Influence of boundary conditions on the one-way edge modes in two-dimensional magneto-optical photonic crystals

The influence of boundary conditions on the one-way edge modes in two-dimensional magneto-optical photonic crystals is studied theoretically by the supercell method. The numerical results reveal that tailoring the boundary could bring some new properties, but would not change the intrinsic one-way character for edge modes in the band gap generally. Changing the boundary conditions, more than one edge modes and waveguide modes can appear, which could couple and split into new ones. Two independent channels for one-way edge modes can be realized. The frequency of the edge Dirac point can be tunable.     

Ray Modes in Random Gap Systems

A disordered photonic crystal with spectral degeneracies in the form of Dirac nodes is considered. Disorder can create a random gap at the Dirac nodes, which leads to the formation of random edge modes. We study the distribution of these edge modes and find from symmetry considerations that the discrete anisotropy of the photonic crystal is spontaneously broken for the propagation of photons from a local photon source. This effect can be understood as the spontaneous creation of a ray mode or as the creation of a one‐dimensional waveguide in a two‐dimensional photonic crystal through strong random scattering. The phenomenon must be distinguished from Anderson localization of photons in a single band crystal and can be considered as angular localization, since it creates geometric states rather than confining the photons to an area of the size of the localization length. The propagation of the photon intensity is described by a Fokker‐Planck equation, whose drift term is determined by the spectrum of the photonic crystal near the Dirac node.     

Bragg polaritons: strong coupling and amplification in an unfolded microcavity

Periodic incorporation of quantum wells inside a one-dimensional Bragg structure is shown to enhance coherent coupling of excitons to the electromagnetic Bloch waves. We demonstrate strong coupling of quantum well excitons to photonic crystal Bragg modes at the edge of the photonic band gap, which gives rise to mixed Bragg polariton eigenstates. The resulting Bragg polariton branches are in good agreement with the theory and allow demonstration of Bragg polariton parametric amplification.     

Anomalous propagation loss in photonic crystal waveguides

Propagation loss can occur in photonic crystal waveguides without complete optical confinement. We employ a highly efficient transfer-matrix method which allows for accurate and reliable extraction of the propagation loss even at an extremely low level. The results for a two-dimensional photonic crystal waveguide shows that the loss exponentially decays via the waveguide wall thickness. An anomalous phenomenon is found where the loss for guided modes near the upper band gap edge can be several orders of magnitude smaller than that for modes in the middle of the band gap. This anomaly can be well explained by the localization degree of guided modes at different frequency domains.     

Photonic bands, gap maps, and intrinsic losses in three-component 2D photonic crystal slabs

We obtain the photonic bands and intrinsic losses for the triangular lattice three-component two- dimensional （2D） photonic crystal （PhC） slabs by expanding the electromagnetic field on the basis of waveguide modes of an effective homogeneous waveguide. The introduction of the third component into the 2D PhC slabs influences the photonic band structure and the intrinsic losses of the system. We examine the dependences of the band gap width and gap edge position on the interlayer dielectric constant and interlayer thickness. It is found that the gap edges shift to lower frequencies and the intrinsic losses of each band decrease with the increasing interlayer thickness or dielectric constant. During the design of the real PhC system, the effect of unintentional native oxide surface layer on the optical properties of 2D PhC slabs has to be taken into consideration. At the same time, intentional oxidization of macroporous PhC structure can be utilized to optimize the design.     

双带型光子晶体中双V型四能级原子自发辐射谱中的黑线研究

研究了双带型光子晶体中双V型四能级原子自发辐射的辐射谱.双V型四能级原子同时与真空热库和双带型光子晶体热库耦合.研究发现双V型四能级原子自发辐射谱中有三种不同原因可能引起的黑线：第一种是由于量子干涉效应;第二种是由于各向同性光子晶体带边处态密度具有奇异性;第三种是真空场中的量子干涉和光子晶体禁带内态密度为零共同作用的结果.通过移动光子晶体的带边位置,在各向同性光子晶体带边引入光滑因子,以及在光子晶体中引入缺陷等对这三种黑线的影响,对上述结果进行了分析和讨论. 关键词： 双带型光子晶体 双V型四能级原子 黑线     

Observation of trapped light induced by Dwarf Dirac-cone in out-of-plane condition for photonic crystals

Existence of out-of-plane conical dispersion for a triangular photonic crystal lattice is reported. It is observed that conical dispersion is maintained for a number of out-of-plane wave vectors(k_z). We study a case where Dirac like linear dispersion exists but the photonic density of states is not vanishing, called Dwarf Dirac cone(DDC) which does not support localized modes. We demonstrate the trapping of such modes by introducing defects in the crystal. Interestingly, we find by k-point sampling as well as by tuning trapped frequency that such a conical dispersion has an inherent light confining property and it is governed by neither of the known wave confining mechanisms like total internal reflection, band gap guidance. Our study reveals that such a conical dispersion in a non-vanishing photonic density of states induces unexpected intense trapping of light compared with those at other points in the continuum. Such studies provoke fabrication of new devices with exciting properties and new functionalities.     

