Method of Designing a Corrugated Optical Waveguide Filter

The method of designing a corrugated optical waveguide filter is proposed to yield an arbitrary spectral profile of the reflection coefficient. It gives the functional dependence of the corrugation depth on distance along the wave propagation direction. The basis of the theory of the method is a combination of the effective index approach and the Fourier transformation technique. It represents the spectral profile of the reflection coefficient approximately to Fourier transformation of the spatial profile of the effective refractive index. Examples are presented to illustrate how to apply the technique.     

电光聚合物波导中的锥形结构

提出并设计了一种基于电光聚合物的锥形波导,可用于单模光纤与电光聚合物波导器件之间的连接.锥形波导中采用了宽度锥形和折射率锥形结构.宽度锥形采用劈形形状,通过宽度和折射率的缓慢变化实现模场转换.劈形形状的宽度锥形具有较小的损耗且易于制作,折射率锥形可采用灰度掩膜光刻技术制作.研究了锥形波导的传输损耗与锥形波导的长度、波导宽度和厚度、材料吸收损耗等参数的关系及其优化,分析了锥形波导中的功率传输、模场分布与模式转换效率.结果显示锥形波导的传输损耗小于0.37 dB,光纤-波导-光纤的连接损耗优于1.62 dB,对插入损耗的改善达到8.78 dB,模场转换效率达到了83.7%.     

Dispersion characteristics of complex refractive-index planar slab optical waveguide by using finite element method

In this paper, finite element method (FEM) mode analyses of planar slab optical waveguide having complicated refractive index profile are presented. We try to estimate the dispersion graph, mode cut-off condition, group delay and waveguide dispersion for the case of α-power and chirped-type refractive index profile. In order to obtain the more accurate result, we have derived the higher-order polynomial, which establishes the suitable relationship between b and V for different profile of optical waveguide. On the basis of the derived polynomials, the waveguide dispersion is analyzed for different type of refractive index profile waveguide. Our study shows that the waveguide dispersion can be substantially reduced when we deployed the optical waveguide having linearly chirped-type refractive index profile. Earlier too, the arbitrary refractive index profile has been analyzed but to the best of our knowledge chirped-type refractive index profile has not been analyzed till date for the case of planar slab optical waveguide.     

Fast convergence and higher-order mode calculation of optical waveguides: perturbation method with finite difference algorithm

We present an efficient algorithm for determining mode eigenvalues as well as field distributions of optical waveguides with two-dimensional transverse refractive index profile. The algorithm is devised with the analytical perturbation correction method combined with the finite difference approximation of Helmoltz's equation. The technique is simple and does not involve solving any eigenvalue equation or matrix formalism. The algorithm reduces abruptly the computation time required for the field convergence to mode, and can calculate any higher-order modes without the need of any pre-conditioning the field w.r.t. waveguide geometry, or calculation of previous order modes and/orthogonalization. The analysis can yield precisely both scalar and polarized modes. By applying it to waveguide problems whose solutions are otherwise known, the efficacy of the method has been established.     

A design method for dielectric multilayer optical filters

A generalized design method for an optical filter consisting of a dielectric multilayer structure is proposed to get an arbitrary profile of the wavelength dispersion of reflectivity or transmittance. The basic concept of the method lies in the fact that the wavelength dispersion of the reflectivity is approximately determined by taking the inverse Fourier transformation of the refractive index profile of the multilayer structure. Construction of a filter with only three different values of refractive index is described.     

有限元法求解任意折射率分布光纤模场分布

 应用有限元方法求解了任意径向非均匀折射率分布园柱对称介质波导中纵向场耦合波动方程定解问题所对应的变分问题,该方法不受弱导或高斯模场分布等限制,可方便地求解光纤中介质波导的模场分布。用此方法研究了带阶跃环的三角型分段折射率分布光纤中归一化模场半径与芯层传输功率比值随光纤不同结构参数的变化规律。     

Efficient coupling of a laser to a waveguide using a taper designed by conformal mapping

Maximising the optical power collected in a waveguide from the diffracting field of a semiconductor laser is desirable in optical fibre communication systems. However, the spot size and phase front curvature of the laser field usually makes a poor overlap with the mode of the receiving waveguide. Various proposals have been made to improve this coupling. This paper presents the design of a tapered waveguide section, having the correct geometry and refractive index profile, to efficiently capture and transform the rapidly diffracting light from a semiconductor laser to a planar wavefront in a straight waveguide. Experimentally, such an approach requires the refining of available techniques (UV exposure, ion implantation or diffusion) to obtain the required grading of the refractive index profile within the tapered input section of the receiving waveguide.     

