Orthonormal polynomials in analysis of single-mode fiber coupling

Zernike polynomials have been widely used for wave-front analysis because of their orthogonality over a uniform circular pupil. However, the pupil is not uniform but weighted by the backpropagated fiber mode in analyzing fiber coupling efficiency. Zernike polynomials are not appropriate for a weighted pupil due to their lack of orthogonality over such pupil. We emphasize the advantages of using orthonormal polynomials in fiber coupling systems. The orthonormal polynomials over weighted pupil are derived by matrix approach. The effects of primary aberrations are investigated based on the orthonormal polynomials. The accuracy of the Strehl ratio approximation for primary aberrations is evaluated.     

熔锥型微纳光纤耦合器的理论与实验研究

针对熔融拉锥系统制得的熔锥型微纳光纤耦合器,选择适当的连续函数描述其光场分布,采用归一化的三角分布和矩形分布的加权叠加,以及高斯分布和三角分布的加权叠加实现了模场沿耦合器区域的连续变化;利用局部模式耦合理论推导出腰区及腰区附近锥形区的耦合系数计算公式,并得到微纳光纤耦合器输出光功率随拉伸长度的变化曲线.计算结果表明,随着拉伸长度的增加,光能量在两臂中来回交替耦合的程度变小并且呈现包络样,直至腰区耦合功能消失.通过实时监测拉制微纳光纤耦合器的输出光功率,得到火焰扫描宽度以及氢气流量对双纤失去耦合效应拉伸长度的影响:火焰扫描宽度(均匀腰区)越宽,拉伸长度临界值越大;氢气流量(熔融度)越大,拉伸长度临界值越小.实验结果显示,当光纤耦合器腰区直径达到1.6μm时,耦合功能消失,两输出端口光功率相同且恒定,微纳光纤耦合器具备稳定的光学传输特性.     

Analysis of electrooptically induced waveguides in strontium barium niobate and optical modulators

An electrooptically induced optical waveguide can be formed by applying a DC voltage between electrodes fabricated on the surface of a crystal with strong electrooptic coefficients (for example, strontium barium niobate). Calculations of the refractive index profile and the optical mode size for such waveguides are presented. Approximate solutions for the fundamental mode are used to analyse the power coupling between a single-mode step-profile fibre and these waveguides. The power transmission losses in the straight and S-shaped waveguides are estimated by using a finite-difference beam propagation method (FD-BPM). The calculations predict that a new kind of modulator/switch can be realized with the induced waveguides. The important characteristics of these devices are discussed and compared with LiNbO₃ optical waveguide modulators.     

非平行波导耦合理论研究

利用耦合模理论对非平行波导耦合特性进行了研究，得到了非平行波导的普遍性耦合方程及耦合系数表达式.进一步采用小角度近似，给出了几种情况下的计算结果，并与目前报道的利用其他方法计算的结果做了比较.研究表明，不同方法得到的波导中光功率虽然在远距离处都趋于稳定不变，但稳定功率的大小有明显的差别；另外由新提出方法得到的近距离处光功率随着传输距离的起伏变化更为明显.由于该方法同时考虑了非平行波导中光场相位和振幅对耦合方程和耦合系数的影响，因而所得结果能更全面地反映非平行波导的耦合特性，对实际应用更有意义. 关键词： 非平行波导 耦合方程 耦合系数     

Mode conversion and radiation losses in a step-index optical fibre due to bending

Wave propagation in a step-index optical fibre with a curved section is treated theoretically. Mode conversion and radiation take place. The mode coupling coefficients which depend on the polarization of the incident mode are calculated. Radiation losses at the transition between a straight and a curved fibre section and total losses including the continuous radiation loss due to a uniform bend are evaluated. Comparisons are also made between singly and doubly clad fibres. It is shown that the doubly clad fibre can tolerate a sharper bend.Requests for reprints should be sent to Professor G. L. Yip.     

Calculation of the frequency response in step-index plastic optical fibers using the time-dependent power flow equation

The time-dependent power flow equation, which is reduced to its time-independent counterpart is employed to calculate frequency response and bandwidth in addition to mode coupling and mode-dependent attenuation in a step-index plastic optical fiber. The frequency response is specified as a function of distance from the input fiber end. This is compared to reported measurements. Mode-dependent attenuation and mode dispersion and coupling are known to be strong in plastic optical fibers, leading to major implications for their frequency response in data transmission systems.     