二维函数光子晶体

光子晶体是由两种或两种以上不同介电常数材料所构成的周期性光学纳米结构.光子晶体结构可分为一维、二维和三维,其中二维光子晶体已成为研究的热点.可调带隙的二维光子晶体可以设计出新型的光学器件,因此,对它的研究具有重要的理论意义和应用价值.本文提出的二维新型函数光子晶体可以实现光子晶体带隙的可调性.所谓二维函数光子晶体,即组成它的介质柱的介电常数是空间坐标的函数,它不同于介电常数为常数的二维常规光子晶体.二维函数光子晶体是通过光折变非线性光学效应或电光效应使介质柱的介电常数成为空间坐标的函数.运用平面波展开法给出了TE和TM波的本征方程,由傅里叶变换得到二维函数光子晶体介电常数ε(r)的傅里叶变换ε(G),其傅里叶变换比常规二维光子晶体的复杂.计算发现当介质柱介电常数为常数时,其傅里叶变换与常规二维光子晶体的相同,因此二维常规光子晶体是二维函数光子晶体的特例.在此基础上具体研究了二维函数光子晶体TE波和TM波的带隙结构,其介质柱介电常数函数形式取为ε(r)=k·r+b,其中k,b为可调的参数.并与二维常规光子晶体TE波和TM波的带隙结构进行了比较,发现二维函数光子晶体与二维常规光子晶体TE波和TM波的带隙结构有明显的区别,二维函数光子晶体的带隙数目、位置以及宽度随参数k的变化而发生改变.从而实现了二维函数光子晶体带隙结构的可调性,为基于二维光子晶体的光学器件的设计提供了新的设计方法和重要的理论依据.     

Enhanced photonic band-gap confinement via Van Hove saddle point singularities

We show that a saddle point Van Hove singularity in a band adjacent to a photonic crystal band gap can lead to situations which defy the conventional wisdom that the strongest band-gap confinement is found at frequencies near the midgap. As an example, we present a two-dimensional square photonic crystal waveguide where the strongest confinement is close to the band edge. The underlying mechanism can also apply to any system that is described by a band structure with a gap. In general, the saddle point favors the appearance of a very flat band, which in turn results in an enhanced confinement at band-gap frequencies immediately above or below the flat band.     

Energy Squeeze of Ultrashort Light Pulse by Kerr Nonlinear Photonic Crystals

Self-phase modulation can efficiently shape the spectrum of an optical pulse propagating along an optical material with Kerr nonlinearity. In this work we show that a one-dimensional Kerr nonlinear photonic crystal can impose anomalous spectrum modulation to a high-power ultrashort light pulse. The spectrum component at the photonic band gap edge can be one order of magnitude enhanced in addition to the ordinary spectrum broadening due to self-phase modulation. The enhancement is strictly pinned at the band gap edge by changing the sample length, the intensity or central wavelength of the incident pulse. The phenomenon is attributed to band gap induced enhancement of light-matter interaction.     

Photonic band gap via quantum coherence in vortex lattices of Bose-Einstein condensates

We investigate the optical response of an atomic Bose-Einstein condensate with a vortex lattice. We find that it is possible for the vortex lattice to act as a photonic crystal and create photonic band gaps, by enhancing the refractive index of the condensate via a quantum coherent scheme. If high enough index contrast between the vortex core and the atomic sample is achieved, a photonic band gap arises depending on the healing length and the lattice spacing. A wide range of experimentally accessible parameters are examined and band gaps in the visible region of the electromagnetic spectrum are found. We also show how directional band gaps can be used to directly measure the rotation frequency of the condensate.     

Experimental evidence of photonic crystal waveguides with wide bandwidth in two-dimensional Al_2O_3 rods array

A cross-shaped photonic crystal waveguide formed by a square lattice Al_2O_3 rods array is numerically and experimentally investigated. The band gap of the TE mode for the photonic crystals and transmission characteristics of waveguides are calculated by the plane wave expansion method and the finite element method.We perform the experiments in the microwave regime to validate the numerical results. The measured reflection and transmission characteristics of the photonic crystals show a large band gap between 8.62 and 11.554 GHz(relative bandwidth is 29.34%). The electromagnetic waves are transmitted stably in the waveguides, and the transmission characteristics maintain a high level in the band gap.     

二维正方晶格光子晶体禁带特性

基于平面波展开法,以碳化硅构成二维正方晶格光子晶体,数值模拟了TE模、TM模二维光子晶体的禁带特性,结果表明,TE模更容易形成光子禁带。同时设计了以碳化硅构成二维正方晶格光子晶体波导,数值模拟了TE模、TM模波导的传输特性和禁带特性,结果表明,TE模构成的波导电磁波能够较好的传播,它们的光子禁带都没有出现。研究结论为光子晶体波导器件的开发提供参考。     

Special control of the cutoff frequencies in a 2D photonic crystal coupled-cavity waveguide

We show theoretically that the upper and lower cutoff frequencies of the guided band in a 2D photonic crystal coupled-cavity waveguide can be controlled independently or synchronously by changing two configuration parameters of the waveguide simultaneously. The independent control range for the lower and upper cutoff frequencies can be as large as 68.6% and 67.9% of photonic band gap, respectively. The two cutoff frequencies can also be tuned in the same direction over equal distances up to 25.7% of photonic band gap. These results offer an efficient way for designing the various dispersion relations for photonic crystal waveguides.     

