A wide-angle vector beam propagation method_WP Huang_IEEE_1992
微纳光纤偏振分束器特性研究
微纳光纤偏振分束器特性研究陈哲;翟艳芳;余健辉;张军;杜垚【摘要】The characteristics of the polarization coupling of two micro/nano optical fibers that are closed to each other were investigated by three dimension full vector beam propagation method (3D FVBPM). The analytical results of their characteristics of the polarization coupling show that a polarization beam splitter (PBS) based on coupled micro/nano optical fiber can be constructed. Considering the polarization splitting performance of the component, the geometric parameters of the PBS, such as the diameter of micro/nano optical fiber and the gap between them are optimized. The optimal parameters are as follows: the diameter of about 0. 9 μm, the gap of about 0. 5 μm and the length of 218 μm. Numerical simulations show that we can acquire fabrication tolerances for the polarization splitter at a wavelength of 1 550 nm when the extinction ratio of polarization of both output ports of the splitter are larger than 15 dB, such as a bandwidth of about 10 nm, overlapping length of ±2μm, and about -3 ~2 nm for the diameter and gap respectively.%采用3维全矢量光束传输法研究两相邻微纳光纤的偏振耦合特性,证实利用微纳光纤偏振耦合特性能很好地实现偏振分束,构成光纤偏振分束器.在保证偏振分束性能的条件下,通过研究微纳光纤偏振分束器的几何特性对偏振分束性能的影响,优化设计了微纳光纤耦合型偏振分束器,得到耦合区的最优参数为直径0.9 μm、间隙0.5 μm及耦合长度218 μm.结果表明,在1.55 μm工作波长处分束器可实现偏振分束输出,其带宽约为10 nm,耦合区长度容差为±2μm,直径与间距容差均为-3 ～2 nm,偏振消光比大于15 dB.【期刊名称】《深圳大学学报（理工版）》【年(卷),期】2012(029)002【总页数】7页(P129-135)【关键词】光纤光学;光纤耦合;3维全矢量光束传输法;偏振;数值分析;微纳光纤【作者】陈哲;翟艳芳;余健辉;张军;杜垚【作者单位】暨南大学光电信息与传感技术广东省普通高校重点实验室,广州510632;暨南大学理工学院,广州510632;暨南大学理工学院,广州510632;暨南大学光电信息与传感技术广东省普通高校重点实验室,广州510632;暨南大学理工学院,广州510632;暨南大学光电信息与传感技术广东省普通高校重点实验室,广州510632;暨南大学理工学院,广州510632;暨南大学理工学院,广州510632【正文语种】中文【中图分类】O436.3偏振分束器是将构成基模的两个正交偏振模进行分束的光学器件，其在偏振无关光器件、光波分复用等系统中应用广泛［1-2］.目前常见的偏振分束器包括薄膜偏振分束器［2］、双折射偏振分束器［3］和光波导偏振分束器［4-5］等.其中光波导偏振分束器因具有体积小、连接损耗小、易集成等优点，已成为集成光学及光通信系统的一种重要器件.目前研究结构类型主要有:定向耦合器［5］、非对称Y型［6］及线栅型［7］偏振分束器.近几年，微纳光波导的相关研究日益成为热点.文献［8］对脊型纳米线光波导方向耦合器的TE/TM偏振分束器作了研究;文献［9］报道在气凝胶衬底上弯曲2根直径为420 nm的纳米光纤做成的X形耦合器，耦合长度仅5 μm;文献［10］利用FDTD方法对微纳光纤的倏逝场耦合特性做了研究，可知两根微纳光纤间的强倏逝波耦合具有高效、耦合长度短的特点.而利用熔融玻璃拉制的微纳光纤制作偏振分束器的研究目前未见报道.本文运用3维全矢量光束传输法 (three dimension full vector beam propagation method，3D FVBPM)，研究两相邻微纳光纤的偏振耦合特性，表明利用微纳光纤偏振耦合特性可构成微纳光纤耦合型偏振分束器.在保证偏振分束性能的条件下，同时考虑器件微型化，通过研究器件几何特性对偏振分束性能的影响，优化设计该偏振分束器耦合区的参数.计算结果表明，基于微纳光纤偏振耦合特性的偏振分束器，能很好地实现TE/TM偏振分束，有利于超高集成度光学器件的发展.1 数值模型与基本原理微纳光纤偏振分束器由输入波导、耦合区及弯曲输出波导组成，其物理模型如图1(a).由于该器件实现偏振分束的主要结构在于耦合区，因此耦合区几何参数是设计时最关注的参数.在优化设计时，为减小计算量，本研究对器件的物理结构作了简化:假设微纳光纤表面足够光滑，忽略表面粗糙度引起的散射［10］，且不考虑输出波导弯曲部分的影响，主要集中于耦合区的参数计算.简化后物理结构如图1(b)，使用此结构建立数值计算模型.图1(c)为该数值模型耦合区微纳光纤横截面图.图1 数值模型示意图Fig.1 Schematic diagram of the mathematic model由耦合模理论［11］可知，当两传播常数相等时波导间的耦合效率最高，因此本研究采用两根直径相同的微纳光纤(直径D1=D2=D).利用传统耦合模理论［11］，在标量近似下，分析微纳光纤间的倏逝波耦合基本特性.以下用标量场ψ近似表示某一偏振方向的本征模 (TE或TM模)，ψ满足标量波动方程对于TE(TM)模，由以上标量波动方程可得对称和反对称模，分别为:对称模和反对称模以下仅考虑TE 偏振情况，对于耦合区的电场可近似作对称模与反对称模叠加，在耦合区z位置上总横向电场的幅度E可表示为［11］其中，E+(x)=a+ψ+;E－(x)=a－ψ－;a+和a－为对称与反对称模式幅度.在耦合区z=0处，入射场为其中，E1(x)为光纤1横截面本征模式.当光传输至耦合长度的位置，可得光纤2横截面本征模式为TE/TM两偏振耦合长度分别为当两光纤发生耦合时，耦合作用破坏了单根光纤的圆对称性，因此耦合强度与模场的偏振方向相关，使TE与TM偏振有不同的耦合长度，且，即圆对称性破坏引起的要大于ΔβTM，这是因为TE偏振模倏逝场耦合比TM偏振模要强.根据耦合模理论［11］，输入光纤中的光能量通过倏逝场耦合到相邻光纤，偏振耦合效率随耦合区长度呈周期性振荡，因此总存在耦合区长度L满足为整数)，且为奇数的条件.器件若取此长度，则可实现两偏振分束.为保证获得偏振分束耦合区长度最短，应取2 仿真结果及性能分析图1(b)为利用微纳光纤偏振分束器的简化数值模型.设输入光中心波长为1 550 nm，纤芯折射率n均为1.46，dgap为两微纳光纤侧向间距，L为耦合区长度.在图1(c)中，横向电场TE模(TM模)沿x(y)方向，光从input端输入，设置TE偏振(TM偏振)沿z方向传播，在1、2两端分别监测两偏振分量光功率输出和，x为偏振水平分量，y为偏振垂直分量.两相邻的微纳光纤之间强倏逝场耦合，能获得高达97%以上的最大耦合效率和很短的耦合长度，这有利于器件尺寸最小化.同时最小耦合效率达到30%以上［9］，但若实现高消光比偏振分束则需要较小的，增大间距或增加光纤直径可减小同时也会增大器件耦合区长度，因此改变间距 (或直径)会同时带来器件耦合区长度和消光比的变化，且间距 (或直径)的变化会引入器件尺寸与性能间的矛盾，因此为设计出既有良好偏振消光比又具有最小尺寸的微纳光纤偏振分束器，依次研究以下内容:直径与间距变化分别对最小偏振耦合效率的影响;在消光比最大且耦合长度最小的条件下，优化器件的直径与间距，并对器件带宽做了分析;考虑到器件的实际应用及加工制作，分析入射光偏振角度对器件性能的影响及容差.2.1 直径与间距对最小耦合效率的影响为初步确定直径与间距的优化范围，以最小耦合效率ηTE/TMmin 和最佳耦合区长度Lc(表示给定器件直径与间距参数后实现偏振分束效果最佳时所对应的最小耦合区长度)为优化判据，主要研究了直径对和Lc的影响，及间距与的变化关系，结果见图2.由图2(a)可见，在一定的直径变化范围内，随着直径的增大，减小，Lc增加，与Lc的反向变化曲线在D=0.9 μm左右处相交，如图2(a)虚线标识部分;图2(b)中，在dgap=0 ～1.0 μm，随间距的增大而减小，在dgap＞0.5 μm以后，减小到5%以下.因此增大直径 (或间距)可减小，同时增加器件的耦合区长度，这是由于直径 (或间距)增加会减少两光纤间的模场重叠.由上述结论可知，欲使器件实现较高偏振消光比及尺寸最小化，可初步将最优直径选择在0.8～1.0 μm，最优间距选择在0.4～1.0 μm.图2 直径D和间距dgap分别对耦合特性的影响Fig.2 The influence of changein D and dgap on coupling between two micro/nano fibers，respectively 2.2 几何参数优化分析由于实际中对偏振光的检测是对x和y分量的测量，因此，为使设计更接近实际应用，下文的仿真计算采用x和y方向分量的消光比近似TE和TM偏振消光比.由于TE和TM模具有正交性，所以可同时入射相等的x和y偏振分量分析器件的分束性能.仿真中，设置入射光为中心波长1 550 nm且与x轴成45°的线偏振光.首先优化直径参数，结合图2主要计算D=0.8、0.9及1.0 μm的情况，表1为取初始估计值dgap=0.4 μm，最佳耦合区长度及两输出端消光比随不同直径的变化，其中ERi(i=1，2)表示光从1和2端口输出的消光比，计算公式为依据式 (5)可知，表1中ERi结果为负数表示TM偏振输出，正数表示TE偏振输出，因此以下消光比大小的比较是指ERi绝对值的比较.由表1可知，当dgap=0.4 μm不变，随 D=0.8、0.9、1.0 μm的依次变化，对应器件的最佳耦合区长度依次由短到长 (112～276 μm)，同时输出消光比绝对值由低到高.比较3种直径情况下，D=0.8 μm时得到的Lc最小 (即为最优值)，而D=1.0 μm时得到的ERi绝对值最大 (即为最优值).考虑器件消光比与尺寸的设计要求，且从表1可知Lc的增加幅度要大于ERi绝对值的增加幅度，则选择Lc为最主要判据，ERi绝对值为次要判据，折中选择D=0.9 μm作为器件的优化直径，下面讨论该直径模型下间距的优化.表1 直径、最佳耦合区长度与输出消光比的关系(dgap=0.4 μm)Table 1 Diameter，optimal overlpping length and extinction ratio with dgap=0.4 μmD/μm Lc/μm ER1/dB ER2/dB 0.8 112.0 13.78 －13.94 0.9 167.2 －17.91 18.61 1.0 279.0 －20.46 20.65在确定D=0.9 μm后，为了取得最优间距本研究计算了间距在0.4～0.8 μm范围内，最佳耦合区长度与两端口输出消光比的结果，如表2.由表2可知，固定D=0.9 μm不变，最佳耦合区长度和两输出端输出消光比的绝对值均随着dgap的增加而增大，即 dgap从0.4 μm 增加到0.8 μm，Lc增加了约为300 μm，ER1与ER2的绝对值均增大了约5 dB，且Lc的增加幅度要远大于ERi绝对值的增加幅度.可见直径不变时，需求得最佳间距，以均衡器件尺寸的最小化与其消光比的提高.综上分析，可选择Lc为最主要判据，ERi绝对值为次要判据，折中考虑，选取最佳间距值为0.5 μm左右.此外，表2中ER1为负值，ER2为正值，说明TM 偏振从1端口输出，而TE偏振从2端口输出，TE/TM偏振消光比分别为20.59 dB和19.83 dB，最终选取D=0.9 μm，dgap=0.5 μm，L=218 μm 为分束器最优几何参数.表2 间距、最佳耦合区长度与输出消光比的关系(D=0.9 μm)Table 2 dgap，optimal overlapping length and extinction ratio with D=0.9 μmdgap/μm Lc/μm ER1/dB ER2/dB 0.4 167.2 －17.91 18.61 0.5 218.0 －19.83 20.59 0.6 324.0 －21.03 22.68 0.7 367.8 －23.13 22.92 0.8 476.2 －23.30 23.33对最优几何参数用Rsoft-Beamprop软件仿真其偏振分束效果，入射与x轴成45°的线偏振光后，器件输出在x-y平面模场分布如图3，其中Ex表示横模的x方向分量，Ey表示横模的y方向分量.可见x方向分量 (TE偏振)从端口2输出，y方向分量 (TM偏振)从端口1输出.图3 x-y平面模场输出剖面图Fig.3 Mode field output profile in the x-y plane 2.3 带宽分析对器件的间距与直径参数优化分析后，还需考虑偏振分束器的带宽问题.由表2可知，dgap=0.4 μm和0.6 μm这两组参数，也具有一定的参考意义，因此对这3组参数均做了带宽分析，仿真结果如图4，其中Ey表示TM偏振，Ex表示TE偏振.以TE与TM偏振消光比15 dB作为选择标准，从图4中可见，在dgap=0.4μm的情况下，λ在1.546～1.556 μm内，即带宽为10 nm;dgap=0.5 μm时，λ在1.546～1.555 μm范围内，即带宽为9 nm;当dgap=0.6 μm 时，λ 在1.547～1.555 μm 范围内，即带宽为8 nm，因此随着间距的增大，消光比得到了提高，而带宽略有减小.综上，对D=0.9 μm的模型，在间距为0.4、0.5和0.6 μm情况下均能获得约8～10 nm的带宽 (消光比＞15 dB)，表明所设计的偏振分束器在一定的通信波段范围内实现了TE/TM偏振光分束.图4 不同间距下偏振消光比随波长的变化Fig.4 Extinction ratios versus wavelength with different gaps2.4 入射光偏振角度对器件性能的影响为获得D=0.9 μm，dgap=0.5 μm，L=218 μm这组最优参数下器件的分束比率，计算入射光偏振角度与耦合比的关系，结果如图5，输出端口耦合比Ri(i=1，2)分别为R1=P1/(P1+P2)，R2=P2/(P1+P2)，P1和P2分别为两端各自的总光功率输出.当入射偏振角为0°时 (TE偏振输入)，99.06%的TE偏振从2端口输出，剩余0.94%从1端口输出;当入射偏振角为90°时 (TM偏振输入)，99.34%的 TM偏振从1端口输出，剩余0.66%从2端口输出，可见此偏振分束器能高效率地将两种偏振态分开.图5 耦合比随入射光偏振角度的变化Fig.5 Coupling ratios versus polarization angle of incident light考虑到实际应用中入射光偏振角度的任意性，还研究了入射光偏振角在0°～175°范围内器件1和2两端消光比绝对值变化，如图6.由于图6具有对称性，只需分析0°～90°.入射偏振角从0°～10°，从28 dB变化到27 dB，从18 dB变化到0 dB，结合图5可知，此时95%以上的光从2端输出，2端可获得TE偏振光;入射偏振角从10°～80°，从27 dB变化到0 dB，从0 dB变化到27 dB，其中在45°位置时，约20 dB，由图5可知耦合比近50%，为器件偏振分束的入射偏振最佳角度;入射偏振角从80°～90°，从0 dB变化到18 dB，从27 dB变化到28 dB，结合图5可知，此时95%以上的光从1端输出，可从1端获得TM偏振光.可见，当入射线偏振光的方向与x轴夹角在30°～60°内，在15～23 dB时，可实现TE/TM偏振光分束，当入射光偏振角为45°时的偏振分束效果最好.图6 消光比随入射光偏振角度的变化Fig.6 Extinction ratios versus polarizationangle of incident light3 容差分析如图7，在对D=0.9 μm，dgap=0.5 μm，L=218 μm这组优化参数的容差分析中，本研究主要考虑了偏振消光比随耦合区长度、直径及间距的变化.将两偏振消光比同时获得15 dB以上作为制作容差选择标准，由图7(a)可见，耦合区长度在216～220 μm时，偏振消光比大于15 dB，耦合长度容差达±2 μm，图7(a)中还显示了两偏振消光比的峰值略微错开，这是由于L=218 μm不完全满足的条件.由图7(b)可见，直径在0.897～0.902 μm内，偏振消光比大于15 dB，即直径容差为－3～2 nm.由图7(c)可见，dgap在0.497～0.503 μm内，偏振消光比大于15 dB，即间距容差为－3～2 nm.可见偏振消光比对直径或间距的变化非常敏感，器件对直径和间距的精度控制要求较高.此外，本研究还考虑了微纳光纤直径的微小变化对带宽的影响，如图7(d)，其中实虚线分别表示TM/TE两种偏振，菱形、正方形和三角形依次表示直径取0.898、0.900和0.902 μm的结果，这3个不同直径在TE偏振时消光比的峰值依次为如图中P1、P2和P3点，对应波长依次为1.546、1.550和1.554 μm，可见直径增加2 nm使偏振消光比的峰值向长波方向漂移4 nm，但带宽基本没有变化，TM偏振时亦然.因此，优化直径变化±2 nm(在容差范围内)会引起两种偏振消光比的峰值发生约±4 nm漂移，而带宽基本没有影响.图7 几何参数容差分析及直径微变对带宽的影响Fig.7 Tolerance analysis forthe geometric parameters，and the influence of micro-variation in diameter on bandwidth结语本文采用3D FVBPM的方法，主要研究构成偏振分束器的两相邻微纳光纤的偏振耦合特性，即最小偏振耦合效率分别随两光纤的直径和间距的变化关系，并讨论直径或间距的变化对器件偏振消光比及耦合区长度的影响.分析结果表明，利用微纳光纤偏振耦合特性能很好实现TE/TM偏振分束，构成微纳光纤偏振分束器.直径或间距变化时，耦合区长度和偏振消光呈现反向优化关系.以15 dB以上作为偏振消光比的选择标准，优化微纳光纤偏振分束器耦合区的几何参数，计算结果表明，在分束器光纤直径为0.9 μm，两者间距为0.5 μm，耦合长度为218 μm的最优参数下，可实现TE偏振光从2端口输出，消光比为20.86 dB，TM偏振光从1端口输出，消光比为19.79 dB，带宽约10 nm(偏振消光比≥15 dB)，耦合区长度容差为±2 μm，直径与间距容差均为－3～2 nm.可见器件制作对直径和间距的精度控制要求较高.熔融玻璃拉制微纳光纤具有很强倏逝场，利用其有望制作出更小的偏振分束器.