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.     

Tuning of the photonic band gaps and the reflection spectra of a one-dimensional photonic crystal based on silicon and a liquid crystal

The reflection spectra and the photonic band gaps of a one-dimensional composite photonic crystal are calculated for different filling factors (the ratio of the thickness of a silicon layer to the lattice constant A). A change in the refractive index of the filler in a photonic crystal leads to the shift of both edges for certain side photonic bands. It is shown that, with a change in the refractive index from 1.49 to 1.69, the shift of the edges (the tuning effect) can reach the value A/λ = 0.04 for the main photonic band and 0.08 for a side band. An additional criterion for designing a photonic crystal is the estimation of the sharpness of the edges of photonic bands in the reflection spectra.     

一维光子晶体的透射谱特性

利用传输矩阵法研究了一维光子晶体的透射谱特性,数值模拟得到了可见光波段一维光子晶体中的透射谱特性,计算结果表明可见光波段入射波长变化时,透射谱禁带宽度发生变化。研究结果为可见光波段一维光子晶体器件的设计提供了理论依据。     

Photonic band gaps structure properties of two-dimensional function photonic crystals

The tunable two-dimensional photonic crystals band gap, absolute photonic band gap and semi-Dirac point are beneficial to designing the novel optical devices. In this paper, tunable photonic band gaps structure was realized by a new type two-dimensional function photonic crystals, which dielectric constants of medium columns are functions of space coordinates. However for the two-dimensional conventional photonic crystals the dielectric constant does not change with space coordinates. As the parameter adjustment, we found that the photonic band gaps structures are dielectric constant function coefficient, medium columns radius, dielectric constant function form period number and pump light intensity dependent, namely, the photonic band gaps position and width can be tuned. we also obtained absolute photonic band gaps and semi-Dirac point in the photonic band gaps structures of two-dimensional function photonic crystals. These results provide an important theoretical foundation for design novel optical devices.     

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.     

Giant third-harmonic in porous silicon photonic crystals and microcavities

A giant enhancement (no less than by 10³) of the optical third-harmonic generation in one-dimensional porous silicon microcavities and photonic crystals was observed experimentally. The enhancement is due to the resonant enhancement of the fundamental field in the cavity mode and the fulfillment of the phase matching condition at the photonic band gap edges of the photonic crystal and in the vicinity of the microcavity mode.     

一维光子晶体光谱控制实验研究

光子晶体的禁带特性为伪装材料的光谱控制研究提供了一条新的技术途径。利用传输矩阵的方法建立了一维光子晶体光谱透射、反射的理论模型,针对伪装材料近红外高反射、中远红外低发射的要求,优选Ag,MgF2和ZnS等材料作为光子晶体的薄膜材料,采用真空蒸发镀膜的方法制备出Ag/MgF2,Ag/MgF2/ZnS 4种不同周期结构的一维光子晶体,并实验研究了一维光子晶体的光谱反射和透过特性。结果表明:材料和周期结构对一维光子晶体光谱特性有不同的影响,通过优化设计可以实现在伪装波段内的光谱特性要求。     

Anisotropic photonic crystals and microcavities based on mesoporous silicon

A technique to prepare one-dimensional anisotropic photonic crystals and microcavities based on anisotropic porous silicon exhibiting optical birefringence has been developed. Reflectance spectra demonstrate the existence of a photonic band gap and of an allowed microcavity mode at the photonic band gap center. The spectral position of these bands changes under rotation of the sample about its normal and/or under rotation of the plane of polarization of the incident radiation. The dependence of the shift of the spectral position of the photonic band gap edges and of the microcavity mode on the orientation of the polarization vector of incident electromagnetic wave with respect to the optical axis of the photonic crystals and microcavities was studied.     

一维光子晶体禁带的展宽

作为一维光子晶体的应用基础，一维光子晶体的禁带是研究的重点。通过传输矩阵的方法分析了一维光子晶体禁带的特性，讨论了影响带宽的因素。说明了相对带宽对光子晶体设计的重要性。在这个基础上讨论了扩展一维光子晶体带宽的方法，提出了在角域范围内对光子晶体进行叠加的方法，为设计制造一维光子晶体提供了一种行之有效的方法。分别对2个、3个和4个晶体的叠加进行了分析，最后计算了所设计的合成晶体的反射率。其中4个晶体的叠加，相对带宽达到57．52％，极大地展宽了一维光子晶体的禁带，从而证明利用角域的叠加来展宽一维光子晶体的禁带是非常有效的。     

可见光波段SiO2/CdSe一维光子晶体及缺陷模的研究究

采用SiO2/CdSe构建了可见光波段一维光子晶体结构,并在其中引入LiTaO3缺陷层。利用传输矩阵法,分析了电磁波在无缺陷与含LiTaO3缺陷层两种光子晶体中的带隙结构,系统地研究了缺陷层参数对光子晶体可见光波段带隙结构的影响规律。计算结果表明：LiTaO3的引入,有利于带隙宽度的增加,调整缺陷层结构参数,缺陷模的位置可在不同颜色区域出现,如红光、黄光等缺陷模。该结构有望用于制作可见光波段的滤波器。     

Analysis of tunable bandgaps in liquid crystal-infiltrated 2D silicon photonic crystals

We present a theoretical study on two-dimensional photonic crystals composed of silicon and the E7 liquid crystal. We analyze how the optical axis orientation of the liquid crystal influences the photonic bands and bandgaps, for the case when the Maxwell equations can be decoupled into the TE and TM modes. We consider two different structures, a triangular lattice of E7 liquid crystal cylinders in a silicon background and a triangular lattice of silicon cylinders in an E7 liquid crystal background. The effect of the liquid crystal anisotropy on the geometry of the irreducible Brillouin zone allows us to propose a simplified way to calculate the photonic bandgaps. Results show that the bandgap width and center frequency have a 60° periodicity for both structures. Using the plane-wave expansion method, we determined the maximum bandgap and the optimal radius of the cylinders for each structure. Finally, for the second structure, we propose an optical switch with a 50% duty cycle. These structures can be applied to design tunable photonic devices.     