Spontaneous emission from photonic crystals: full vectorial calculations

Quantum electrodynamics of atom spontaneous emission from a three-dimensional photonic crystal is studied in a full vectorial framework. The electromagnetic fields are quantized via solving the eigenproblem of photonic crystals with use of a plane-wave expansion method. It is found that the photon density of states and local density of states (LDOS) with a full band gap vary slowly near the edge of band gap, in significant contrast to the singular character predicted by the previous isotropic model. Therefore, the spontaneous emission can be solved by conventional Weisskopf-Wigner approximate theory, which yields a pure exponentially decaying behavior with a rate proportional to the LDOS.     

Effect of the dielectric background on dispersion characteristics of metallo-dielectric photonic crystals

We theoretically study the effect of the dielectric background in two-dimensional metallo-dielectric photonic crystals. The metallo-dielectric photonic crystal consists of a square lattice of circular metallic rods embedded into a dielectric background. We calculate the photonic band structure by means of the plane wave method and the frequency-dependent finite-difference time-domain method. The transfer matrix method is used to obtain the reflectivity characteristics. Results show that the band structures shift toward lower frequencies and become flatter when the background dielectric constant increases. In addition, degeneracy can be broken and new gaps can be created in function of the dielectric background. We also found that the relative band gap width Δω/ω_g grows with increasing background dielectric constant and widths as large as 42.3% and 13.8% for the second and third band gaps can be achieved for ε_b = 9. We have investigated the origin of the new gap in these structures by studying the electric-field distribution at the band edges for the first five modes.     

Localization and Amplification of the Electromagnetic Field in a Globular Photonic Crystal

Using the wave equation, the electromagnetic field distribution is calculated in a globular photonic crystal on the basis of artificial opal in the [111] direction. The electromagnetic field is found to be localized at the edge of the photonic band gap in the first surface pore of the sample. The effect of pumping on a sample is estimated as well. The results open up prospects for the application of artificial opals to solve photon and gravitational conversion problems.     

Effective permittivity and permeability of one-dimensional dielectric photonic crystal within a band gap

We take a finite dielectric photonic crystal as a homogeneous slab and have extracted the effective parameters. Our systematic study shows that the effective permittivity or permeability of dielectric photonic crystal is negative within a band gap region. This means that the band gap might act as ε-negative materials （ENMs） with ε 〈 0 and μ 〉 0, or μ-negative materials （MNMs） with ε 〉 0 and μ 〈 0. Moreover the effective parameters sensitively rely on size, surface termination, symmetry, etc. The effective parameters can be used to design full transmission tunnelling modes and amplify evanescent wave. Several cases are studied and the results show that dielectric photonic band gap can indeed mimic a single negative material （ENM or MNM） under some restrictions.     

Modes of capillary photonic-crystal fibers with hollow core

A rigorous method of integral equations has been used to calculate the dispersion characteristics, fields, and radiation patterns of the leaky modes of photonic-crystal fibers with a shell in the form of a bounded 2D photonic crystal composed of parallel quartz capillaries contacting each other and a core in the form of a defect of a photonic crystal with one capillary removed. It is shown that, when thick-walled capillaries (with an air content in the shell of about 28%) are used, these fibers can be single mode and have an overlap integral of the fundamental-mode field with the dielectric medium that is smaller by a factor of more than two (in comparison with similar fibers formed by air channels of circular cross section). The significant dispersion of the group velocity of the fundamental modes of fibers near the edge of the photonic crystal band gap has been found.     

Spectral properties of a two-dimensional resonant metal-dielectric photonic crystal

We have studied the transmission spectra of resonant two-dimensional photonic crystals of two types, one of which consists of nanocomposite cylinders that form a square lattice in vacuum and the other of which consists of cylindrical holes that form a square lattice in nanocomposite matrix. The nanocomposite consists of metallic nanospheres that are dispersed in a transparent matrix and is characterized by an effective resonant dielectric permittivity. We show that, depending on the position of the resonant frequency of the nanocomposite with respect to the boundaries of the band gap, there arises either an additional transmission band in the transmission spectrum in the band gap or an additional band gap in the continuous spectrum of the photonic crystal. As the structural and geometric parameters of the system change, both the additional transmission band and the additional band gap are considerably modified. We analyze particular features of the spatial distribution of the electromagnetic field intensity in crystals. The considered effects can be used to extend the possibilities of creating new photonic crystals with specified properties.