参考文献/References:［1］Komatsu M，Saitoh K，Koshiba M，et al.Design of miniaturized silicon wire and slot waveguide polarization splitter based on a resonant tunneling［J］.Optics Express，2009，17(21):19225-19234.［2］LI Xiao-ping，YI Xin-jian，SHI Tie-lin.A micro polarized beam splitter for DWDM［J］.Laser Technology，2006，30(4):377-380.(in Chinese)李晓平，易新建，史铁林.一种用于DWDM系统的薄膜型微小偏振分束器［J］.激光技术，2006，30(4):377-380.［3］LI Guo-hua，LI Ji-zhong.Ploarization-independent beamsplitter madeof birefringent crystal［J］.Laser Technology，1992，16(1):58-60.(in Chinese)李国华，李继仲.用双折射晶体制做偏振无关分束器［J］.激光技术，1992，16(1):58-60.［4］Fukuda H，Yamada K，Tsuchizawa T，et al.Ultrasmall polarization splitter based on silicon wire waveguides［J］.Optics Express，2006，14(25):12401-12408.［5］HUANG Wan-wen，ZHANG Yao，LI Bao-jun.Ultracompact wavelength and polarization splitter in periodic dielectric waveguides ［J］.Optics Express，2008，16(3):1600-1609.［6］Hayakawa T，Asakawa S，Kokubun Y.Arrow-B type polarization splitter with asymmetric Y-branch fabricated by a self-alignment process ［J］.Journal of Lightwave Technology，1997，15(7):1165-1170.［7］GUO Chu-cai，YE Wei-min，YUAN Xiao-dong，et al.Research on sub-wavelength grating polarizing beam splitter［J］.Acta Optica Sinica，2010，30(9):2690-2695.(in Chinese)郭楚才，叶卫民，袁晓东，等.亚波长光栅偏振分束器的研究［J］.光学学报，2010，30(9):2690-2695.［8］WANG Jian-wei，DAI Dao-xin，SHI Yao-cheng，et al.Design of compact TE/TM polarization beam splitter based on silicon-on-insulator ridge nanowire directional coupler［J］.Laser＆ Optoelectronics Progress，2010，47(5):051301-1-051301-6.(in Chinese)王剑威，戴道锌，时尧成，等.基于绝缘体上硅脊型纳米线光波导方向耦合器的TE/TM偏振分束器［J］.激光与光电子学进展，2010，47(5):051301-1-051301-6.［9］Tong L，Lou J，Gattass R R，et al.Assembly of silica nanowires on silica aerogels for microphotonic devices［J］.Nano Letters，2005，5(2):259-262.［10］HUANG Ke-ji， YANG Shuang-yang， TONG Li-min.Modeling of evanescent coupling between two parallel optical nanowires［J］.Applied Optics，2007，46(9):1429-1434.［11］Okamoto K.Fundamentals of Optical Waveguides［M］.Amsterdam:Elsevier Press，2006:180-183.。
美借助非线性材料显现出隐藏物体图像该技术可广泛应用于医学成像、飞行安全等领域
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飞行员在风暴和涡流发生时所需 的雷达系统等。下一步 ， 研究人员计划融入其他 的信号处理技术 ， 进一 步提升成像的清晰程度 ， 并拟以声音或超声波替代光线 ， 将其应用于生物医药成像仪器、 夜视镜和水下侦 测乃至涉及保密和安全 目的的隐写术等。
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Measurement of colliding beam-beam parameters with wide-angle beamstrahlung
a rX iv:physics /98122v1[physics.acc-p h]14D ec1998Measurement of Colliding Beam Parameters with Wide Angle Beamstrahlung G.Bonvicini,D.Cinabro and E.Luckwald Wayne State University,Detroit MI 48201February 9,20081Introduction Machine issues at particle factories are dominated by luminosity optimiza-tion,which is the overlap of the density functions ρof the two beams over space and time.For a single beam crossing,L =c dV dτρ1(r ,τ)ρ2(r ,τ),(1)where dV is the volume element and τis a time variable of order of the beam-crossing duration.Optimal luminosity is achieved by perfect transverse overlap of two equal and Gaussian beams squeezed to the limit allowed by the tune shift.For a single beam crossing,that reads L 0(t )=N 1(t )N 2(t )c 4πσx (t )σy (t ),(2)where the N 1,2and σx,y,z are the beam populations and spatial dimensions at any given time t (which is a run-time variable of order one hour).This formula becomes rather complex over time.Particles are deflected by the other beam at each crossing,significantly affecting the Twiss matrixof the machine.The beam currents N i (t )decrease due to beam lifetime also causing the machine’s Twiss matrix to drift.If the machine is perfectly sym-metric,the transverse dimensions will change but the beams will maintain perfect overlap.1WSU-HE-98-012 Even symmetric machines have some degree of asymmetry,and beams start moving independently in the transverse plane as soon as the run starts. At B-Factories such as CESR,PEP-II,and KEK,beams have horizontal dimensionsσy of order several microns,with aspect ratiosǫ=σy/σx∼0.02−0.04.A drift of5microns is enough to spoil the luminosity.A better description of the luminosity over time should beL(t)=L0(t)(1−w(t)).(3) w(t)is the positive-defined waste parameter due to non-instantaneous opti-mal overlap.If w(t)is known,the wasted integrated luminosity is defined asL w=f dtL0(t)w(t),(4) where f is the machine frequency.The waste parameter can be readily derived from the convolution integrals,Equations1and2.Dropping the time dependence,one getsLw=1−WSU-HE-98-013 In this paper,a technique is proposed by which six of the seven pa-rameters can be passively monitored with the observation of wide angle beamstrahlung.In case of non-zero waste,which is called a“pathology”, the responsible parameter is identified unambiguously,and the amount of needed correction is measured.The seventh parameter can easily be mea-sured in a beam scan also using the wide angle beamstrahlung signal.Seven parameters to characterize the beam-beam collision is a large num-ber.It is easiest to discuss the problem if it is broken into two parts.•The machine is perfectly symmetric,that is,the machine optics is ex-actly the same for both beams.In Figure1,that means that the two beams have zero offsets,zero rotation,and the same transverse dimen-sions,resulting in only two parameters.Dropping indices,they are the transverse dimensionsσx andσy.If the machine is symmetric,beams maintain optimal overlap,but the optics is affected by the varying currents.The luminosity is determined by the transverse size of the beam.The case of measuring the transverse beam size is discussed in Section3.•The beams move independently in the transverse plane due to ma-chine asymmetry decreasing overlap and luminosity.In section4the measurements of the relative sizes of the two beams,their transverse displacement,and the angle between them are described.In this paper the use of large angle beamstrahlung,which is described in detail in reference[3],is described as a beam-beam monitor that allows com-plete control over both the beam-beam interaction strength and transverse rge-angle beamstrahlung observables,combined in a sim-ple2-dimensional diagram which is called the beamstrahlung diagram,mon-itors the wasted luminosity.In Section2the information content of large angle beamstrahlung is discussed.Section3covers the symmetric machine case,concentrating on measurements of the beam size.Section4covers asymmetric machines,in-troduces the beamstrahlung diagram,and shows how the waste parameter can be measured.The use of the beamstrahlung diagram to eliminate wasted luminosity is shown in Section5.Three appendices are included for com-pleteness.Appendix A derives in a simple way three crucial properties of large angle synchrotron radiation.Appendix B provides a description of the beam-beam simulation developed for this paper and Appendix C evaluates the simulation’s accuracy.WSU-HE-98-014 2Large Angle BeamstrahlungThe properties of large angle radiation,emitted by a ultra-relativistic parti-cle,differ dramatically from the classical synchrotron radiation formulae[4]. Appendix A shows that the approximations used in reference[3]and in this paper are valid at large angles for all present and proposed e+e−collid-ers,if beamstrahlung detection is to be done at or near the“magic angle”described in[3].Three properties of large angle radiation are derived in Appendix A.Of particular interest is the100%linear polarization,either parallel or perpendicular to the bending force,obtained at certain azimuthal locations at large angle.At CESR for example,it is possible to detect such radiation in vis-ible light at a location5meters away from the interaction point,at a 6mrad angle.The beam-beam interaction occurs over a volume of order 300µm×7µm×7mm,and particles are typically deflected laterally by10−2 mrad.Thus the light detector is seen at the same angle by all of the beam, and throughout the dynamic beam-beam collision.These are the conditions termed as“CESR conditions”and used for the calculations of Sections4 and5.Afixed fraction of the beamstrahlung energy is collected at such a location,effectively measuring the total energy up to a constant.Dif-ferent polarization components can also be easily observed,byfiltering the observed light through polarimeters.The two polarization components can be used to build the radiation vectors U1from one beam and U2from the other beam,which are two-dimensional vectors in thefirst quadrant.Thefirst dimension is the horizon-tal component of the polarized