These can be viewed as a particular case of a much more general class of heterostructures that can be grown by combining opal vertical deposition and chemical vapour deposition of oxides. A further step is made by applying electron beam lithography to provide lateral definition and facilitate three-dimensional structuring.     

1 × 3 Beam splitter based on self-collimation effect in two-dimensional photonic crystals

The analysis and simulation result of a 1 × 3 beam splitter in a two-dimensional square-lattice photonic crystal is presented in this paper, where the light is self-collimated as dictated by the self-collimation effect. The frequency and the direction of propagation of the self-collimated beam are obtained by the equal-frequency contours (EFCs) plot which is calculated by plane wave expansion method. Then a line defect is introduced by simultaneously varying the radii and the dielectric constant of the rods along the proper direction, the self-collimated beam propagation in such structure is simulated by the two-dimensional finite-difference time-domain (2D FDTD) method with perfectly matched layer absorbing boundary conditions. The simulation results show that the self-collimated beam can be split into three beams. With the same principle, a 1 × 7 beam splitter is realized by introducing different line defects along (X direction. Such devices can greatly enhance photonic crystals for usage in high-density optical integrated circuits.     

Analytical investigation of one-dimensional photonic crystals with a dielectric-superconducting pair defect

We have studied the dielectric-superconducting pair defect embedded into one-dimensional photonic crystals by an analytical method based on the Kronig-Penny model. The superconducting defect has been considered by using of two-fluid model whose permittivity depends on the frequency and superconductor parameters. We have showed that in contrast to the usual defect modes, superconducting defect modes are nearly invariant upon the change of defect size and with increasing defect sizes, the enhancement behavior is observed in the peak of electric field profiles. In addition, the physical parameters have less effect on the defect modes, which is placed under cutoff frequency of superconductor.     

一维磁化等离子体光子晶体非互易特性研究

在理想条件下,为了研究等离子体回旋频率、等离子体频率、等离子体层厚度、周期常数和入射角在TM模式下对一维磁化等离子体光子晶体的非互易特性的影响,用利用传输矩阵法计算得到的TM波正向和反向传播的透射率来研究其非互易特性。研究结果表明,增加等离子体回旋频率和入射角度能够改善非互易特性;而一味地增加等离子体频率和等离子体层厚度将会使得非互易传播特性变得恶化;增加周期常数不能明显地改善非互易传播特性,但是通过改变外加磁场的施加方式能够改善其非互易特性。     

Temperature tunability of cavity-semiconducting waveguide coupling in a two-dimensional photonic crystal

We study the coupling efficiency between a cavity resonator and semiconducting waveguide in a two-dimensional photonic crystal by varying the temperature. We used the revised plane wave expansion and finite difference time domain methods to evaluate the coupling efficiency. The photonic crystal waveguide is composed of a row of InSb semiconducting materials, and the efficiency was calculated at various temperatures. The findings indicate that the temperature can be used as a useful efficiency controller.