迭代法重建平板光波导折射率分布

提出了一种用于重建渐变折射率平板光波导折射率分布的方法,这种方法通过数值法求解亥姆霍兹方程．从光波导的低阶模开始采用迭代法顺次对各个模式对应的“转折点”位置进行校正．并多次重复迭代以消除“转折点”外折射率分布的变化对相应模式“转折点”位置的影响。借助WKB近似原理说明了这种方法迭代过程中“转折点”坐标的收敛性。对折射率按照指数规律变化的平板光波导的折射率分布重建结果证明这种方法具有较高的精度。分析表明：这种方法克服了WKB法固有的缺陷,即忽略模式“转折点”外折射率分布对相应模式传输常鞋的影响和“转折点”处相移的不确定性,因而比逆WKB法具有更好的自洽性和精确性。     

Sixth moment optimization of multi-channel Bragg filters

The design of multichannel optical filter is studied theoretically. New efficient two-step method based on combination of 6-th moment minimization and straightforward numerical minimization is developed. It is applied to find a fiber Bragg grating profile with minimal refractive index variation for 5 ÷ 32 channels. Obtained results are closer to the theoretical limit than previously reported.     

New design for a variable optical attenuator based on a bent channel waveguide

We present a new method for bend loss control in a curved channel optical waveguide and employ it in a novel design of a thermo-optic variable optical attenuator. We show that the introduced asymmetric refractive index profile of the waveguide structure, combined with the optimal placement of the heating electrodes, leads to a significant increase of the dynamic range of the attenuator. PACS 42.82.Et; 42.70.Jk; 42.79.Ta     

一种简单精准的渐变折射率分布光波导分析方法

渐变折射率分布的光波导分析对光波导器件的设计和研究至关重要, 近年来已提出了多种分析方法, 然而在简便性或准确性上都存在着不足. 为此, 提出了一种分析渐变折射率分布光波导的方法, 能够结合现有的Wentzel-Kramers-Brillouin近似法和离散化的波动方程, 构建模场分布, 再结合变分运算方程和修正的模式本征方程, 计算出较为精确的有效折射率. 与其他分析方法相比, 该方法较为简单, 而且有一定的精度.     

Gradient-index narrow-bandpass filter fabricated with glancing-angle deposition

Glancing-angle deposition (GLAD) is a fabrication method capable of producing thin films with engineered nanoscale porosity variations. GLAD can be used to create optical thin-film interference filters from a single source material by modification of the film refractive index through control of film porosity. We present the effects of introducing a layer of constant low density into the center of a rugate thin-film filter fabricated with the GLAD technique. A rugate filter is characterized by a sinusoidal refractive-index profile. Embedding a layer of constant refractive index, with a thickness equal to one period of the rugate index variation, causes a narrow bandpass to appear within the filter's larger stop band. Transmittance measurements of such a gradient-index narrow-bandpass filter, formed with titanium dioxide, revealed an 83% transmittance peak at a vacuum wavelength of 522 nm, near the center of the stop band, with a FWHM bandwidth of 15 nm.     

A simple reflection-type two-dimensional refractive index profile measurement technique for optical waveguides

We report a new configuration of a reflection-type confocal scanning optical microscope system for measuring the refractive index profile of an optical waveguide. Several improvements on the earlier design are proposed; a light emitting diode at 650 nm wavelength instead of a laser diode or He-Ne laser is used as a light source for better index precision, and a simple longitudinal linear scanning and a curve fitting techniques are adapted instead of a servo control for maintaining an optical confocal arrangement. We have obtained spatial resolution of 800 nm and an index precision of 2 × 10⁻⁴. To verify the system’s capability, the refractive index profiles of a conventional multimode fiber and a home-made four-mode fiber were examined with our proposed measurement method.     

An analytical study of a doubly clad compressed ellipse optical waveguide

Using an analytical method based on boundary matching technique, the modal behavior and cutoff frequencies of a compressed ellipse doubly clad optical waveguide is studied. The proposed waveguide consists of a core region of higher refractive index with two cladding regions: one is inner cladding and the other is outer cladding. We take appropriate orthogonal coordinates for the proposed structure and impose the boundary conditions to obtain the characteristic equation. The effect of the width of inner cladding layer on the dispersion characteristic is observed. It is found that the width of inner cladding is able to tailor the dispersion characteristic and cutoff condition of the waveguide up to a certain limit.     