beamstrahlung power signal and the second is the vertical.The total energy vector U is defined as U1+U2.At large angles the polarization components and radiation spectrum factorize[6]and a different orientation of the polarimeters would simply rotate the horizontal and vertical axes..As mentioned in the Introduction,at present and proposed machines, beams are veryflat(ǫ∼0.02−0.04).It is convenient to develop the theory only forflat beams which leads to two simplifications.First,terms of order ǫand higher can be neglected in equations as needed.Second,a natural preferred orientation exists in the transverse plane,which is adopted to produce the results of this paper.It should be noted that two counters on each side,each looking at a dif-ferent polarization component,and in absence of background,are enough to extract complete information from beamstrahlung.As an example,given theWSU-HE-98-015 formulae in Appendix A,U x can be measured by measuring the x−polarized component at zero degrees in azimuth,and U y by the x−polarized compo-nent at45degrees.3Symmetric MachinesIf a machine is perfectly symmetric,the beam currents and transverse di-mensions of the beams will evolve,while maintaining perfect overlap.Mea-surements of the beam sizesσx andσy,determine the luminosity.In this case most of the interplay between machine and beam-beam interaction is through the dynamic beta effect.The dynamic beta effect is proportional to the average electricfield seen by one particle over many beam crossings,hence it is proportional to the charge in the other beam,times the average inverse impact parameter b between particles of beam1and particles of beam2[7],b<E1>∝N2<f(ǫ).(9)σ2xσzThe beam length,σz,is usually constant,and will not be considered here, but clearly a beamstrahlung detector can also be used to monitor the beam length,for example during machine studies.The function f(ǫ)varies slowlyf(ǫ)∼1+11.4ǫ,(10) and can be considered nearly constant in the following.WSU-HE-98-016 The result above assumes“stiff”beams.A stiffbeam is one where the beam particles do not change their transverse position appreciably during the collision.Appendix B shows that dynamic effects are negligible.Inflat beams most of the impact parameter is due to the distance in x be-tween the particles,and the energy radiated is almost only dependent onσx. For perfect overlap of stiffGaussian beams the energy U is unpolarized[6]. No information can be extracted out of polarization,and beamstrahlung cannot monitor passively symmetric changes inσy.The total power radi-ated is thus sensitive toσx.However,as pointed out in references[3,6],a scan of one beam along the vertical axis will produce the characteristic camelback feature in the plot of U versus the beam-beam offset seen in Figure3,which has already been used in the detection of beamstrahlung[8].Theσy can be precisely determined by measuring the peak-valley distance d shown in Figure3.The relation between d andσy isd∼3.97σy(1−5.4ǫ).(11) Currently,the CESR beams are artificially perturbed with an amplitude of order0.01σy to measure the beam-beam interaction by observing the effect of the perturbation on the other beam via the lock-in effect[2].It is conceivable that this technique could ultimately be used to determineσy without scanning.Note that a beam scan could also be used to measureσx separating it fromσz.A beamstrahlung monitor can be very useful even when a machine is perfectly symmetric,allowing purely passive monitoring of the beam-beam interaction and thus the beam length orσx.It can be used to measure σy in a beam scan.The next Section,which deals with purely asymmetric pathologies,shows that this method is truly valuable when beams are not colliding head on in the transverse plane and may have different transverse sizes.4Asymmetric MachinesIf a machine is asymmetric,as all real machines are to some degree,the two beams will drift independently in the7-dimensional space that induces luminosity waste.For the purpose of studying asymmetric machines,a single pass beam-beam simulation program was written.The program generates complex beam-beam configurations involving all the pathologies shown in Figure1.These configurations are,in principle,computable analytically inWSU-HE-98-017Paramter ValueσxσyσzNγWSU-HE-98-018 scan as discussed in the previous section.The beamstrahlung diagram plots U1,U2normalized by U0.In the figures below the contribution from the pathological beam is represented by the dashed arrow.The diagram has four degrees of freedom.The total power monitors the beam-beam interaction strength,and three independent dimensionless asymmetries can be defined.As mentioned in Section3if the collision is perfect and the beams are stiffthe beamstrahlung radiation is unpolarized.Thus the normalized U i’s are equal and the vector from each beam in a perfect head-on collision are on top each other at45degrees as shown in Figure4.With the U0normalization one obtains the perfect collision point at(1,1)for both beams.The effect of dynamic beams can be estimated from Table2in Ap-pendix C.For example at CESR dynamic beams increase U x by0.9%and U y by2.7%,moving the perfect collision axis0.5degrees above45degrees. Such a small modification is nearly invisible in Figure4and can be neglected.Figure5shows for stiffbeams the beamstrahlung diagrams for each pathology shown in Figure3.Each has a unique pattern,which a feedback algorithm can discern and correct.In general,if beam1is smaller in x(y) than beam2,then it will radiate less energy in x(y).Figure6is the same as Figure5,but for dynamic parison of the twofigures shows very little difference.The effect of dynamic beams is small.Thus the beamstrahlung diagram presented in this paper is a universal display of the pattern associated with beam-beam pathologies at CESR,PEP-II,KEK,and in the future at a∼1TeV e+e−machine.Figure7is the same as Figures5and6,but with an offset in x,18µm, or0.06σx,comparable to the resolution of beam position monitors.Again very little change is observed with respect to Figure5showing that small horizontal offsets have small impact.Asymmetries corresponding to each pathology in Fig.3are defined asA1=(U y/U x−1)Θ(U y/U x−1),(12)A2=(U2y/U1y−1)Θ(U2y/U1y−1),(13)A′2=(U2x/U1x−1)Θ(U2x/U1x−1),(14)A3=|sin(U1,U2)|,(15) whereΘis the Heaviside function meaning in this case that the asymmetries A i are not defined when the argument of the Heaviside function becomes neg-ative.The indexing was chosen to indicate that the second,a beam bloated vertically,and third,a beam bloated horizontally,pathologies are generatedWSU-HE-98-019 from both a zero dipole moment and a non-zero quadrupole moment in the transverse charge distribution,and as such they should be equally ranked.These asymmetries are not independent.The usefulness of these beam-strahlung asymmetries is shown in Figure8which displays their dependence on the waste parameter defined in Equation3.Each asymmetry’s contribu-tion to the waste parameter of Section1isw i∼∂w∂A i )Aj=min.,j<i.(18)Eq.17represents the main result of this paper.The derivatives are com-puted,the asymmetries are measured,and the waste parameter is obtained. Note that if the asymmetries were completely independent,the specifications A j=min.would have been unneeded.Asymmetries2and2’represent both quadrupole corrections,and can be interchanged without harm.For horizontal offsets between the two beams an asymmetryA′1=(U x/U y−1)Θ(U x/U y−1)(19) can be defined.We note that for a10%change in luminosity,the values of the asymme-tries change by0.1for A1and A′1,0.25for A2and A′2and0.05for A3.Thus these asymmetries have excellent sensitivity to wasted luminosity.5The Virtual OperatorHere examples are shown of how the beamstrahlung diagram and the asym-metries defined in Equations12-15and19can by used to eliminate wastedWSU-HE-98-0110 luminosity even in the presence of multiple pathologies in the beam-beam collision.We demonstrates this by studying the complete set of six double patholo-gies,shown in Figure9,which can be derived from the four single pathologies shown in Figure3.Figure10represents the beamstrahlung diagrams cor-responding to the pathologies displayed in Figure9.A feedback program, dubbed the Virtual Operator,finds the highest-ranking asymmetry,mini-mizes it by changing the appropriate collision parameter,and obtains the beamstrahlung diagrams of Figure11,displaying only one pathology which is trivial to correct.Two comments