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.     

外磁场作用下一维光子晶体的光传输特性

采用光学传输矩阵方法,研究了外磁场作用下一维光子晶体的光传输特性.在外磁场作用下,介质介电函数在回旋频率ω.附近受到强烈的调制,使组分材料的色散关系发生明显改变,导致光子晶体的能带发生变化,透射谱出现复杂结构.在光子带隙中出现窄通带,窄带中的光是局域的.这表明,在不改变光子晶体组分材料的条件下,可以通过改变外磁场的大小,调制光子晶体的能带及其光传输性质.     

基于石墨烯的可调谐太赫兹光子晶体结构

本文将石墨烯引入到常规光子晶体中构建一种新型光子晶体, 首次从理论上严格导出了决定其能带结构的色散关系, 由于色散关系中石墨烯电导率的存在导致了它具有与常规光子晶体有所不同的特殊光学性质, 我们发现, 随着费米能增大, 低频段能带迅速向高频移动, 而高频段能带移动缓慢, 导致了常规光子晶体没有的能带压缩现象的发生, 究其原因在于石墨烯在低频段电导率迅速变化, 而高频段电导率变化缓慢, 导致能带向高频压缩, 使得光波原先允许频率变成禁止传播, 而禁止频率变成允许传播.     

一维函数光子晶体的研究

本文提出一种新型函数光子晶体, 其折射率是空间位置函数. 由费马原理, 我们给出光在一维、 二维和三维函数光子晶体中的运动方程, 以及一维函数光子晶体的色散关系、 带隙结构和透射率, 再利用传输矩阵理论研究函数光子晶体周期数、 入射角和介质层的厚度等对透射率和禁带结构的影响, 计算发现通过选择不同的折射率空间分布函数, 可以得到比传统光子晶体更宽或更窄的禁带结构. 这样为我们设计不同带隙结构的光子晶体提供理论依据.     

Si-based two-dimensional photonic crystals coupled to one-dimensional Bragg mirrors

Planar two-dimensional photonic crystals can be combined with a one-dimensional Bragg mirror to control the quality factor and out-of-plane coupling of optical Bloch modes. We have investigated the optical properties of such structures fabricated on silicon. The photonic crystals are fabricated in the upper Si layer deposited on top of quarter-wave thick SiO₂-polycrystalline Si layers. The optical properties are probed by the room-temperature photoluminescence of Ge/Si self-assembled islands as an internal source. We show that an enhancement of the quality factor can be obtained by controlling the thickness of the silicon upper layer in which the two-dimensional photonic crystal is etched and by controlling the air filling factor of the photonic crystal. Quality factors of 2200 around 1100 nm are obtained by this method for defect-free photonic crystals with a square lattice pattern. The experimental results are supported by three-dimensional finite-difference time-domain (FDTD) calculations of the radiated modes for the investigated structures.     

Optical properties of mesoporous one-dimensional photonic crystals

The systematic features in the reflectance spectra of broadband optical radiation from the surface of one-dimensional photonic crystals based on mesoporous structures are presented. The dispersion dependence for electromagnetic waves in the mesoporous one-dimensional photonic crystal is established. On its basis, reflectance and transmittance spectra are calculated for particular structures, and the microscopic parameters of the samples under study are determined. The developed theory is used to explain the shape of reflectance spectra in mesoporous photonic crystals based on silicon, quartz, and aluminum oxide.     

Photonic band gaps based on tetragonal lattices of slanted pores

We describe broad new classes of three-dimensional (3D) structures which, when made of silicon, exhibit robust 3D photonic band gaps of up to 25% of the gap center frequency. The proposed photonic crystals are readily amenable to very high precision microfabrication using established techniques such as x-ray lithography and template inversion. Each architecture consists of a set of oriented cylindrical pores emanating from a two-dimensional (2D) square lattice mask with a two-point basis. Large bandwidth, microcircuits for light may be incorporated within the resulting photonic band gaps using an intercalated 2D photonic crystal layer.     

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.     

Synthesis and photonic band gap characterization of high quality photonic crystal heterostructures

High quality photonic crystal heterostructures with a thin titania planar defect layer between its two constitutional photonic crystals were fabricated and their structural and optical properties were analyzed. The results suggest that the thin planar defect layer is beneficial to separate the two constitutional photonic crystals from each other and to reduce the roughness of the interface. The quality of the resulting photonic crystal heterostructures is improved largely and the main features of the photonic band gaps of the two constitutional photonic crystals are inherited. The predominant optical quality of these heterostructures (e.g. deep double photonic band gaps and steep photonic band edges) may afford new flexibility and functionality for engineered photonic behavior in practical devices such as late-model light-operated switches.