Dramatic enhancement of third-harmonic generation in three-dimensional photonic crystals

We have observed a dramatic enhancement of third-harmonic generation in 3D polystyrene-air photonic crystals pumped by a near infrared laser beam. As the pump wavelength is tuned, the peak of the enhancement occurs when the third-harmonic wavelength approaches the short-wavelength edge of the band gap. We show that the origin of the enhancement is phase matching provided by the periodic structure of the photonic crystals.     

Periodic,quasi‐periodic,and random quadratic nonlinear photonic crystals

Quadratic nonlinear photonic crystals are materials in which the second order susceptibility χ⁽²⁾ is spatially modulated while the linear susceptibility remains constant. These structures are significantly different than the more common photonic crystals, in which the linear susceptibility is modulated. Nonlinear processes in nonlinear photonic crystals are governed by the phase matching requirements, which are determined by the reciprocal lattice of these crystals. Therefore, the modulation of the nonlinear susceptibility enables to engineer the spatial and spectral response in various three‐wave mixing processes. It enables to support the efficient generation of new optical frequencies at multiple directions. We analyze three wave mixing processes in nonlinear photonic crystals in which the modulation is either periodic, quasi‐periodic, radially symmetric or even random. We discuss both one‐dimensional and two‐dimensional modulations. In addition to harmonic generations, we outline several new possibilities for all‐optical control of the spatial and polarization properties of optical beams in specially designed nonlinear photonic crystals.     

光子晶体光纤四波混频光谱中相位匹配特性的研究

与传统光纤不同,光子晶体光纤可以具有多个零色散波长,在四波混频光谱中,具有更丰富的相位匹配特性。目前很多文献报道了光子晶体光纤非线性光学特性的实验结果,但对其产生机理及光谱的变化规律缺乏详细的理论分析。为此对光纤中四波混频原理进行了分析,给出了高增益的相位匹配条件。利用多极法计算了光子晶体光纤的非线性系数及色散特性。对具有多个零色散波长光子晶体光纤的相位失配特性进行了分析,得到了相位匹配波长随泵浦波长及泵浦功率的变化规律。给出了相位匹配曲线,分析了不同色散曲线的相位匹配波长特点,两个零色散波长光子晶体光纤,在四波混频光谱中将激发出四个新的波长。实验得到了两个零色散波长光子晶体光纤的四波混频光谱,与理论分析一致,验证了相位匹配理论的可靠性。多个零色散波长光纤,能产生丰富的相位匹配曲线,会出现更多的四波混频波长,可以有效的控制光孤子及超短脉冲的四波混频及共振散射产生的光谱特性。为光子晶体光纤中基于四波混频的波长变换及超连续谱的研究提供了理论指导。     

用转移矩阵法数值研究二维正方介质柱光子晶体的传输特性

利用转移矩阵方法对二维正方介质柱光子晶体的传输特性进行了研究,数值计算研究了不同晶格、同一晶格柱体截面面积不同、放置方位角不同时光子晶体的传输特性。数值结果表明光子禁带的宽度与中心频率和晶格结构有很大关系,正方晶格更易形成平坦光子禁带,柱体截面面积大,则形成的禁带较宽,在其他因素相同的条件下柱体放置的方位角对光子禁带有重要影响。数值研究表明在正方介质柱下设计宽平坦光子禁带时,可以首先考虑正方晶格结构,其次设法使柱体截面尽量大一些,最后可通过柱体放置方位角来微调光子禁带的宽度与中心频率以达到设计要求。     

Modified phase matching conditions for second harmonic generation in a finite one-dimensional photonic crystal near the bragg condition: Weak and strong diffraction

Enhanced noncollinear second harmonic generation in a finite one-dimensional photonic crystal is analyzed theoretically under conditions of pump field localization near the Bragg reflection. It is shown numerically that phase-matched second-harmonic generation can be implemented in a finite one-dimensional photonic crystal that does not satisfy the conventional phase-matching conditions calculated for effective Bloch modes with narrow spectral lines. The intensity of the generated second-harmonic signal exceeds the second-harmonic intensity attained under the conventional phase-matching conditions by more than an order of magnitude. This phenomenon is explained by interference between Bloch modes having similar amplitudes, wavenumbers, and spectral widths. Since the spatial spectra of waves propagating in a bounded medium have finite widths, the broadened spectral lines of proximate effective Bloch modes resulting from Bragg diffraction of waves tuned to the first transmission resonances near the photonic bandgap edge overlap, merging into a spectral profile with center shifted relative to the original effective Bloch wavevectors. This effect leads to modified phase matching conditions for second harmonic generation in a finite photonic crystal, which are written for the centers of the spectral profiles resulting from modal overlap, rather than for individual effective wavevectors. Substantially different phase matching conditions are obtained for weakly and strongly diffracted beams, whereas conventional phase matching conditions hold only for transmitted signals in the case of weak diffraction.     