are in order.First,if the largest asymmetry were to be correctedfirst,instead of the highest-ranked,convergence would not be achieved.To prove the point,it is enough to compare Figs.5b,10d and11d. If the sextupole correction is acted uponfirst,A3would have to increase as opposed to being minimized.Second,we wish to prove that minimization of a higher-ranked asym-metry effectively corrects the associated pathology.Although all the double pathologies were tried,only Fig.9c,which corresponds to a vertical offset plus a rotation,is presented.A1and A3are the two most correlated asym-metries.The asymmetry A1is not zeroed,and cannot be zeroed by moving one beam.Figure12shows the dependence of A1versus the vertical offset, showing that minimization of the asymetry gives the desired correction.We did not consider horizontal offsets here,but they could easily have been included,as discussed in the previous Section.6ConclusionThe beamstrahlung diagram and asymmetries derived here demonstrate a complete and rigorous method for luminosity optimization.The wasted luminosity is for thefirst time related to quantities that are instantaneously observable,and specify the necessary correction.We have considered a complete class of beam-beam pathologies.If the machine is perfectly symmetric a beamstrahlung monitor is very useful for measuring the size of the beam.In the case of asymmetric beams a beamstrahlung monitor is extremely powerful.The study of the beam-strahlung diagram derived from the power and polarization of the beam-strahlung signal allows identification of the beam-beam pathology,identifi-cation of the“bad”beam,and measures the correction that needs to be ap-WSU-HE-98-0111 plied.In short the wide angle beamstrahlung signal analyzed in the manner described here is a powerful tool to eliminate wasted luminosity at present and future e+e−colliders.Appendix AThe properties of short magnet radiation werefirst discussed by Coisson in reference[9].In the classical model[4],the bent electron is made to sweep through the detector in a“searchlight”fashion,effectively covering all beam-detector angles.In the Coisson’s model the opposite extreme is adopted,and the angle is kept constant throughout the orbit,the large angle approxima-tion.Both models predict the same power,the same total polarization,and the same typical angle,of order1/γfor the emitted radiation,but they differ dramatically in the spectrum at large angles.The Coisson model is of interest here because the detector’s angle is con-stant throughout the collision at colliders such as CESR.At large angle the classical model predicts a steep fall-offof the power,exponential both in the photon energy and in the cube of the observation angle.The Coisson model predicts three properties of large angle beamstrahlung radiation.They are:•The cutoffenergy,at large angle,does not depend onγ.There is no exponential fall-offas predicted by the“searchlight”approxima-tion,making detection possible.In particular at6mrad at CESR,for example,visible radiation is at or below the cutofffrequency.•The polarization is linear at afixed location in azimuth with an eight-fold pattern,(cos22φ,sin22φ)around the azimuth.The angleφis the angle between the net transverse force experienced by the beam and the detector location.Thus the pattern of the polarization provides information about the beam-beam overlap.•The large angle double differential spectrum is proportional to(γθ)−4, and not exponential.The large angle power scales as1/γ2.Thus the situation at B factories is more favorable than at higher energy machines.These properties are re-derived here in an elementary way for constant large angle of detection.Consider an extremely relativistic particle,γ>> 1,undergoing a vertical deflection,due for example to a horizontal dipole magnet exerting a force F over a lengthσz.Radiation of energy k=hωWSU-HE-98-0112 is detected at an angleθwhich is much larger than1/γ.In the laboratory frame the radiated energy is equal to[4]U=2mc2γ2F2σz.(20)A simpler derivation is possible by studying the radiation in the rest frame of the radiating particle.Note that all quantities in the particle rest frame are starred as shown in Figure13.The radiation will have a dipole pattern with angular intensity proportional to the squared sine of the angle between the direction of detection and the direction of the force.The force maintains its vertical direction and has a modulusF∗=2γF.(21)The angle is very large in the laboratory frame,and the corresponding di-rection in the rest frame is very close to the backward direction.In a pertur-bative treatment the angleθ∗is taken with respect to the direction opposite the direction of motion(Fig.13).If only small angular components along the direction of the force are consideredI(θ∗)∝cos2θ∗.(22)The intensity is essentially constant at small angles in the rest frame.The relation between the energies and angles in the lab and radiating particle rest frames is given byk=k∗γθ∗22,(24)θ=2WSU-HE-98-0113ω∗c∼O(cσzθ2),(28) which shows that the cutofffrequency at large angle does not depend onγ, thefirst prediction by the Coisson model.At CESR,ωc∼1016sec−1,which is of order of the visible light frequency.The polarization vector of the emitted radiation in the radiating particle rest frame is given by[4]E∗(R)=e2sin2φ=+K22cos2φ=−K22=8UWSU-HE-98-0114 The energy in the lab frame,U,contains a dependence onγ2.The angular factor integrates to a constant(which agrees with Equation8in Ref.[3]), leaving the1/γ2dependence.This is purely due to kinematics.At CESR, for example,10nW of visible beamstrahlung are available between6and7 mrad.Appendix BA beam-beam interaction simulation was developed from the program de-scribed in reference[10].Gaussian beams in all three dimensions are as-sumed.Beams are sliced in3-dimensional cells.The cells are typically 0.25-0.5σalong each axis and extend out to3-4σin each direction.Thus a total of103to3×104cells are simulated.The beams are then made to cross each other.In thefirst step,thefirst layer of the positron beam encounters thefirst layer of the electron beam.The electricfields are purely transverse to O(1/γ),and are computed assuming that the charge is located in a sphere located in the center of the cell.This is the“cloud-in-cell”model.Assuming cylindrical coordinates,a cell in beam one gets a total transverse deflection[7]∆r′1j=−2N2r eb2ij.(37)The summation runs over the cells in the opposite layer,b ij is the impact parameter between cell j in beam one and cell i in beam two,and P2i is the fraction of charge in cell i.At the end of each layer-layer interaction positions and velocities are updated,r′j=r′j+∆r′j,(38)r j=r j+r′j∆z.(39)∆z is the unit step taken along the beam direction.This allows for dynamic beams,with each beam pinching the other as the collision progresses,and the luminosity is computed as an overlap of the dynamic density functions.The program of reference[10]was found to be unfit for the simulation offlat beams.If the lattice is chosen to have the same number of cells in each dimension,the cells will be asflat as the beam.If the charge is then concentrated in the centers,a large force will be calculated,where in reality the total force is small,due to the cancellations of the large x components in the integral over the cells.Figure14illustrates this.WSU-HE-98-0115 To reduce this problem the number of cells in x should be enlarged to make each cell square in the transverse plane.This solution is very CPU time-consuming.A solution was found by replacing each cell with a line of charge,called a“matchstick,”and computing the integral∆r′ij=−2N2r e P ib2ij.(40)For the purpose of improving the convergence of the program,the match-sticks were kept horizontal throughout the interaction.Assuming matchstick lengths L i and L j,the solution to the integral above is∆r′ij=−2N2r e P i2(42)t2=b x+L i−L j2(44)t4=b x+L j−L i2∆z∆r′.(48) The energy vector U for each beam is computed by summingU x= ∆U xj= 2N3mc2P j r eγ2F2y∆z.(50) The program continues to interact the beams,layer by layer,updating trajectories with Equations38-39,until the beams fully cross each other.AnWSU-HE-98-0116 Quantity Bin=0.3σAnalyticU x(1012eV).3979.4051.4013.4049.4163 L/L0 1.00 1.00WSU-HE-98-0117 polarization.The luminosity increases by12%.The luminosity calculation was checked,for round beams,against the program of reference[10]and our simulation agrees to within1%.Figure15shows the analytical versus simulation comparison of U y/U x when twoflat beams are separated by a vertical offset.We conclude that our simulation method has a precision of order few per thousand for beamstrahlung computations.References[1]P.Bambade,SLAC-CN-303,1985;P.Bambade et al.,Phys.Rev.Lett.62:2949,1989.