Influences of the Current Transverse Profile on the Transverse Mode Competition of VCSELs Diodes

A spatially independent model of vertical-cavity surface-emitting lasers (VCSELs) is derived by integrating the spatially dependent rate equations over the cross section of the cavity of a VCSEL. The angular and radial non-uniformities of the injection current are taken into account. The well-known LP modes of a weakly-guiding cylindrical waveguide are employed to describe the transverse modal structure in the VCSEL cavity. This model is solved in a self-consistent way by using the 4th order Runge-Kutta method. The dependence of transverse mode competition on the current intensity, the angular and radial non-uniformities of the injection current, and the geometrical parameters of the electrical contact are thoroughly investigated and analyzed. The results are useful to the optimum design of the optical transverse modal structure of VCSELs.     

Multipole Excitation of Localized Plasmon Resonance in Asymmetrically Coated Core–Shell Nanoparticles Using Optical Vortices

Plasmonic interactions between an asymmetrically coated core–shell (ACCS) nanoparticle and an optical vortex produce a novel engagement of the spin angular momentum (SAM) and the orbital angular momentum (OAM) of the input. Simulations based on a discrete dipole approximation (DDA) indicate that the SAM and the OAM of the incident beam determine the modal order of resonance, correctly identifying the peak wavelength, and both the direction and magnitude of optical torque exerted upon the excited, localized plasmon resonance in the ACCS particle. These simulations also indicate higher-order resonances, including hexapole and octupole modes, and a zero-order resonance (expressible as a monopole mode), can be excited by judicious selection of the SAM and OAM. A detailed symmetry analysis shows how the multipoles associated with eigenmode excitations connect to the radiation multipoles at the heart of the multipole expansion. It is also shown how additional, distorted resonance modes due to the asymmetricity of the structure are also exhibited. These specific plasmonic characteristics, which cannot be realized by plane wave excitation, become possible through the ACCS asymmetry engaging with the distinct optical vortex nature of the excitation.     

Two-dimensional characterization of atmospheric profile retrievals from limb sounding observations

Limb sounders measure atmospheric radiation that is dependent on atmospheric temperature and constituents that have a radial and angular distribution in Earth-centered coordinates. In order to evaluate the sensitivity of a limb retrieval to radial and angular distributions of trace gas concentrations, we perform and characterize one-dimensional (vertical) and two-dimensional (radial and angular) atmospheric profile retrievals. Our simulated atmosphere for these retrievals is a distribution of carbon monoxide (CO), which represents a plume off the coast of south-east Asia. Both the one-dimensional (1D) and two-dimensional (2D) limb retrievals are characterized by evaluating their averaging kernels and error covariances on a radial and angular grid that spans the plume. We apply this 2D characterization of a limb retrieval to a comparison of the 2D retrieval with the 1D (vertical) retrieval. By characterizing a limb retrieval in two dimensions the location of the air mass where the retrievals are most sensitive can be determined. For this test case the retrievals are most sensitive to the CO concentrations about 2° latitude in front of the tangent point locations. We find the information content for the 2D retrieval is an order of magnitude larger and the degrees of freedom is about a factor of two larger than that of the 1D retrieval primarily because the 2D retrieval can estimate angular distributions of CO concentrations. This 2D characterization allows the radial and angular resolution as well as the degrees of freedom and information content to be computed for these limb retrievals. We also use the 2D averaging kernel to develop a strategy for validation of a limb retrieval with an in situ measurement.     

低阶模式校正自适应光学系统的非等晕限制

分析了非科尔莫戈罗夫湍流情况下,自适应光学系统低阶模式校正时的非等晕误差、泽尼克系数角相关函数、残余相位结构函数以及长曝光光学传递函数,并定义了一个新变量－－模式校正因子,用来有效评价目标非等晕误差对低阶模式校正自适应光学系统补偿效果的影响。此外还给出了光波水平大气传输时模式校正因子以及低阶模式校正系统长曝光光学传递函数的数值计算结果。     

Study of spatial-temporal characteristics of optical fiber based on ultrashort-pulse interferometry

We demonstrate a method for reconstruction of the modal intensity distribution of light at the output of an optical fiber. Spatial modes of the optical fiber are separated in time as a result of differences in group velocity and are detected experimentally by observation of the interference of the modal field distribution with the time-gating reference field. The detected interference patterns of the modal fields are analyzed, providing the spatial impulse response of the fiber. We also use interferometric correlation to determine the spatiotemporal characteristics of the fiber modes, such as pulse width, linear chirp, and group velocity, for each mode.     

Modified finite volume method applied to radiative transfer in 2D complex geometries and graded index media

A modified finite volume method with unstructured triangular meshes is proposed to solve the RTE in 2D complex geometries and for graded index media. In such media, the RTE has an additional term corresponding to “angular redistribution”. This term is due to the change in the orientation of the direction of propagation for the radiation along curved optical paths. Some benchmark cases applied to a slab (1D) and a square cavity (2D) with linear and nonlinear refractive graded index are used to validate the new method. New results are presented for a disk with radial graded index.     

Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light

A higher-order Poincaré sphere and Stokes parameter representation of the higher-order states of polarization of vector vortex beams that includes radial and azimuthal polarized cylindrical vector beams is presented. The higher-order Poincaré sphere is constructed by naturally extending the Jones vector basis of plane wave polarization in terms of optical spin angular momentum to the total optical angular momentum that includes higher dimensional orbital angular momentum. The salient properties of this representation are illustrated by its ability to describe the higher-order modes of optical fiber waveguides, more exotic vector beams, and a higher-order Pancharatnam-Berry geometric phase.     

The receptance method applied to ring-stiffened cylindrical shells: Analysis of modal characteristics

The receptance method is applied to determine the natural frequencies and mode shapes of circular cylindrical shells stiffened by rings. The receptances of cylindrical shell and of a ring to forces in the radial and circumferential directions are derived in terms of the modal characteristics of each. A matrix equation of free vibration, which must be solved by an iterative technique, results by eliminating the angular variable. An iterative solution is practical, since the size of the matrices remains at two times the number of stiffening rings, regardless of the number of modes of the unstiffened cylinder and rings included in the solution. The validity of the method is demonstrated by comparing results for specific cases with the results obtained theoretically and experimentally by others. When various stiffener configurations are being considered for a given cylindrical shell, the modal characteristics of the shell without stiffeners may be calculated once and used repeatedly to calculate the frequencies of the stiffened shell configurations. The form of the results offers potential for simplifications which are presented in a companion paper.     

Electrically pumped two-dimensional Bragg grating lasers

We demonstrate electrically pumped InGaAsP two-dimensional Bragg grating (2DBG) lasers with two line defects. The 2DBG structure uses a weak 2D index perturbation surface grating to control the optical modes in the plane of the wafer. Measurements of the 2DBG lasers show that modal control in both the longitudinal and transverse directions is due to the gratings and defects. The 2DBG lasers are promising candidates for single-mode, high power, and high efficiency large-area lasers.     

Cutoff frequencies in optical fibres with central refractive-index depression

Exact analytical solutions are given for modal cutoff frequencies in round optical fibres with a central refractive-index depression represented by a radial index distribution Rp in the core. The cutoff frequencies Vc for modes with azimuthal order m are the solutions of Jq−1(2Vc/{2+p})=0, where q = 2m/(2 + p). An accurate analytical approximation formula for the cutoff of the LP11 mode is developed, which even circumvents the calculation of real-order Bessel function zeros. For the LP02 mode, as well as for all other circularly symmetric modes, the exact cutoff frequency is merely a linear function of the profile parameter p. This revised version was published online in November 2006 with corrections to the Cover Date.     

光学无源谐振腔的矩阵理论(柱坐标)(Ⅱ)——轴对称稳定光学无源谐振腔的计算

本文的目的是探讨应用文献[1]中提出的光学无源谐振腔的矩阵方程,解决腔中振荡横模的具体计算方法问题,并讨论其精度。为了便于与已有公式较可靠的结果相比,我们挑选了由两面对称的球面反射镜组成的、菲涅耳数N≤1的各种稳定腔作为计算对象;还分别用数学试验法和文献[1]中得出的误差上限公式,求出所得结果的误差。结果表明:对于基横模,所得结果与文献[3,6]的结果在报道的精度内很好地符合;对于包括高阶模在内的各阶横模,文献[1]中所得公式的误差上限都是正确的,但往往大大偏高。计算结果实际上往往具有高得多的精度。文中对g=0,0.5,0.8,0.9,0.95,菲涅耳数N=1的稳定腔,列出了l=0,p=0,1,2,3,4,5的各阶横模的本征值;绘出了l=0,1,2,p=0,1,2各阶横模场的相对振幅与位相分布曲线。还绘出了上述诸类稳定腔中N=1/π时TEM₀₀,TEM₀₁模的场分布曲线。从所得结果中得出了一些新的规律,并进行了某些讨论。本文结果表明:用这种矩阵理论,确实可以较为方便地一次求得模损耗不极近于1的、角模数l任意给定而径模数p不同的、所有各阶横模的性质,并能给出所得结果的误差上限,保证其具有相当高的精度。由于所用坐标系关系,本方法仅适用于具有理想轴对称性的谐振腔。 关键词：     

双芯光子晶体光纤中的模式干涉

应用全矢量超格子叠加模型分析了双芯光子晶体光纤(PCF)的模式特征.双芯PCF的基模和二次模分别由偏振方向不同的两个偶模和两个奇模组成，讨论了这四个模式的模式电场奇偶性.基于对双芯PCF模式电场奇偶性的认识，讨论了光纤中的矢量模式干涉问题.分析表明，不同偏振态模式的干涉不会引起芯间的功率转移，双芯PCF的芯间功率耦合是由相同偏振模式的干涉引起的.在相同偏振模式干涉过程中，光功率在两个芯子中呈余弦振荡，光纤的两个芯子一般存在约π／2的相位差.还讨论了两个不同偏振方向的耦合系数与波长的关系. 关键词： 光子晶体光纤 双芯光纤 模式 干涉 耦合     