含负折射率材料的一维光子晶体的光学传输特性

采用光学传输矩阵方法,模拟研究了由正折射率材料和负折射率材料交替组成的一维光子晶体的光学传输特性.计算了这种含负折射率材料的一维光子晶体的透射谱和色散关系.结果表明,在正入射时,含负折射率材料的光子晶体的带隙要比传统的光子晶体要大得多,并具有狭窄的透射带,从光学薄膜理论的色散关系出发解释了形成上述现象的原因.讨论了在不同的偏振模式下,光以中心波长入射时,反射率随着入射角度的变化关系.发现含负折射率材料的一维光子晶体具有更好的角度特性,可以用来实现对中心波长的全方位反射.     

光子晶体表面结构的改变对成像的影响

负折射率材料因为其奇异的特性成为广泛研究的对象,尤其是光子晶体平板的完美成像.硅材料以其良好的物理性质成为当今集成光学领域中应用最广的材料之一.本文以硅介质柱在空气中周期性排列构成六角结构的光子晶体平板为例,运用平面波展开法进行光子晶体能带计算并运用时域有限差分法模拟改变光子晶体平板成像并讨论表面结构对成像的影响.光子晶体平板等效折射率为-1时,通过改变上下侧最外层介质柱的半径或是侧向移动最外层介质柱发现:当光子晶体平板表面结构发生改变时光子晶体平板仍能成像但像点强度发生变化.当光子晶体平板表面结构的改变在一定范围时,所成像的位置发生改变且位置变化符合光子晶体成像经典的Veselago关系;当光子晶体表面结构的变化超过该范围时,所成像与物的相位发生反相同时像点位置发生"巨变",此时Veselago关系已不成立.数值模拟表明:光子晶体平板表面结构的改变可以有效地改变该光子晶体平板所成像的强度、位置和相位.     

The disorder effect on the performance of novel waveguides constructed in two-dimensional amorphous photonic materials

On the basis of two-dimensional amorphous photonic materials,we have designed a novel waveguide by inserting thinner cylindrical inclusions in the centre of basic hexagonal units of the amorphous structure along a given path.This waveguide in amorphous structure is similar to the coupled resonator optical waveguides in periodic photonic crystals.The transmission of this waveguide for S-polarized waves is investigated by a multiple-scattering method.Compared with the conventional waveguide by removing a line of cells from amorphous photonic materials,the guiding properties of this waveguide,including the transmissivity and bandwidth,are improved significantly.Then we study the effect of various types of positional disorder on the functionality of this device.Our results show that the waveguide performance is quite sensitive to the disorder located on the boundary layer of the waveguide,but robust against the disorder in the other area in amorphous structure except the waveguide border.This disorder effect in amorphous photonic materials is similar to the case in periodic photonic crystals.     

Optical properties of one-dimensional photonic crystals obtained by micromatchining silicon (a review)

The theoretical and experimental investigations of photonic band gaps in one-dimensional photonic crystals created by micromatchining silicon, which have been performed by the author as part of his doctoral dissertation, are presented. The most important result of the work is the development of a method of modeling photonic crystals based on photonic band gap maps plotted in structure–property coordinates, which can be used with any optical materials and in any region of electromagnetic radiation, and also for nonperiodic structures. This method made it possible to realize the targeted control of the optical contrast of photonic crystals and to predict the optical properties of optical heterostructures and three-component and composite photonic crystals. The theoretical findings were experimentally implemented using methods of micromatchining silicon, which can be incorporated into modern technological lines for the production of microchips. In the IR spectra of a designed and a fabricated optical heterostructure (a composite photonic crystal), extended bands with high reflectivities were obtained. In a Si-based three-component photonic crystal, broad transmission bands and photonic band gaps in the middle IR region have been predicted and experimentally demonstrated for the first time. Si–liquid crystal periodic structures with electric-field tunable photonic band-gap edges have been investigated. The one-dimensional photonic crystals developed based on micromatchining silicon can serve as a basis for creating components of optical processors, as well as highly sensitive chemical and biological sensors in a wide region of the IR spectrum (from 1 to 20 μm) for lab-on-a-chip applications.     