[2]D.Sagan,J.Sikora and S.Henderson,CBN-97-13.[3]G.Bonvicini and J.Welch,CLNS-97-1523,to be published in NuclearInstruments and Methods.[4]J.D.Jackson,“Classical Electrodynamics”,Chapter14.[5]D.Cinabro et al.,Phys.Rev.E57,1193,1998.[6]M.Bassetti et al.,IEEE Trans.Nucl.Science30:2182,1983.[7]J.D.Jackson,“Classical Electrodynamics”,Chapter11.[8]G.Bonvicini et al.,Phys.Rev.Lett.62:2381,1989.[9]R.Coisson,Phys.Rev.A20,524,1979.[10]R.Hollebeek,Nucl.Instr.and Meth.184,331,1981.WSU-HE-98-0118Figure1:A general beam-beam collision.Seven parameters can be seen, corresponding to two transverse dimensions for each beam,a two dimen-sional impact parameter vector connecting the two beam centers,and one relative rotation in the transverse plane.WSU-HE-98-0119Figure2:Normalized power emitted in beamstrahlung,as a function of normalized y−offset.a)ǫ=0.02.b)ǫ=0.04.The distance from minimum to maximum is shown,in units ofσy.U0is defined in Section4.WSU-HE-98-0120Figure3:The four beam-beam pathologies that lead to wasted luminosity;a)a y−offset;b)y−bloating;c)x−bloating;and d)a beam-beam rotation. The pathological beam is represented by the dashed ellipse.WSU-HE-98-0121Figure4:The beamstrahlung diagram corresponding to a perfect beam-beam collision.The two vectors are exactly equal.The dashed arrow is slightly displaced for display purposes.WSU-HE-98-0122Figure5:Beamstrahlung diagrams corresponding to the four pathologies of Figure3.The tips of vectors in part a are displaced for display purposes. Stiffbeams are assumed.WSU-HE-98-0123Figure6:Beamstrahlung diagrams for the same conditions as Figure5,but assuming dynamic beams.WSU-HE-98-0124Figure7:Beamstrahlung diagrams for the same conditions as Figure5,but assuming an x−offset of0.06σx.WSU-HE-98-0125Figure8:Functional dependence of the beamstrahlung asymmetries defined in the text versus the waste parameter of Equation3.WSU-HE-98-0126Figure9:The six possible configurations arising from combinations of any two of the pathologies of Figure3.a)y−offset and y−bloating.b)y−offset and x−bloating.c)y−offset and beam-beam rotation.d)y−bloating and beam-beam rotation.e)x−bloating and beam-beam rotation.f)y−bloating and x−bloating.WSU-HE-98-0127Figure10:Beamstrahlung diagrams corresponding to Figure9.WSU-HE-98-0128Figure11:Beamstrahlung diagrams,corresponding to Figures9and10, after correction of the dominant pare with Figure3.WSU-HE-98-0129Figure12:The dependence of thefirst asymmetry A1,as defined in the text, versus the vertical offset for the case of a vertical offset plus a rotation.WSU-HE-98-0130F*βFigure13:Dipole radiation in a radiating particle’s rest frame.Indicated are the direction of the force and the angle corresponding to the observation angle in the laboratory frame.WSU-HE-98-0131Figure14:Cell-cell interaction in the simulation program.The cell has an aspect ratio similar to the beam aspect ratio.In the“cloud-in-cell”model, all the charge is concentrated in a point in the center of the cell.In the “matchstick-in-cell”model,the charge is spread over a line along the cell.WSU-HE-98-0132Figure15:Radiation polarization versus beam-beam offset.The solid line is the analytic prediction from reference[6],and the dots are from the sim-ulation described in the text.。
基于全局透射边界条件的宽角抛物方程电波预测模型
基于全局透射边界条件的宽角抛物方程电波预测模型郭琪;黎子豪;朱琼琼;龙云亮【摘要】提出了一种新型的基于全局透射边界条件(non-local boundary condition,NLBC)的Greene近似宽角抛物方程(wide-angle parabolic equation,WAPE)电波预测模型,用于求解对流层远距离复杂环境中的电磁波传播特性.采用有限差分法(finite difference method,FDM)求解WAPE得到了三对角线性方程组,可以快速地求解整个空间的电场分布,也可以对不规则的地表环境进行精确建模.本文提出的WAPE模型解决了传统的PE离轴传播角度偏小的问题,将电波的最大传播仰角提升至约50°,同时大大减小了计算区域中上边界吸收层的设置尺寸,从而提高了PE的计算效率.实验证明,当伪微分算子的相位误差不超过0.002时,Tappert、Claerbout和Greene近似形式得到的最大传播角分别为20°、35°和45°.最后,通过与经典的光学双射线模型进行对比,证明本文提出的基于NLBC的Greene近似WAPE模型的可计算传播仰角更大,对上边界处反射电磁波有良好的吸收效果.因此,本文的模型适用于对流层远距离复杂环境中电磁波传播特性的精确预测.【期刊名称】《电波科学学报》【年(卷),期】2019(034)004【总页数】6页(P473-478)【关键词】抛物方程法;全局透射边界;电波传播;Greene近似【作者】郭琪;黎子豪;朱琼琼;龙云亮【作者单位】中山大学,广州510006;中山大学,广州510006;中山大学,广州510006;中山大学,广州510006【正文语种】中文【中图分类】TN011引言如今,无线通信技术已经渗透到人们生活的各个方面, 因此如何对电磁波的传播特性进行精确的预测也成为通信领域的一个重要问题．目前,常用的电波预测模型有积分方程法[1]、时域有限差分法[2]. 然而,由Leontovich等[3]提出的抛物方程法(parabolic equation,PE)由于其具有良好的稳定性、高效性和快速实施性等,近些年来被广泛地应用于对流层电波传播的预测中．求解PE的常见方法有两种:分别是有限差分法(finite difference method,FDM)[4]和傅里叶变换法[5]．虽然傅里叶方法的计算效率优于FDM,但对边界的处理上灵活性较差．因此,在处理复杂地形表面电波传播问题时FDM的精确度更高．在计算PE的过程中,需要对计算空间的上边界设置吸收条件来模拟无限空间．目前常见的方法有[6]:窗函数法、完美匹配层(perfectly matched layer,PML)法、全局透射边界条件(non-local boundary condition,NLBC)．其中,窗函数法最为简便,它是在计算区域上方设置衰减函数,来吸收向上传播的电磁波,避免在上边界处产生强烈的反射．然而,吸收窗的尺寸对吸收电波的效率有着很大的影响,一般至少要将吸收层设为计算高度的三分之一,这会增加整个电波传播的垂直计算空间,影响了PE 的计算效率．PML对大入射角的电波吸收效率较高,适合小范围的电波预测,常被用于雷达散射截面的计算．NLBC法在处理上吸收边界时具有其独特的优势,它既不需要对电场进行谱分解,也不需要设置很大的垂直计算空间来吸收向上传播的电磁波,它是通过对边界处上一步进之前的全部电场值进行卷积处理来获得下一步进上的吸收边界条件．相比窗函数法,NLBC方法大大减小了计算空间,提高了计算效率,因此NLBC被广泛地应用于求解基于FDM的PE模型中．然而,目前基于NLBC的PE电波计算模型的最大传播仰角只能达到约35°[7]．本文推导了基于NLBC的宽角PE(wide-angle parabolic equation,WAPE)算法,可以迭代式地快速求解出整个空间的电场值分布．采用FDM求解WAPE得到了三对角线性方程组,并对不规则的地表环境进行精确建模．又引入Greene近似系数将WAPE的最大传播仰角提升到约50°[8]．实验证明,当伪微分算子的相位误差不超过0.002时,Tappert、Claerbout[9]和Greene近似形式的最大传播角分别为20°、35°和45°．此外,本文还针对文献[8]中采用的吸收窗函数法由于需设置较大高度而影响远距离PE计算效率的问题,引入了NLBC法处理上边界吸收条件,该方法不需要设置很大的吸收层,因此提高了PE的计算效率．最后,通过与光学双射线模型进行对比,证明了本文推导的基于NLBC的Greene近似WAPE的可计算传播仰角更大,对上边界处反射电磁波有良好的吸收效果．综上所述,该模型适合于对流层远距离复杂环境下电磁波传播特性的精确预测．1 基于NLBC的WAPE算法首先,我们通过麦克斯韦方程组得到二维的标量波动方程:(1)再引入辅助减函数u(x,z)=e-ikxψ(x,z),得到简化后的电场波动方程:k2(n2-1)u(x,z)=0．(2)式中,大气折射率n在水平方向上是均匀的．再将公式(2)分解得到(3)公式(3)中第一部分是电波的前向分量,后一部分是电波的后向分量．在PE中,我们假设忽略了电波传播的后向分量．Q参数为伪微分子算子,可以表示为(4)从物理意义上看,Q的近似程度直接影响到沿x轴正向传播的电磁波在垂直z轴方向扩散传播的精度,也就是最大传播角度的问题．参数Q的近似精度越高,传播角度就越大．我们知道,对Q不同的近似可以得到不同的PE近似形式,这里我们引入一项有理式对Q进行近似,Q可以表示为(5)式中,不同Q近似形式的相关系数见表1．表1 算子Q不同近似形式下的相关系数Tab.1 The coefficients of different approximations for operator Q近似形式χ1χ2χ3χ4传播角/(°)Tappert10.51020 Claerbout10.7510.2535 Greene0.999 8710.796 2410.301 0245假设在自由空间中,平面波以θ角度传播,则伪微分算子Q的相位解为(6)根据式(6)对三种不同近似下的Q算子进行实验仿真．如图1所示,假设Q相位误差为0.002,可以看出Tappert、Claerbout和Greene近似形式的最大传播角分别为20°、35°和45°,说明本文采用的Greene近似算子Q的传播仰角最大．接着,我们将式(5)代入电波的前向分量,得到以下通用的近似WAPE传播模型:(7)图1 伪微分算子Q的不同近似形式传播角度对比Fig.1 Comparisons of the different approximations of the operator Q采用FDM对式(7)进行计算,对计算区域内的点,我们采用Crank-Nicolson的差分格式进行处理,对下边界我们采用Leontovich阻抗边界条件进行处理,如下:(8)通过计算可以得到下式:(9)接着,对计算区域的上边界我们采用NLBC来处理,如图2所示．可以看到在(xm, zb)处,NLBC表达式定义为(10)图2 基于NLBC的差分格式示意图Fig.2 The finite difference scheme based on the NLBC我们对式(10)左边进行差分得到(11)同时,对式(10)右边进行差分得到(12)式中,Il=g(ξ)dξ．(13)将式(11)和式(12)代入式(10)得(14)最后,对式(14)进行化简得(15)式中:(16)(17)(18)将式(16)至(18)代入式(15),最后得到上边界zb处的计算式为(19)由公式(9)和公式(19)结合起来可得到以下求解公式:(20)式中,矩阵系数可以表示为(21)以上就是基于NLBC的Greene近似WAPE算法．当求出电场值后,我们可以得到电波的传播因子为PF=20lg|u|+10lg(d)．(22)2 算例分析假设初始源为Levy高斯天线,水平极化,频率为100 MHz,波束宽度为30°,仰角为0°,天线放置在离地面20 m的高度,地面为中等干燥地面,ε=20,σ=0.01 S/m．我们引入光学双射线模型来对比实验结果．首先,选取水平距离为4 km,从图3中可以看出,在低于1 km的高度,三者与双射线模型都吻合得较好,然而在高于1.5 km的高度,相比传统法的Tappert近似和Claerbout近似,Greene近似PE算法在垂直方向上的传播高度最高．由于传播角度与传播高度成正比,因此说明本文提出的Greene近似算法的传播角度最大．其次,我们将天线频率设置为70 MHz,高度为50 m,波束宽度为30°,仰角为0°．采用PE模型对平坦地面上的电波传播损耗情况进行仿真计算,结果如图4所示．可以看到,本文推导的基于NLBC的Greene近似PE模型可以准确地模拟电波的传播损耗(propagation loss, PL)情况．水平距离为3 km时可计算电波传播高度达到3.4 km,通过计算可以得出传播仰角刚好约为50°．从表2可以看出,当频率为100 MHz时,Tappert、Claerbout和Greene近似形式的传播角分别为31°、35°和39°．当频率为70 MHz时,Tappert、Claerbout和Greene近似形式的传播角分别为34°、46°和50°．而光学射线模型可以计算整个空间即90°范围内的电波特性．因此, Greene近似PE可计算的电波传播角度更大,更接近于光学射线模型的计算范围．同时,实验证明电波的传播角会随着频率的增大而减小．图3 水平距离4 km 处的PE传播因子对比图Fig.3 Propagation factor for the PE models at a distance of 4 km图4 基于Greene近似的WAPE电波传播损耗图 (传播角约50°)Fig.4 PL for the WAPE propagation models with propagation angle of 50°表2 不同近似PE 模型的传播角度对比Tab.2 Propagation angle for different PE models频率TappertClaerboutGreene双射线100 MHz30.96°34.99°38.66°90°70 MHz34.00°46.40°50.19°90°接着,我们将地表设置为不规则地面,频率设为1.3 GHz,波束宽度为14°,如图5所示,Greene近似PE模型可以准确地模拟不规则地表引起的电磁波反射效应和绕射效应．同时,我们可以看出图4和图5中上边界处没有任何反射波出现,说明NLBC 方法对向上传播的电磁波吸收效果很好．同时,对比窗函数法,采用NLBC法的计算时间提高了约20%．其次,我们对比传统的吸收窗函数法和NLBC法在上边界处对电波的吸收效果．这里我们先假设垂直计算区域高度设定为500 m,将频率设置为400 MHz．从图6中我们可以看出采用NLBC边界处理上边界时,没有上边界的反射电波传播回计算区域,然而当采用窗函数法时,由于垂直高度的限制,无法对向上传播的电磁波全部吸收,导致大量的电波反射回计算区域,因此,窗函数法的传播因子曲线产生了强烈的振荡．最后,我们将本文算法应用于大气波导环境下的电波传播特性计算,例如悬空波导环境．如图7所示,将电波频率设置为1 800 MHz,天线放置在50 m的位置,可以看出电波产生折射效应,被陷获在大气波导层中．说明我们的算法可以应用在不均匀大气环境的电波传播预测中．