Design of the spot size for single-mode Ti/Mg:LiNbO3, channel waveguide for optimum coupling with fibers

Abstract

To improve the coupling effciency between fibers and conventional Ti:LiNbO₃ diffused channel waveguides, it is feasible that the elliptical mode pattern of the channel waveguide can be modified by the Ti/Mg double diffusion method. By means of the three-dimensional beam propagation method, we successfully show that the mode size of the waveguide fabricated by this method is well matched to that of the fiber for TE and TM polarizations separately.     

Optimal direct coupling from single-mode fibers to Ti:LiNbO3, channel waveguides

We investigate the optimal direct coupling from single-mode fibers to Ti:LihbO₃, channel waveguides using a very general formula and a heuristic optimization technique in this article. The coupling efficiency of the optical power depends on both the fiber positions and the modal sizes of the incident fields. From our numerical simulation, it is found that the optimal positions of the fiber axes are not in alignment with the peaks of the waveguiding modal fields and that the coupling efficiency can be improved by microlenses.     

钛扩散铌酸锂矩形波导中的双折射耦合对传播常数的影响

 从亥姆霍兹方程出发，得到了各向异性光波导在弱导近似下的耦合模理论。耦合系数包括偏振耦合项和双折射耦合项。并用马卡提里近似下的模式作为零级近似。用一级微扰法计算了折射率渐变分布的钛扩散铌酸锂矩形波导的传播常数。在给定参数的情况下，得到双折射项引起的传播常数的改变约为主微扰项的3%，因此双折射耦合对钛扩散铌酸锂矩形波导的性能影响不可忽略，这对设计和分析与它相关的光波导器件具有指导意义。     

Refined modeling of traveling-wave Ti:LiNbO3 channel waveguide modulator

A refined computation model for traveling-wave operation of external electro-optical phase modulators made of a single titanium in-diffused lithium niobate channel waveguide (Ti:LiNbO₃WG) is described. The modulator circuit model outlined as two traveling-wave coupled microstrips includes microwave losses and dispersion. In the optimization procedure, we consider different circuit load conditions. The influence of a dielectric overlay covering the electrodes is examined. The consolidated techniques of conformal mapping, multiple image, and finite element are used to investigate the microwave characteristics of the structure, and the refractive effective index method is used in calculating the characteristics of the diffused anisotropic optical channel. The performances of Y-cut and Z-cut substrate configurations are compared. We have verified that the Y-cut substrate modulator gives the best overall performance, and that the overlay presence causes significant improvements in the evaluated modulation efficiency and in the bandwidth. A model of the modulator that takes electrode thickness into account permits one to obtain a wider bandwidth.     

半径渐变同轴波导模式耦合系数研究

为了用耦合波理论研究一些同轴结构的高频特性,推导了半径渐变同轴波导内模式耦合系数的计算公式,发现半径渐变圆波导模式耦合系数只是同轴波导模式耦合系数的特例。对同轴波导中的模式及其本征方程根的特点进行了讨论,通过建立同轴波导模式和矩形波导模式之间的对应关系,给出了同轴波导模式本征方程根的快速计算方法。对所给模式耦合系数公式进行了验证,耦合波理论计算结果与有限元方法计算结果吻合良好。     

半径渐变同轴波导模式耦合系数研究

 为了用耦合波理论研究一些同轴结构的高频特性，推导了半径渐变同轴波导内模式耦合系数的计算公式，发现半径渐变圆波导模式耦合系数只是同轴波导模式耦合系数的特例。对同轴波导中的模式及其本征方程根的特点进行了讨论，通过建立同轴波导模式和矩形波导模式之间的对应关系，给出了同轴波导模式本征方程根的快速计算方法。对所给模式耦合系数公式进行了验证，耦合波理论计算结果与有限元方法计算结果吻合良好。     

新型结构波导光栅耦合器的耦合特性分析和数值模拟

针对一种新型结构的波导光栅耦合器,通过求解波在直角坐标系下电场分量的亥姆霍兹方程获得了TE导模和TE辐射模的电场。运用模耦合理论分析了光束通过光栅被耦合到波导当中的情况。数值模拟了在不同的波导和光栅结构参数下耦合系数的变化情况。     

Thermal tuning of a fixed Bragg grating for IR light fabricated in a LiNbO3:Ti channel waveguide

We investigate a thermally tunable integrated narrow-bandwidth interference filter for light in the infrared wavelength region around 5=1550 nm fabricated in a channel waveguide in lithium niobate. The filter is based on a holographically recorded and thermally fixed refractive-index Bragg grating. The device is connected to optical single-mode fibers and works polarization-independent. We measure a peak reflectivity of 95% and a linewidth (FWHM) of 0.09 nm. By temperature-controlling the peak wavelength of the filter is tuned. For the linear thermal expansion coefficient of lithium niobate along the c axis the value !₃₃=(4.5ǂ.5)᎒^-6 K^-1 is obtained. Permanent illumination of the filter with incoherent light allows us to adjust the peak reflectivity. Dedicated to Prof. K. Ringhofer on the occasion of his 60th birthday.     