表层厚度渐变一维耦合腔光子晶体的反射相位特性及其应用

利用传输矩阵法研究了表层厚度渐变的一维非对称耦合腔光子晶体的反射相位特性. 研究表明, 光子禁带内(包括缺陷模附近)的反射率在98%以上, 且基本不受表层厚度影响, 特别是, 在非正入射情况下, 简并的缺陷模随着表层厚度的变化会发生分裂; 进一步研究发现, 在缺陷模分裂处附近, TE, TM偏振的反射相位以及它们之间的相位差均敏感地依赖于表层厚度的变化, 从而使得反射光的偏振态也随表层厚度的变化而敏感变化, 其物理机理在于缺陷模分裂所造成的剧烈相位变化. 基于上述特性, 设计了一种表层厚度呈二维周期变化的一维光子晶体结构, 从该结构反射的激光经透镜聚焦后, 在聚焦区域同时存在各种偏振态(包括沿不同方向的线偏振、左旋或右旋圆偏振、椭圆偏振等)的子光束, 它们叠加后在聚焦区域将产生具有无规相位和无规偏振态的光场. 以上结果能有效降低激光的相干性, 在激光核聚变等领域有潜在的应用价值.     

Resonant modes in photonic multiple quantum well structures with single-negative materials

A type of photonic multiple quantum well (PMQWs) structure made of two different photonic crystals (PCs) with two kinds of single-negative materials is investigated. It is demonstrated by transfer matrix method that omnidirectional resonance modes are generated. The number of the resonance modes can be controlled by adjusting the periodic structure of the constituents. The resonance tunneling modes are weak dependence on incident angle and the scaling of the barrier photonic crystals. When the losses are taken into account, the effects of the losses coming from ENG media and MNG media on the resonance modes are striking difference.     

Tunable band gaps in electro-optical photonic bi-oriented crystals

Electrically induced birefringence is studied in photonic bi-oriented crystals in terms of molding lightflow in optical devices. In photonic bi-oriented crystals, misorientation of dielectric anisotropic grains results in a dielectric contrast at the grain boundaries. The translational periodicity of the optical constants depends upon a regular network of twisted dielectrics. Due to the anisotropy of the bicrystalline structure the direction of light propagation determines the dielectric contrast at the grain boundaries. In a specific crystallographic arrangement the optical properties of the bi-oriented crystal can be tuned by the electro-optical effect: the periodic dielectric contrast is electrically induced and photonic bandgaps are generated by applying external electric fields. The geometrical requirements for tunable photonic bicrystals are evaluated based on materials employed for electro-optical applications. Tunable photonic bi-oriented crystals may be candidates for fast optical switches, modulators and multiplexers in the optical communication network. Received: 5 July 2001 / Revised version: 3 August 2001 / Published online: 15 October 2001     

Hartman effect in one-dimensional photonic crystals with a three-level atomic defect layer

The Hartman effect in one-dimensional photonic crystals contained a defect layer doped with two-level, and three-level atoms is discussed. It is shown that the transmitted phase time in one-dimensional photonic crystals contained a defect layer reaches to a positive constant as the periodic number N increases. However, for a defect layer doped by two-level atoms, the transmitted phase time reaches to negative constant by increasing periodic number N. In addition, for defect layer doped by three-level atoms, the transmitted phase time can be controlled from positive to negative just by the Rabi-frequency of coupling field.     

二维正方晶格各向异性光子晶体缺陷模

为了得到对TM和TE模具有相同缺陷模的共振微腔,通过在完整各向异性碲介质柱二维正方光子晶体中,引入各向同性的介质圆柱作为点缺陷,利用超胞平面波展开法计算该光子晶体的缺陷模,系统计算了在同时改变点缺陷介质柱介电常数和半径两种情况下的两种偏振缺陷模的变化规律。结果表明,在完全禁带中,缺陷介质柱介电常数从5.44变化到38.44、半径与晶格常数的比从0.05变化到0.50的整个区域,均会出现对TM和TE模具有相同缺陷模,且随着介电常数的减小,缺陷模随着缺陷半径的变化趋于缓慢,归一化共振频率在0.241 8~0.243 2之间可调,在引入ε_e＜ε_o的各向异性介质柱缺陷时,亦可得到对TM和TE模具有相同缺陷模,且共振频率的可调范围增大,该研究为光子晶体器件的设计提供了理论依据。     