LIGA technology for the synthesis of diffractive refractive intraocular lenses

The manufacturing of test diffractive refractive intraocular lenses is illustrated by means of LIGA (deep X-ray LIthography and GAlvanoplastics and polymer forming). Dynamic X-ray lithography used while rotating the substrate versus an X-ray mask fixed in a beam of synchrotron radiation (SR) yields smooth optical 3D surfaces with roughnesses of 10–30 nm rms in polymethylmethacrylate (PMMA) layers. The axisymmetric diffractive refractive profile of a lens is predetermined by the radial angular function of the X-ray mask topology. The quality of the optical surface is reproduced for the nickel master form, which is electroplated onto a gold layer atop the PMMA relief. The optical quality also remains high for replicated lenses synthesized in this manner during silicon polymerization.     

用耦合波理论求解渐变折射率光纤的传播常数和模式场

本文应用耦合波理论来计算任意渐变折射李光纤的传播常数和模场分布.将无限伸展的抛物型折射率分布光纤作为一个理想波导,任意径向不均匀折射率分布光纤便可以视作该理想波导的微扰,其模场可以展开成一组完备的理想波导模的叠加.然后,模场和传播常数可以通过耦合波方程求得.进一步将一阶微分方程组形式的耦合波方程变换成线性方程组,使计算过程大大简化.文中给出了数值计算结果,并将其与准确值进行了比较.     

Optical circulators in two-dimensional magneto-optical photonic crystals

We propose an optical circulator formed of a magneto-optical cavity in a 2D photonic crystal. With spatially engineered magnetic domain structures, the cavity can be designed to support a pair of counterrotating states at different frequencies. By coupling the cavity to three waveguides, and by proper matching of the frequency split of the cavity modes with the coupling strength between the cavity and the waveguide, ideal three-port circulators with complete isolation and transmission can be created. We present a guideline for domain design needed to maximize the modal coupling and the operational bandwidth for any given magneto-optical constant.     

Loss measurement of plasmonic modes in planar metal-insulator-metal waveguides by an attenuated total reflection method

We report experimental excitation and characterization of surface plasmon modes in planar metal-insulator-metal (MIM) waveguides. Our approach is based on determining the width of the reflection angular spectrum in the attenuated total reflection (ATR) configuration. Owing to its transverse character, the ATR configuration provides a more straightforward and simpler way to determine the loss of plasmonic modes in MIM structures, compared to using tapered end couplers with multiple waveguide samples or scanning near-field optical microscopy. In this Letter, two waveguide structures with Au claddings and 50/200 nm SiO(2) cores are investigated. The propagation lengths measured at λ = 1.55 μm are 5.7 and 18 μm, respectively, in agreement with the theoretical predictions.     

Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber

Acousto-optic interaction in optical fiber is examined from the perspective of copropagating optical and acoustic vortex modes. Calculation of the acousto-optic coupling coefficient between different optical modes leads to independent conservation of spin and orbital angular momentum of the interacting photons and phonons. We show that the orbital angular momentum of the acoustic vortex can be transferred to a circularly polarized fundamental optical mode to form a stable optical vortex in the fiber carrying orbital angular momentum. The technique provides a useful way of generating stable optical vortices in the fiber medium.     

大芯径大数值孔径阶跃光纤传导模特征方程求解

导出了相邻阶第二类变型贝塞尔函数的比值在小宗量的逼近形式,利用Lentz—Thompson方法计算相邻阶第一类贝塞尔函数的比值在小宗量的值,计算精度为浮点数系统的最低有效位。从而解决了求解大芯径、大数值孔径阶跃光纤的特征方程时．贝塞尔函数溢出双精度浮点数表示范围的问题。分别对多模石英光纤和大芯径大数值孔径的聚合物光纤的传导模特征方程进行了求解,石英光纤的传导模特征值计算结果与Optiwave公司的软件一致;对于聚合物光纤,算法给出了所有模式的计算结果,其中模式角向序数小于70的计算结果与Optiwave公司的软件一致,而Optiwave公司的软件不能计算角向序数大于70的模式。     

On a relation of the angular frequency to the Aharonov–Casher geometric phase in a quantum dot

By analysing the behaviour of a neutral particle with permanent magnetic dipole moment confined to a quantum dot in the presence of a radial electric field, Coulomb-type and linear confining potentials, then, an Aharonov–Bohm-type effect for bound states and a dependence of the angular frequency of the system on the Aharonov–Casher geometric phase and the quantum numbers associated with the radial modes, the angular momentum and the spin are obtained. In particular, the possible values of the angular frequency and the persistent spin currents associated with the ground state are investigated in two different cases.     

Symmetry and degeneracy in microstructured optical fibers

The symmetry of an optical waveguide determines its modal degeneracies. A fiber with rotational symmetry of order higher than 2 has modes that either are nondegenerate and support the complete fiber symmetry or are twofold degenerate pairs of lower symmetry. The latter case applies to the fundamental modes of perfect microstructured optical fibers, guaranteeing that such fibers are not birefringent. We explore two numerical methods and demonstrate their agreement with these symmetry constraints.