极化子荧光及其断层扫描对Ti:LiNbO3光波导表征研究

小极化子(Nb⁴⁺_Li)荧光处于700—950 nm谱段，对不同化学还原程度同组分的纯铌酸锂晶体的研究表明荧光的强度反映了化学还原程度的强弱.从小极化子浅层能级出发，提出以“1中心3级态跃迁”来描述小极化子的受激荧光过程.钛扩散铌酸锂光波导(Ti：LiNbO₃)表面还原程度的均匀性可能在波导制造的热扩散过程中被破坏.在对铌酸锂波导表面、深部的扫描结果中，荧光的强度呈现出表面与深部、波导内与外的差异，表面的强度是深部的6—8倍.研究表明，利用非损伤性的极化子荧光谱，对加工过程热处理进行检控是非常有效的.同时，波导内与外的荧光强度差异间接反映了波导的横切面的外形.     

Near-stoichiometric Ti:LiNbO3 strip waveguide with varied substrate refractive index in waveguide layer

We report the near-stoichiometric Ti:LiNbO3 strip waveguides fabricated by vapour transport equilibration (VTE) at 1060 C for 12 h and co-diffusion of 4-8 μm wide, 115-nm thick Ti-strips. Optical studies show that these waveguides are monomode at 1.5 μm and have losses of 1.3 and 1.1 dB/cm for the TM and TE modes, respectively. In the waveguide width/depth direction, the mode field follows a Gauss/Hermite-Gauss profile. A secondary ion mass spectrometry study reveals that the Ti profile follows a sum of two error functions along the width direction and a complementary error function in the depth direction. Micro-Raman analysis shows that the Li-composition in the depth direction also follows a complementary error function. The mean Li/Nb ratio in the waveguide layer is about 0.98. The inhomogeneous Li-composition profile results in a varied substrate index in the guiding layer, and the refractive index profile in the guiding layer is given.     

Characteristic of a broadband Ti:LiNbO3 optical modulator with buried electrodes and etched grooves in the buffer layer

Traveling wave Ti:LiNbO₃ Mach-Zehnder optical modulators with buried electrodes and etched grooves in the SiO₂ buffer layer are analyzed by the finite element method. The tradeoff between the bandwidth BW and the half-wave voltage Vπ is discussed. The value of BW/Vπ is used to weight the total performance of the modulator. Taking a thick buffer layer and etching deep grooves in the buffer layer are demonstrated as two effective methods to improve the performance of the modulator. A 3-dB optical bandwidth of 18 GHz with half-wave voltage 5V at a wavelength of 1.55 pm could be obtained even though the electrode is not very thick. When the requirement of half-wave voltage is not very critical, a bandwidth of more than 100 GHz can be obtained.     

Modal approach to waveguide coupling when gaps, offsets and rotations of one waveguide with respect to the other are present

In this paper, optical power coupling when waveguide separations, translations and rotations are present is addressed using a modal expansion technique. Numerical results are presented and discussed for Hermite-Gaussian input and output guided-mode profiles.     

Design and experiments for the waveguide to coaxial cable adapter of a cavity beam position monitor

The waveguide to coaxial cable adapter is very important to the cavity beam position monitor (CBPM) because it determines how much of the energy in the cavity could be coupled outside. In this paper, the waveguide to coaxial cable adapter of a CBPM is designed and experiments are conducted. The curve shapes of experiments and simulations are very similar and the difference in reflection is less than 0.1. This progress provides a reliable method for designing the adapter.     