Refractive index design and validation for evanescent field power maximization in optical fibre sensors

The viability and operation of evanescent field-based optical fibre sensors is largely determined by the fraction of the total supported modal field power in the evanescent field. As this fraction is highly dependent on the refractive index profile of the fibre, one design strategy for fibre sensors is to maximize this field power fraction over the class of all refractive index profiles. This paper documents this design strategy for circular geometry optical fibres, where the goal is to maximize the evanescent field power fraction for a particular mode via the selection of an optimal refractive index profile. The axially symmetric profiles obtained approximate “holey” annular structures, the performance of which can be validated using existing waveguide analysis techniques.     

锥形脊结构半导体光放大器的有限元分析

为提高半导体光放大器与单模光纤耦合效率，建立了半导体放大器的锥形脊结构模型。在该模型下利用有限元数值模拟方法分析，计算了波导区折射率、锥尖宽度、条形波导尺寸、渐变折射率波导层对锥形脊结构模式扩展的影响。通过完善锥形脊结构参量的设计，获得了锥形脊结构半导体光放大器与单模光纤95％的耦合效率。     

基于插值的全矢量有限差分法求解阶跃光波导本征模式

给出了一种适合求解阶跃折射率分布光波导本征模式的全矢量有限差分法.该方法充分考虑了电场分量在折射率分布跃变处的不连续性, 在拉格朗日插值的基础上得到了一种精度较高的差分格式.为了验证其有效性,对一种典型结构、折射率阶跃分布的波导作了计算,并与其它方法的结果作了比较.最后对不理想刻蚀情况做了模拟计算.     

用于折射率传感的聚合物基狭缝波导的模拟与制备

设计了在极近红外波段(890 nm)的聚合物基狭缝波导微环折射率传感器.分析了波导高度、宽度及狭缝宽度对灵敏度的影响,以找到最佳的设计标准用于折射率传感.采用电子束光刻工艺制备了硅母版模,并用独特的氟化聚合物PFPE从硅母版模上成功制备了柔性软模具.采用紫外软压印工艺制备了聚合物基狭缝波导.波导的宽度和高度以及狭缝波导的宽度分别约为510 nm、830 nm和234 nm,聚合物狭缝波导残留层的厚度约为350 nm.制备的狭缝波导具有高的高宽比并与低成本批量生产工艺相兼容.     

Dispersion Characteristics of Arbitrary Periodic Structures with Rectangular Grooves

The dispersion characteristics of a circular cylindrical waveguide with periodic surface corrugations consisting of rectangular grooves with smoothing are examined using the Space Harmonic Method (SHM). The whole structure is divided into two regions, one describing the propagation volume and one inside the grooves. In the first region, the Floquet theorem is applicable and the field distribution is expressed as a summation of spatial Bloch components, whereas in the second one an appropriate Fourier expansion of standing waves is used. Applying the boundary conditions an infinite system of equations is obtained, which is solved numerically by truncation. Several cases are considered, including the limiting cases of a sinusoidal and a rectangular corrugation profile, to check the accuracy of the method proposed as well as its dependence on the corrugation profile. Numerical results are presented only for transverse magnetic modes, although the formalism can be easily extended to include all kinds of waves that can in principle propagate in such a structure.     

Simulation of micro/nanometer-scale self-organized lightwave network (SOLNET) using the finite difference time domain method

A simulator for self-organized lightwave network (SOLNET) is developed. The simulator is based on the finite difference time domain method. SOLNET enables us to construct self-aligned coupling waveguides between misaligned micro/nanometer-scale optical devices by self-focusing, which arises from an increase in refractive index induced by write beams in photo-refractive materials. The SOLNET simulator reveals that an L-shaped nanometer-scale optical waveguide of SOLNET is grown from a 0.5-μm-wide optical waveguide when write beams are introduced from the optical waveguide into photo-refractive materials, where a wavelength filter is embedded. The SOLNET simulator also reproduces coupling path construction between a 2-μm-wide optical waveguide and a 0.5-μm-wide optical waveguide having a wavelength filter on the core edge. The optical waveguides are placed with misalignment of 0.5-μm offset. By introducing write beams from the 2-μm-wide optical waveguide, the incident write beams and reflected write beams from the wavelength filter merge into one optical waveguide in the photo-refractive materials, constructing a self-aligned coupling waveguide.