Mode energy transformation between two connected multimode general square-law-index optical waveguides

A coherent states method is used to investigate the mode coupling coefficients in the most general buttjoint problem for two multimode general square-law-index optical waveguides, when two different waveguides with elliptical cross-sections are to be butt-jointed with axis displacement, tilt and some turning of symmetry axes with respect to each other. The explicit expressions for the mode coupling coefficients and recurrence relations for the mode overlap integrals are obtained; the sum rules for the mode coupling coefficients are formulated and a method of experimental data analysis is proposed for this general problem. The method of calculating mode coupling coefficients is proposed for the case of the butt-joint problem when the waveguide cross-sections are only partially overlapping and then it is used to investigate the influence of misalignment on mode power distribution and pulse dispersion in the second waveguide. The experimental data are compared and it is shown that the coupling coefficients obtained in square-law-index model can be used in dispersion calculations forα-profile fibres in the case when the valueα is not far from the valueα=2.     

Dynamics of two-mode radiation in optical waveguides with strong mode coupling

Amplitude equations, as well as the effective dispersion and nonlinearity parameters, which define the dynamics of a wave packet formed by two strongly coupled modes, are derived with allowance for the frequency dependence of the linear mode coupling coefficient. These equations are used to study the onset of the modulation instability of the two-mode wave packet, soliton-like pulses, and compression modes. Unlike single-mode systems, the last two effects in optical waveguides may arise for both a negative and positive disper-sion of the waveguide material.     

Modal redistribution and power loss in on-fibre devices

The mode coupling and optical power loss taking place in on-fibre devices are investigated. These devices are fabricated by removing the cladding of a multimode fibre and replacing it with a new material such as electro-optic or magneto-optic. Under an application of an external field the index of this modified cladding increases, leading to coupling among guided modes and coupling to radiation modes, resulting in optical power loss. The coupling among guided modes and the power loss are calculated as a function of the change in the index under the field and the length of the active region for the case when HE_1m modes are excited individually or in a group. Results indicate that on-fibre devices may be used as low-loss devices for applications involving sensors and delay lines.     

二极管激光器侧泵浦波导耦合系统设计

 为了提高面阵二极管激光器侧泵浦板条激光器泵浦光的利用率，本文采用光线追迹的方法，通过数字模拟设计出了高耦合效率的波导耦合系统。实验测试结果表明，其耦合效率达到85%以上，泵浦光在板条内分布均匀。     

Collinear interaction of optical waveguide modes with an increasing space-charge wave

Collinear interaction of optical modes in a thin-film semiconductor waveguide with a space-charge wave increasing along its propagation direction has been investigated. Analytical solutions to the equations of coupled unidirectional and counterpropagating waveguide modes at their phase matching are obtained for the first time, and the dependence of the mode conversion efficiency on the space-charge wave amplification level, the coupling coefficient, and the length of the interaction region of optical modes is analyzed.     

Coupling coefficient of two-core microstructured optical fiber

In this paper, coupled-mode theory is applied to a two-core microstructured optical fiber for the first time to calculate the coupling coefficients for different fiber structures by employing a simple effective index model approach. The dependence of the mode coupling properties upon the geometrical parameters of the two-core structures (air-hole arrangement, hole size, and pitch size) and wavelength are evaluated systematically. The effective index coupled-mode theory is compared with the finite-element method based super-mode theory in details and the results show good agreement. The coupling characteristics are proven to be insensitive to the longitudinal strain by considering the photoelastic effects.     

Nonlinear optical properties of a three-dimensional anisotropic quantum dot

The linear and nonlinear optical properties in a three-dimensional anisotropic quantum dot subjected to a uniform magnetic field directed with respect to the $z$-axis have been investigated within the compact-density matrix formalism and the iterative method. The dependence of the linear and nonlinear optical properties on the characteristic frequency of the parabolic potential, on the magnetic field, and on the incident optical intensity is studied in detail. Moreover, taking into account the position-dependent effective mass, the dependence of the linear and nonlinear optical properties on the dot radius is investigated. The results show that the optical absorption coefficients (ACs) and refractive index (RI) changes of the anisotropic quantum dot (QD) are strongly affected by these factors, and the position effect also plays an important role in the optical ACs and RI changes of the anisotropic QD.     