图5 不规则地表上的WAPE电波传播损耗图Fig.5 PL for the WAPE propagation models on irregular terrain图6 不同吸收边界方法的电波传播因子对比图Fig.6 Propagation factor for different upper boundary condition图7 大气波导环境中的WAPE电波传播损耗图Fig.7 PL for the WAPE propagation models in elevated duct environment3 结论本文针对对流层复杂环境中的电波传播特性预测问题,提出了一种新型的基于NLBC吸收边界的Greene近似WAPE模型．采用FDM求解WAPE,对不规则地表进行精确建模．引入Greene近似系数将WAPE的最大传播仰角提升至约50°．采用NLBC处理上吸收边界处的反射电波,提高了PE的计算效率．通过与光学模型做对比,证明本文提出的PE电波模型可计算传播仰角更大,对上边界处反射电磁波有良好的吸收效果．综上所述,本文提出的新型PE模型适用于对流层远距离复杂环境中的电波传播特性的精确预测．然而,由于本文的算法属于单向PE算法,又由于忽略了后向分量,对城市小区域环境下的计算精度不高．因此,未来将继续研究更高精度近似形式下的双向PE法,并将其应用在更加复杂的大气环境电波传播预测中．参考文献【相关文献】[1] AKORLI F K, COSTA E. An efficient solution of an integral equation applicable to simulation of propagation along irregular terrain[J]. IEEE transactions on antennas and propagation, 2001, 49(7): 1033-1036.[2] 葛德彪, 闫玉波. 电磁波时域有限差分方法[M]. 西安: 西安电子科技大学出版社, 2002.GE D B, YAN Y B. Finite-difference time-domain method for electromagnetic waves[M]. Xi’an: Xidian University Press, 2002.(in Chinese)[3] LEONTOVICH M A, FOCK V A. Solution of the problem of propagation of electromagnetic waves along the Earth’s surface by method of parabolic equations[J]. Journal of physics-USSR, 1946, 10(1): 13-23.[4] 黎杨. 抛物型方程的有限差分解法及其在复杂电磁环境中的应用[D]. 武汉: 武汉理工大学, 2010. LI Y. The finite-difference method to parabolic equation and its application in complex electromagnetic environments[D]. Wuhan: Wuhan University of Technology, 2010. (in Chinese)[5] 郭建炎, 王剑莹, 龙云亮. 森林中电波传播的抛物方程法[J]. 电波科学学报, 2007, 22(6): 1042-1046.GUO J Y, WANG J Y, LONG Y L. Parabolic equation model for wave propagation in forest environments [J]. Chinese journal of radio science, 2007, 22(6): 1042-1046. (in Chinese) [6] LEVY M F. Parabolic equation methods for electromagnetic wave propagation[M]. London: IEE Press, 2000.[7] 任明. 电波传播损耗预测的抛物型方程模拟[D]. 杭州: 杭州电子科技大学, 2012.REN M. Simulation of parabolic equation for predicting radio wave propagation loss[D]. Hangzhou: Hangzhou Dianzi University, 2012. (in Chinese)[8] GUO Q, ZHOU C, LONG Y L. Greene approximation wide-angle parabolic equation for radio propagation[J]. IEEE transactions on antennas and propagation, 2017, 65(11): 6048-6056.[9] CLAERBOUT J F. Fundamentals of geophysical data processing with applications to petroleum prospecting[M]. New York: McGraw-Hill, 1976.[10] MCNAMARA D A, PISTORIUS C W I, MALHERBE J A G. Introduction to the uniform geometrical theory of diffraction[M]. Norwood: Artech House, 1990.。
5 光束传播法
166
BEAM PROPAGATION METHODS
computation time, (2) the discretization widths in the lateral directions must be uniform, (3) the simple transparent boundary condition cannot be used at the analysis boundaries, (4) very small discretization widths cannot be used in the lateral directions, (5) the polarization cannot be treated, (6) it is inadequate for large-index-difference optical waveguides, (7) the number of sampling points must be a power of 2, and (8) the propagation step has to be small. But it is investigated here because the FFT-BPM is historically important and the line of thinking it exempli®es is very interesting and useful. 5.1.1 Wave Equation The scalar Helmholtz equation is expressed as
168
BEAM PROApproximation Let us try to solve the wave equation (5.11), which is based on the Fresnel approximation. First, we separate the variables of the wave function f of the Fresnel wave equation into the propagation direction and the lateral directions: f x; y; z A x; y exp gz: 5:12
Ka波段基片集成波导罗特曼透镜多波束阵列天线
Ka波段基片集成波导罗特曼透镜多波束阵列天线Xue Fei;Lang Huaqing;Yang Lina【摘要】利用基片集成波导结构完成Ka波段罗特曼透镜仿真设计.在设计中基于罗特曼透镜原理与基片集成波导,利用Matlab在HFSS中得到罗特曼透镜轮廓及透镜的结构中旁壁形状,并对基片集成波导缝隙阵列天线进行设计比较,完成对15×32槽多波束阵列天线的设计,设计了一个单层基片集成波导-金属波导垂直转接的结构.最后, 将各个部分结合在一起, 完成中心频点为35 GHz基片集成波导罗特曼透镜多波束阵列天线设计,其带宽为600 MHz,增益为27. 1 dB,扫描角度为90°.【期刊名称】《航空兵器》【年(卷),期】2019(026)003【总页数】6页(P56-61)【关键词】基片集成波导;罗特曼透镜;缝隙天线;多波束阵列天线【作者】Xue Fei;Lang Huaqing;Yang Lina【作者单位】【正文语种】中文【中图分类】TJ765.3;TN8200 引言随着毫米波高频段系统的发展，平面化、集成化对传统天线的设计提出了更高要求，即需要开发出高性能、低成本的平面阵列天线。
基片集成波导结合了普通平面电路和金属波导的双重优点，能满足现代波束成型网络对性能、外形、重量、加工工艺、成本等诸多方面的要求[1-3]。
多波束天线形成有相控阵天线和透镜天线两种类型[4]。
透镜天线利用同一天线口径形成多个独立且相互重叠的窄波束,虽然其调零分辨率不及相控阵天线,但可以实现波束的最佳空域覆盖,而相控阵天线需要大量集成移相器、功分器或定向耦合器,实现起来非常复杂。
罗特曼透镜则能形成多个波束，覆盖很宽的角度范围、增益高，是经典波束形成网络之一。
现有的罗特曼透镜主要基于微带形式设计实现[5-8]，由于微带在高频损耗较大且设计较为复杂，因此本文将基片集成波导技术与罗特曼透镜结合，实现Ka波段基片集成波导罗特曼透镜多波束阵列天线。
激光专业英语
2011年技术物理学院08级（激光方向）专业英语翻译重点！！！作者：邵晨宇Electromagnetic电磁的principle原则principal主要的macroscopic宏观的microscopic微观的differential微分vector矢量scalar标量permittivity介电常数photons光子oscillation振动density of states态密度dimensionality维数transverse wave横波dipole moment偶极矩diode 二极管mono-chromatic单色temporal时间的spatial空间的velocity速度wave packet波包be perpendicular to线垂直be nomal to线面垂直isotropic各向同性的anistropic各向异性的vacuum真空assumption假设semiconductor半导体nonmagnetic非磁性的considerable大量的ultraviolet紫外的diamagnetic抗磁的paramagnetic顺磁的antiparamagnetic反铁磁的ferro-magnetic铁磁的negligible可忽略的conductivity电导率intrinsic本征的inequality不等式infrared红外的weakly doped弱掺杂heavily doped重掺杂a second derivative in time对时间二阶导数vanish消失tensor张量refractive index折射率crucial主要的quantum mechanics 量子力学transition probability跃迁几率delve研究infinite无限的relevant相关的thermodynamic equilibrium热力学平衡（动态热平衡）fermions费米子bosons波色子potential barrier势垒standing wave驻波travelling wave行波degeneracy简并converge收敛diverge发散phonons声子singularity奇点（奇异值）vector potential向量式partical-wave dualism波粒二象性homogeneous均匀的elliptic椭圆的reasonable公平的合理的reflector反射器characteristic特性prerequisite必要条件quadratic二次的predominantly最重要的gaussian beams高斯光束azimuth方位角evolve推到spot size光斑尺寸radius of curvature曲率半径convention管理hyperbole双曲线hyperboloid双曲面radii半径asymptote渐近线apex顶点rigorous精确地manifestation体现表明wave diffraction波衍射aperture孔径complex beam radius复光束半径lenslike medium类透镜介质be adjacent to与之相邻confocal beam共焦光束a unity determinant单位行列式waveguide波导illustration说明induction归纳symmetric 对称的steady-state稳态be consistent with与之一致solid curves实线dashed curves虚线be identical to相同eigenvalue本征值noteworthy关注的counteract抵消reinforce加强the modal dispersion模式色散the group velocity dispersion群速度色散channel波段repetition rate重复率overlap重叠intuition直觉material dispersion材料色散information capacity信息量feed into 注入derive from由之产生semi-intuitive半直觉intermode mixing模式混合pulse duration脉宽mechanism原理dissipate损耗designate by命名为to a large extent在很大程度上etalon 标准具archetype圆形interferometer干涉计be attributed to归因于roundtrip一个往返infinite geometric progression无穷几何级数conservation of energy能量守恒free spectral range自由光谱区reflection coefficient（fraction of the intensity reflected）反射系数transmission coefficient（fraction of the intensity transmitted）透射系数optical resonator光学谐振腔unity 归一optical spectrum analyzer光谱分析grequency separations频率间隔scanning interferometer扫描干涉仪sweep移动replica复制品ambiguity不确定simultaneous同步的longitudinal laser mode纵模denominator分母finesse精细度the limiting resolution极限分辨率the width of a transmission bandpass透射带宽collimated beam线性光束noncollimated beam非线性光束transient condition瞬态情况spherical mirror 球面镜locus（loci）轨迹exponential factor指数因子radian弧度configuration不举intercept截断back and forth反复spatical mode空间模式algebra代数in practice在实际中symmetrical对称的a symmetrical conforal resonator对称共焦谐振腔criteria准则concentric同心的biperiodic lens sequence双周期透镜组序列stable solution稳态解equivalent lens等效透镜verge 边缘self-consistent自洽reference plane参考平面off-axis离轴shaded area阴影区clear area空白区perturbation扰动evolution渐变decay减弱unimodual matrix单位矩阵discrepancy相位差longitudinal mode index纵模指数resonance共振quantum electronics量子电子学phenomenon现象exploit利用spontaneous emission自发辐射initial初始的thermodynamic热力学inphase同相位的population inversion粒子数反转transparent透明的threshold阈值predominate over占主导地位的monochromaticity单色性spatical and temporal coherence时空相干性by virtue of利用directionality方向性superposition叠加pump rate泵浦速率shunt分流corona breakdown电晕击穿audacity畅通无阻versatile用途广泛的photoelectric effect光电效应quantum detector 量子探测器quantum efficiency量子效率vacuum photodiode真空光电二极管photoelectric work function光电功函数cathode阴极anode阳极formidable苛刻的恶光的irrespective无关的impinge撞击in turn依次capacitance电容photomultiplier光电信增管photoconductor光敏电阻junction photodiode结型光电二极管avalanche photodiode雪崩二极管shot noise 散粒噪声thermal noise热噪声1.In this chapter we consider Maxwell’s equations and what they reveal about the propagation of light in vacuum and in matter. We introduce the concept of photons and present their density of states.Since the density of states is a rather important property，not only for photons，we approach this quantity in a rather general way. We will use the density of states later also for other(quasi-) particles including systems of reduced dimensionality.In addition,we introduce the occupation probability of these states for various groups of particles.在本章中，我们讨论麦克斯韦方程和他们显示的有关光在真空中传播的问题。
遥感专业名词中英对照
地面 Ground
地面分辨率 Ground resolution