On the theory of diffraction of light in photonic crystals with allowance for interlayer disordering

Electrodynamic Green’s functions are used to construct an analytical theory of the Bragg diffraction of polarized light in photonic crystals having a close-packed structure. For opal-based photonic crystals, the Bragg diffraction intensity is calculated with allowance for permittivity periodic modulation and for the presence of an optical crystal boundary and interlayer disordering, which usually appears during sample growth. A comprehensive study is made of the effect of the structure disorder caused by the random packing of growth layers on diffraction. For a random constructed twinned fcc structure, the average structure factor and the scattering (diffraction) cross sections (which are dependent on the linear polarization of the incident and scattered waves) are calculated. Numerical examples are used to show that the theory developed can be applied to analyze and process experimental diffraction patterns of real photonic crystals having a close-packed structure disordered in one direction.     

Negative refraction and the spectral filtering of terahertz radiation by a photonic crystal prism

We demonstrate how micromachined photonic crystals can be used to negatively refract terahertz frequency light. The photonic crystals, which are constructed from conventional dielectric materials, manipulate the incident beam via interaction with their photonic bands. Consequently, we show that different components of a broadband beam incident on the structure may be positively or negatively refracted, depending upon its frequency and that the structure can be used as an effective spectral filter of THz radiation.     

Graphene-based photonic crystal

A novel type of photonic crystal formed by embedding a periodic array of constituent stacks of alternating graphene and dielectric discs into a background dielectric medium is proposed. The photonic band structure and transmittance of such photonic crystal are calculated. The graphene-based photonic crystals can be used effectively as the frequency filters and waveguides for the far infrared region of electromagnetic spectrum. Due to substantial suppression of absorption of low-frequency radiation in doped graphene the damping and skin effect in the photonic crystal are also suppressed. The advantages of the graphene-based photonic crystal are discussed.     

多个单负材料缺陷一维光子晶体的孪生缺陷模

分析了含有多个单负材料缺陷层的一维光子晶体中缺陷模的性质。在两种单负(负介电常量或负磁导率)材料交替堆叠形成的一维光子晶体中,掺入了多个周期排列的单负材料缺陷层,得到在该光子晶体的零有效相位(zero-effective phase)带隙内存在孪生缺陷模。通过改变缺陷的数目或缺陷层的厚度,可调节缺陷模的频率间隔,但缺陷模的数目总保持为两个。计算结果显示,该孪生缺陷模的频率对入射角度的依赖较弱;随着入射角度的改变,缺陷模频率的相对改变量总保持在0.03以下。此外,对应缺陷模频率的电场在该光子晶体中传播时,将被强烈地局域在缺陷层与周期结构的交界面上。     

Spiral three-dimensional photonic crystals for telecommunications spectral range

Three-dimensional photonic crystals consisting of periodic arrays of spiral columns were fabricated in a commercially available photoresist (SU-8) by a direct laser writing technique. Tailoring the pre- and post-processing conditions for the photoresist has enabled the recording of extended, self-supporting periodic structures with sub-diffraction resolution. Pronounced photonic stop gaps were observed at wavelengths between 1.5 and 1.8 μm, close to the telecommunications region. These structures can be used as accurate and robust templates for subsequent infiltration by materials with higher refractive index. PACS 42.65.Re; 42.70.-a; 42.70.Qs     

Extending the zero-effective-phase photonic bandgap by one-dimensional ternary photonic crystals

A novel method to enlarge the zero-effective-phase bandgap has been presented in the one-dimensional photonic crystals by sandwiching the third material between the two single-negative materials to form a one-dimensional ternary periodic structure. The band-edges formula for the one-dimensional ternary photonic crystal is derived based on the effective-medium theory and the expressions of the upper and lower frequency limits for the ternary photonic crystals are obtained. Then two schemes to enlarge the zero-effective-phase bandgaps are put forward. Moreover, the angular- and polarization-dependences of the photonic bandgap are investigated. Finally, the role of the dispersion in the sandwiched layer on the bandgap extending has been discussed and two schemes are also presented to enlarge the zero-effective-phase photonic bandgap.