Variational analysis of Er:Ti:LiNbO3 waveguide lasers based on Gaussian/two-half Gaussian mode field distribution

Starting with two dimensional, scalar wave equation, a variational equation was established for the fundamental TE and TM modes guided in Ti:LiNbO₃ waveguides on the basis of assuming a symmetric Gaussian mode field function in the width direction and two-half Gaussian trial functions in the depth direction. The controllable waveguide fabrication parameters, including channel width, diffusion temperature, initial Ti-strip thickness and diffusion time, dependent of fundamental mode size, effective pump area, coupling efficiency between pump and laser modes, and the coupling loss between a Ti:LiNbO₃ waveguide and a fiber were numerically calculated for Z-cut Er:Ti:LiNbO₃ channel waveguide lasers at three possible emission wavelengths 1532,1563 and 1576 nm and two possible pump wavelengths 1480 and 980 nm. The calculated results were compared with those of Gaussian/Hermite–Gaussian mode field distribution in detail.     

LaF3∶Er,Yb纳米颗粒掺杂有机/无机杂化材料制备光波导放大器及特性研究

采用LaF₃∶Er,Yb纳米颗粒掺杂有机/无机杂化材料作为有源材料,制备了掩埋条形结构光波导放大器,研究了放大器在室温下的增益特性和波导中的频率上转换现象. 当抽运功率60 mW时,波导中明显可见绿色上转换发光,观测到Er³⁺从²H_9/2,²H_11/2,⁴S_3/2,⁴F_9/2到基态⁴I_15/2跃迁分别对应的4个波长分别为405?nm, 520?nm, 544?nm和650?nm的发射峰,分析了其产生机理. 当输入信号光06?mW,抽运功率160 mW时,在1535?nm波长处获得15 dB/cm的相对增益. 关键词： 光波导放大器 增益 上转换     

用于直线感应加速器光源焦斑测量的双锥厚针孔结构设计

研究设计双锥厚针孔结构体,利用小孔成像测量高能强流直线感应加速器光源的焦斑。建立数值计算模型,根据实际光源特性和实验布局条件,模拟光子穿过厚针孔结构的辐射成像过程,分析光源尺寸、分布和偏轴等对焦斑测量的影响。理论计算结果显示对光源物面的空间分辨率可达5 lp/mm。     

Design of tunable asymmetric directional coupler filter using periodically segmented Ti:LiNbO3 waveguides

A tunable wavelength filter is designed using Ti:LiNbO₃ asymmetric directional coupler. One arm of the directional coupler is made of continuous waveguide while the other arm is periodic segmented. This segmentation reduces the lithographic steps and hence the fabrication cost required for such asymmetric coupler based filter. The propagation constant of periodical segmented and continuous waveguides are analysed using Effective-Index-based Matrix Method. The tunability is achieved using electro-optic property of LiNbO₃.     

Enhancing the magnetoelectric coupling of Co4Nb2O9[100] by substituting Mg for Co

We report experimental studies on enhancing the magnetoelectric (ME) coupling of Co₄Nb₂O₉ by substituting the non-magnetic metal Mg for Co. A series of single crystal Co_4−xMg_xNb₂O₉ (x = 0, 1, 2, 3) with a single-phase corundum-type structure are synthesized using the optical floating zone method, and the good quality and crystallographic orientations of the synthesized samples are confirmed by the Laue spots and sharp XRD peaks. Although the Néel temperatures (T_N) of the Mg substituted crystals decrease slightly from 27 K for pure Co₄Nb₂O₉ to 19 K and 11 K for Co₃MgNb₂O₉ and Co₂Mg₂Nb₂O₉, respectively, the ME coupling is doubly enhanced by Mg substitution when x = 1. The ME coefficient α_ME of Co₃MgNb₂O₉ required for the magnetic field (electric field) control of electric polarization (magnetization) is measured to be 12.8 ps/m (13.7 ps/m). These results indicate that the Mg substituted Co_4−xMg_xNb₂O₉ (x = 1) could serve as a potential candidate material for applications in future logic spintronics and logic devices.     

Analysis of Ti:LiNbO3 zero-gap directional coupler for wavelength division multiplexer/demultiplexer

For the purpose of multichannel integrated-optical wavelength division MUX/DEMUX design, the wavelength tuning method of Ti:LiNbO₃ zero-gap directional coupler is analysed by effective-index based matrix method (EIMM). In this method, first, the 2D refractive index profile of the Ti:LiNbO₃ zero-gap directional coupler is transformed into lateral 1D effective-index profile by WKB method. Finally, matrix method is applied to this effective-index profile and the propagation constants are computed from the resonance peaks of the excitation efficiency versus propagation constant characteristics. It has been shown that the channel wavelength tuning can be achieved by varying the Y-branching angle at the input and output of the device or by a slight variation of two-mode-section length. The method of electro-optic fine tuning of the channel wavelength and channel separation of the device has also been investigated. A cascaded structure with proper parameters for four-channel application is also simulated and the results are presented.