地面记录与监测系统 Ground Recording & Monitoring System，GR&MS
地面接收站 Ground receiving station
复共线性 Multi-Collinearity
傅里叶变换 Fourier transform
改进型甚高分辨率辐射仪 Advanced very high resolution radiometer,AVHRR
感光材料 Graphical materials
高度 Altitude
高分辨率可见光波段传感器 Haute resolution visible,HRV
高分辨率视频 High resolution video,HRV
高分辨率图像传递装置 High resolution picture transmission,HRPT
地球资源技术卫星 Earth resources technology satellite,ERTS
地球资源卫星 Land satellite,LANDSAT
地物波谱特征 Ground spectrum characteristics
电磁波 Electromagnetic wave
国际电信联盟 International telecommunications union,ITU
国家海洋与大气管理局 National oceanographic and atmospheric administration,NOAA
国家航空航天局 National aeronautics and space administration,NASA
电磁场词汇汉英对照表
八画 变分法 variational method 定向耦合器 directional coupler 取向 orientation 法拉第感应定律 Faraday’s law of induction 实部 real part 空间分量 spatial components 波导 waveguide 波导波长 guide wave length 波导相速度 guide phase velocity 波阻抗 wave impedance 波函数 wave function 波数 wave number 泊松方程 Poisson’s equation 拉普拉斯方程 Laplace’s equation 坡印亭矢量 Poynting vector 奇异性 singularity
焊接专业英语词汇
焊接专业英语词汇（焊接及相关工艺英文缩写）AW——ARC WELDING——电弧焊AHW——atomic hydrogen welding——原子氢焊BMAW——bare metal arc welding——无保护金属丝电弧焊CAW——carbon arc welding——碳弧焊CAW-G——gas carbon arc welding——气保护碳弧焊CAW-S——shielded carbon arc welding——有保护碳弧焊CAW-T——twin carbon arc welding——双碳极间电弧焊EGW——electrogas welding——气电立焊FCAW——flux cored arc welding——药芯焊丝电弧焊FCW-G——gas-shielded flux cored arc welding——气保护药芯焊丝电弧焊FCW-S——self-shielded flux cored arc welding——自保护药芯焊丝电弧焊GMAW——gas metal arc welding——熔化极气体保护电弧焊GMAW-P——pulsed arc——熔化极气体保护脉冲电弧焊GMAW-S——short circuiting arc——熔化极气体保护短路过度电弧焊GTAW——gas tungsten arc welding——钨极气体保护电弧焊GTAW-P——pulsed arc——钨极气体保护脉冲电弧焊MIAW——magnetically impelled arc welding——磁推力电弧焊PAW——plasma arc welding——等离子弧焊SMAW——shielded metal arc welding——焊条电弧焊SW——stud arc welding——螺栓电弧焊SAW——submerged arc welding——埋弧焊SAW-S——series——横列双丝埋弧焊RW——RWSISTANCE WELDING——电阻焊FW——flash welding——闪光焊RW-PC——pressure controlled resistance welding——压力控制电阻焊PW——projection welding——凸焊RSEW——resistance seam welding——电阻缝焊RSEW-HF——high-frequency seam welding——高频电阻缝焊RSEW-I——induction seam welding——感应电阻缝焊RSEW-MS——mash seam welding——压平缝焊RSW——resistance spot welding——点焊UW——upset welding——电阻对焊UW-HF——high-frequency——高频电阻对焊UW-I——induction——感应电阻对焊SSW——SOLID STATE WELDING——固态焊CEW——co-extrusion welding——CW——cold welding——冷压焊DFW——diffusion welding——扩散焊SW——stud arc welding——螺栓电弧焊SAW——submerged arc welding——埋弧焊SAW-S——series——横列双丝埋弧焊RW——RWSISTANCE WELDING——电阻焊FW——flash welding——闪光焊RW-PC——pressure controlled resistance welding——压力控制电阻焊PW——projection welding——凸焊RSEW——resistance seam welding——电阻缝焊RSEW-HF——high-frequency seam welding——高频电阻缝焊RSEW-I——induction seam welding——感应电阻缝焊RSEW-MS——mash seam welding——压平缝焊RSW——resistance spot welding——点焊UW——upset welding——电阻对焊UW-HF——high-frequency——高频电阻对焊UW-I——induction——感应电阻对焊SSW——SOLID STATE WELDING——固态焊CEW——co-extrusion welding——CW——cold welding——冷压焊DFW——diffusion welding——扩散焊HIPW——hot isostatic pressure diffusion welding——热等静压扩散焊EXW——explosion welding——爆炸焊FOW——forge welding——锻焊FRW——friction welding——摩擦焊FRW-DD——direct drive friction welding——径向摩擦焊FSW——friction stir welding——搅拌摩擦焊FRW-I——inertia friction welding——惯性摩擦焊HPW——hot pressure welding——热压焊ROW——roll welding——热轧焊USW——ultrasonic welding——超声波焊S——SOLDERING——软钎焊DS——dip soldering——浸沾钎焊FS——furnace soldering——炉中钎焊IS——induction soldering——感应钎焊IRS——infrared soldering——红外钎焊INS——iron soldering——烙铁钎焊RS——resistance soldering——电阻钎焊TS——torch soldering——火焰钎焊UUS——ultrasonic soldering——超声波钎焊WS——wave soldering——波峰钎焊B——BRAZING——软钎焊BB——block brazing——块钎焊DFB——diffusion brazing——扩散焊DB——dip brazing——浸沾钎焊EXB——exothermic brazing——反应钎焊FB——furnace brazing——炉中钎焊IB——induction brazing——感应钎焊IRB——infrared brazing——红外钎焊RB——resistance brazing——电阻钎焊TB——torch brazing——火焰钎焊TCAB——twin carbon arc brazing——双碳弧钎焊OFW——OXYFUEL GAS WELDING——气焊AAW——air-acetylene welding——空气乙炔焊OAW——oxy-acetylene welding——氧乙炔焊OHW——oxy-hydrogen welding——氢氧焊PGW——pressure gas welding——气压焊OTHER WELDING AND JOINING——其他焊接与连接方法AB——adhesive bonding——粘接BW——braze welding——钎接焊ABW——arc braze welding——电弧钎焊CABW——carbon arc braze welding——碳弧钎焊EBBW——electron beam braze welding——电子束钎焊EXBW——exothermic braze welding——热反应钎焊FLB——flow brazing——波峰钎焊FLOW——flow welding——波峰焊LBBW——laser beam braze welding——激光钎焊EBW——electron beam welding——电子束焊EBW-HV——high vacuum——高真空电子束焊EBW-MV——medium vacuum——中真空电子束焊EBW-NV——non vacuum——非真空电子束焊ESW——electroslag welding——电渣焊ESW-CG——consumable guide eletroslag welding——熔嘴电渣焊IW——induction welding——感应焊LBW——laser beam welding——激光焊PEW——percussion welding——冲击电阻焊TW——thermit welding——热剂焊THSP——THERMAL SPRAYING——热喷涂ASP——arc spraying——电弧喷涂FLSP——flame spraying——火焰喷涂FLSP-W——wire flame spraying——丝材火焰喷涂HVOF——high velocity oxyfuel spraying——高速氧燃气喷涂PSP——plasma spraying——等离子喷涂VPSP-W——vacuum plasma spraying——真空等离子喷涂TC——THERMAL CUTTING——热切割OC——OXYGEN CUTTING——气割OC-F——flux cutting——熔剂切割OC-P——metal powder cutting——金属熔剂切割OFC——oxyfuel gas cutting——氧燃气切割CFC-A——oxyacetylene cutting——氧乙炔切割CFC-H——oxyhydrogen cutting——氢氧切割CFC-N——oxynatural gas cutting——氧天然气切割CFC-P——oxypropanne cutting——氧丙酮切割OAC——oxygen arc cutting——氧气电弧切割OG——oxygen gouging——气刨OLC——oxygen lance cutting——氧矛切割AC——ARC CUTTING——电弧切割CAC——carbon arc cutting——碳弧切割CAC-A——air carbon arc cutting——空气碳弧切割GMAC——gas metal arc cutting——熔化极气体保护电弧切割GTAC——gas tungsten arc cutting——钨极气体保护电弧切割PAC——plasma arc cutting——等离子弧切割SMAC——shielded metal arc cutting——焊条电弧切割HIGH ENERGY BEAM CUTTING——高能束切割EBC——electron beam cutting——电子束切割LBC——laser beam cutting——激光切割LBC-A——air——空气激光切割LBC-EV——evaporative——蒸气激光切割LBC-IG——inert gas——惰性气体激光切割LBC-O——oxygen——氧气激光切割激光切割laser cutting(LC);laser beam cutting电子束切割electron beam cutting喷气激光切割gas jet laser cutting碳弧切割carbon arc cutting水下切割underwater cutting喷水式水下电弧切割waterjet method underwater arc cutting氧矛切割oxygen lancing;oxygen lance cutting溶剂氧切割powder lancing手工气割manual oxygen cutting自动气割automatic oxygen cutting仿形切割shape cutting数控切割NC(numerical-control)cutting快速切割high-speed cutting垂直切割square cut叠板切割stack cutting坡口切割beveling;bevel cutting碳弧气割carbon arc air gouging火焰气刨flame gouging火焰表面清理scarfing氧熔剂表面修整powder washing预热火焰preheat flame预热氧preheat oxygen切割氧cutting oxygen/cutting stream切割速度cutting speed切割线line of cut/cut line切割面face of cut/cut face切口kerf切口上缘cutting shoulder切口宽度kerf width后拖量drag切割面平面度evenness of cutting surface/planeness of cutting surface 割纹深度depth of cutting veins/stria depth切割面质量quality of cut face上缘熔化度shoulder meltability/melting degree of shoulder切口角kerf angle缺口notch挂渣adhering slag结瘤dross割炬cutting torch/cutting blowpipe/oxygen-fuel gas cutting torch割枪cutting gun割嘴cutting nozzle/cutting tip快速割嘴divergent nozzle/high-speed nozzle表面割炬gouging blowpipe水下割炬under-water cutting blowpipe水下割条electrode for under-water cutting粉剂罐powder dispenser数控切割机NC cutting machine门式切割机flame planer光电跟踪切割机photo-electric tracing cutting火焰切管机pipe flame cutting machine磁轮式气割机gas cutting machine with magnetic wheels焊接结构welded structure/welded construction焊件weldment焊接部件weld assembly组装件built-up member接头设计joint design焊接应力welding stress焊接瞬时应力transient welding stress焊接残余应力welding residual stress热应力thermal stress收缩应力contraction stress局部应力local stress拘束应力constraint stress固有应力inherent stress固有应变区inherent strain zone残余应力测定residual stress analysis逐层切割法Sach’s methodX射线衍射法X-ray stress analysis小孔释放法Mathar method固有应变法inherent strain method消除应力stress relieving局部消除应力local stress relieving应力重分布stress redistribution退火消除应力stress relieving by annealing温差拉伸消除应力low temperature stress relieving机械拉伸消除应力mechanical stress relieving应力松弛stress relaxation焊接变形welding deformation焊接残余变形welding residual deformation局部变形local deformation角变形angular distortion自由变形free deformation收缩变形contraction deformation错边变形mismatching deformation挠曲变形deflection deformation波浪变形wave-like deformation火焰矫正flame straightening反变形backward deformation焊接力学welding mechanics断裂力学fracture mechanics弹塑性断裂变形elasto-plastic fracture mechanics线弹性断裂力学linear elastic fracture mechanics延性断裂ductile fracture脆性断裂brittle fracture应力腐蚀开裂stress corrosion cracking热应变脆化hot straining embrittlement临界裂纹尺寸critical crack size裂纹扩展速率crack propagation rate裂纹张开位移（COD）crack opening displacement拘束度restraint intensity拘束系数restraint coefficient应变速率strain rate断裂韧度fracture toughness应力强度因子stress intensity factor临界应力强度因子critical stress intensity factors应力腐蚀临界应力强度因子critical stress intensity factor of stress corrosion cracking J积分J-integration罗伯逊止裂试验Robertson crack arrest testESSO试验ESSO test双重拉伸试验doucle tension test韦尔斯宽板拉伸试验Well’s wide plate test帕瑞斯公式Paris formula断裂分析图fracture analysis diagram焊接车间welding shop焊接工作间welding