Shear Viscosity and Temperature Inequalities for Multi-Species Plasmas

The first coefficients in the orthogonal expansions of the velocity distribution functions with respect to Grad's tensorial (three-dimensional) Hermite polynomials are shown to be proportional to ther-modynamic fluxes, if the weight functions are local Maxwellians centered at the mean mass velocity and widened with a mean temperature. Balance equations for the stress tensors are established and reduced to linear algebraic systems under certain restrictions. Explicit solutions for the traces and the tracefree parts of the stress tensors are given.     

用八孔耦合器识别TM0_(1)/TE_(11)混模中TE_(11)模式的方法北大核心CSCD

在高功率微波传输系统中,为了提高功率容量和效率,往往采用过模波导,因此圆波导中往往出现TM_(01)和TE_(11)混合模式的情况。采用角向均匀分布的8孔圆波导耦合器,对提取TE_(11)模式的混合比和极化角度的方法进行了分析和研究。分析了圆波导中TM_(01)和TE_(11)模式在耦合孔处的电场分布,并采用CST对各耦合孔的输出功率进行了模拟计算,得出相互正对的耦合孔的平均功率与8个孔的平均功率之比与模式之间的相位差无关的结论。同时,发现该比值与TE_(11)模式的混合比成线性关系,线性关系中的比例系数是极化角度线性函数。通过线性拟合获得了计算TE_(11)模式混合比和极化方向的表达式。与仿真设定的参数相比,用该表达式计算的结果表明,在TE_(11)模式混合比小于30%时,用其计算TE_(11)模式的混合比和极化角度是可行的,误差不超过10%。在此基础上,给出了实际情况下TE_(11)模式信息的具体判断方法。     

Effects of joints on mode power distribution and losses in multimode optical fibres

The transformation of mode power distribution at a joint between two different (even elliptical) optical fibres is studied. Simple analytical expressions are obtained also in the most general coupling and mismatch configuration, provided that coupling errors and mismatch parameters are small. Detailed calculations of joint losses are performed in each case, including propagation effects in both fibres. Original results are obtained particularly in the cases of misalignment, end separation between the fibres, mismatches in index profiles and coupling between two elliptical fibres. A strong dependence on the launching conditions and the amount of mode coupling is evidenced in all cases.     

A novel power divider with arbitrary power division and high coupling efficiency with a single mode fibre

To improve the coupling efficiency of a conventional Ti: LiNbO₃ channel waveguide with a single mode fibre, a promising Ti-Mg double diffused method has been employed to fabricate a single mode power divider. Calculated numerical results have revealed the feasibility of reducing coupling loss as well as radiation loss, and a set of efficient fabrication parameters for this single mode device can be established. The dependence of asymmetric branching angles and output dividing-power-ratios has been studied by adjusting the branching angle.     

Mode coupling between two connected multimode parabolic-index optical waveguides

Both a displacement of axis and a change in the refractive index distribution function cause mode coupling to occur between two multimode parabolic-index optical waveguides. This coupling is investigated by the coherent states method and the method of the dynamical symmetry group. Expressions for the mode coupling coefficients are obtained and their relationship to the Franck-Condon factors is emphasized. Recurrence relations for the mode overlap integrals and sum rules for the mode coupling coefficients are presented. An analogue of the Franck-Condon principle for the mode coupling coefficients is formulated. A simple geometric method for finding the most intensively coupled modes is also proposed.     

"Ideal" optical delay lines based on tailored-coupling and reflecting, coupled-resonator optical waveguides

We present a design of "ideal" optical delay lines (i.e., constant amplitude and constant group delay over the desired bandwidth). They are based on reflection from coupled-resonator optical waveguides (CROWs). The inter-resonator coupling coefficients are tailored and decrease monotonically with the distance from the input to realize all-pass Bessel filters. The tailored coupling coefficients result in a frequency-dependent propagating distance which compensates for the group velocity dispersion of CROWs. We present a simple formalism for deriving the time-domain coupling coefficients and convert these coefficients to field coupling coefficients of ring resonators. The reflecting CROWs possess a delay-bandwidth product of 0.5 per resonator, larger than that of any kind of transmitting CROW. In the presence of uniform gain, the gain enhanced by slow light propagation and the constant group delay result in efficient and dispersion-free amplifiers.