booth焊接工位welding post/welding station焊接环境welding surroundings焊工welder电焊工manual arc welder气焊工gas welder焊接检验员weld inspector焊工培训welders training焊工模拟训练器trainer of synthetic weld焊工考试welder qualification test焊工合格证welder qualification/welder qualified certification 钢板预处理steel plate pretreatment喷沙sand blast喷丸shot blast矫正straighten开坡口bevelling(of the edge)/chanfering装配assembly/fitting安装erect刚性固定rigid fixing装配焊接顺序sequence of fitting and welding焊接工艺评定welding procedure qualification焊接工艺规程welding procedure specification焊接工艺试验welding procedure test焊接工艺卡welding procedure card工序operational sequence焊接材料消耗定额welding consumables quota焊接工时定额welder-hour quota清渣slag removal清根back gouging/back chipping锤击peening返修次数number of rewelding焊接工作台welding bench装焊平台welding platen电磁平台electromagnetic platen焊接翻转机welding tilter焊接回转台floor turnable positioner焊接变位机positioner焊接滚轮架turning rolls焊接操作机manpulator焊工升降台welder’s lifting platform焊接夹具welding jig/fixture磁力夹紧器magnetic jig螺旋推撑器screw operated tensioning unit焊丝盘绕机welding wire coiler焊条压涂机welding electrode extrusion press红外线加热器infra-red heater干燥箱dryer焊条保温筒thermostat for electrode流量计flow meterCO2预热器CO2heaterCO2干燥器CO2desiccator焊接电缆welding cable电缆夹头welding connector地线earth lead地线夹头earth clamp焊接参数记录仪welding parameter recorder焊缝检测规weld gauge喷嘴通针tip cleaner测温笔tempil stick敲渣锤chipping hammer焊接衬垫backing/welding backing保留垫板fusible backing/permanent backing临时垫板temporary backing焊剂垫flux backing惰性气体衬垫inert-gas backing引弧板run-on tab/end tab/starting weld tab引出板run-off tab/end tab定位板strong-back加强勒stiffener嵌条insert套环ferrule面罩helmet滤光镜片filter glass/welding glass防护镜片cover glass/plain glass气焊眼镜welding goggles焊接机器人welding robot点焊机器人spot welding robot弧焊机器人arc welding robot切割机器人cutting robot焊接机器人生产线robot line for welding焊接机器人工作站welding robot station机器人运动自由degree of free for robot机器人工作空间robot working space轨迹重复精度path repeatability点位重复精度PTP repeatability焊接专家系统welding expert system焊接机器人示数welding robot play back焊接图象识别pattern recognition for welding焊接图象处理welding image processing计算机辅助焊接工艺设计computer-aided welding process programming(CAWPP)计算机辅助焊接结构设计computer-aided design for welding structure焊接烟尘weld fume焊接发尘量total amount of fumes焊接烟尘浓度weld fume concentration焊接烟尘容限浓度threshold limit values of weld fume(TLV)焊接发尘速率weld fume emission rate焊接有害气体welding toxic gases/weld harmful gases标定卫生空气需要量nominal hygienic air requirement焊工尘肺pheumocomsis of welder焊工锰中毒chronic occupational manganese poisoning of welder 焊工氟中毒fluorosis of welder焊工金属烟热metal fume fever of welder电光性眼炎eye-flash(arc eye)电光性皮炎electro-photo dermatitis电弧紫外线灼伤ultraviolet ray burn防电击装置voltage reducing device除尘装置dust collection device焊工手套welding gloves护脚welding spats防护鞋shielding shoes焊接欠缺welding imperfection焊接缺陷weld defect气孔blowhole/gas pore针尖状气孔pinhole密集气孔porosity条虫状气孔wormhole裂纹crack表面裂纹surface crack咬边undercut焊瘤overlap凹坑pit烧穿burn through塌陷excessive penetration未焊透incomplete penetration/lack of penetration未熔合lack of fusion/incomplete fusion未焊满incompletely filled weld根部凹陷root concavity电弧擦伤arc scratch夹渣slag inclusion夹杂物inclusion夹钨tungsten inclusion白点fish eye/flake错边misalignment/dislocation试件test piece试样test specimen无损检验nondestructive test破坏检验destructive test外观检查visual examination超声波探伤ultrasonic inspection直射法超声波探伤straight beam method斜射法超声波探伤angle beam method液浸法超声波探伤immersion method射线探伤radiographic inspection/radiographyX射线探伤X-ray radiographic inspectionγ射线探伤gamma-ray inspectionX射线工业电视探伤X-ray industrial television inspection 磁粉探伤magnetic particle inspection电磁探伤electromagnetic inspection/eddy current test 探伤灵敏度flaw detection sensitivity渗透探伤penetration inspection荧光探伤flurescent penetrant inspection着色探伤dye penetrant inspection密封性检验leak test气密性检验air tight test枕形气密检验pillow test耐压检验pressure test水压检验hydraulic test气压检验pneumatic test液晶检验liquid crystal test声发射检测acoustic emission testing面弯试验face bend testing背弯试验root bend test侧弯试验side bend test横弯试验horizontal bend test纵弯试验axial bend test压扁试验squeezing test。
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Fig. 1. The percentage errors of the propagation constants. Solid: "E; dash: TM. The curves for both LY = 0.5 and a = 0.6 are shown.
A , , - j A z a A , , E;''
optical filtering of obliquely incident waves in corrugated waveguide filters,” IEEE J. Quantum Electron., vol. QE-15, pp. 632-637, 1979. [ l l ] H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. -I., vol. 48, pp. 2909-2947, 1969.
E conventional beam propagation methods (BPM) [21 solve scalar wave equations under paraxial approximation and hence apply only to simulation of scalar wave propagation along waveguide axis in weakly guiding structures. Several numerical algorithms to treat the vectorial wave propagation (vector BPM) have been reported recently [3]-[5]. The VBPM’s are capable of simulating polarized or even hybrid wave propagation in strongly guiding structures. Once of the shortcomings of the current VBPM’s is that the paraxial approximation is still assumed in the governing equations and only waves propagating close to the waveguide axis may be accurately predicted. In the strongly guided structures, guided modes may be formed by bouncing waves propagating at large angles with the waveguide axis. Even for weakly guided structures, radiation caused by longitudinal index perturbations may occur at large angles off the waveguide axis. Furthermore, a reference refractive index must be assumed in all the paraxial (scalar and vector) propagating algorithms. The choice of the reference index is critical for the accuracy of the numerical solutions. Although an optimum reference index may be obtained by a modal calculation [ 5 ] , to determine the optimum refractive index in practice is cumbersome and difficult in practical applications.
=
-jA, and n = n(x, y , z ) is the refractive index of the medium. A time dependence of e j w l has been assumed. The parameter n , is a reference refractive index and should be chosen to be close to the weighted average of the effective index of the structure. The differential operators are defined by A,,E,
.eo Q 2 .
d .*
- TE - - TM
I
I
I
I1 Wide Angle
(3)
-.eo I
1.30
1.35
1.40
I
1.45
1.50
Reference Index no
where i = x , y wide-angle schemes of different orders may be derived from (1). For n = 1, the following equation is obtained: 2
1
The parameter a is a controlling factor that affects the order of accuracy, the stability and the dissipation of the numerical solutions. The algorithm is stable for a 2 0.5 [5]. Equation (4) may be solved by a standard LDU decomposition for the tridiagonal linear equations in the 2-D cases. For the 3-D structures, more sophisticated numerical solvers such as ORTHOMIN may be used. Note that virtually no extra computation is required for the wide-angle scheme in comparison with the paraxial VBPM and hence the new scheme is expected to be as efficient as the paraxial one. At the edges of the computation window, the transparent boundary condition is used For the assessment, we first simulated the guided modes of a step-index symmetric slab waveguide. We calculate the percentage errors in the propagation constants for the TE and the T M guided-modes. The refractive indices chosen for the guiding and the cladding layers are n , = 1.5, n2 = 1.3, respectively. The total width of the guiding layer is D = 0.5 p m . The wavelength is A = 1.5 pm. The step sizes are A x = 0.02 p m and Az = 0.01 p m , and the window size was W = 10 p m . Fig. 1 shows the percentage errors of the propagation constants for the TE (solid) and the T M (dash) modes as functions of the reference index no. Two scheme parameters a = 0.5 and a = 0.6 are used and the two sets of curves are indistinguishable. Substantial improvement in the accuracy is observed for the wide-angle scheme in comparison with the paraxial scheme. In addition, the errors in the propagation constants are almost independent of no and therefore the choice of the reference index is no longer critical as in the paraxial VBPM. The dependence of numerical dissipation as a function of no is also examined and found to have similar behavior as the paraxial VBPM [5].
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IEEE PHOTONICS TECHNOLOGY LE’ITERS, VOL. 4, NO. 10, OCTOBER 1992
[8] R. Kowarschik, “Diffraction efficiency of sequentially stored gratings in transmission volume holograms,” Optica Acta., vol. 25, pp. 67-81, 1978. [9] H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated circuits. New York: McGraw-Hill, 1991, ch. 3, 4. [lo] K. Wagatsuma, H. Sakaki, and S. Saito, “Mode conversion and