2005 Vol. 17, No. 10

Recommend Articles
高功率激光与光学
LD pumped 2 μm solid-state laser with high pulsed repetition rate
zhang xing-bao, yao bao-quan, wang yue-zhu, ju you-lun
2005, 17.
Abstract:
A CW LD end pumped high pulsed repetition rate (PRF) Tm,Ho:YLF laser was reported. The fiber-coupled laser diode of 792 nm as a pumping source pumped the liquid-nitrogen-cooled Tm,Ho:YLF crystal. The average output power of 4 W was obtained and extraction efficiency was more than 85% in dynamic running. The PRF varied from 1~50 kHz by using an A-O Q-switch. The peak power of 12 kW and pulse width of 32 ns were achieved at PRF of 10 kHz. At the same time several important factors in the 2 μm laser design were analyzed.
Laser damage threshold of telluride transmitting infrared fluoroaluminate glass
yuan xin-qiang, fan you-yu, feng ji-tian, hu he-fang
2005, 17.
Abstract:
After introducing the low-phonon energy oxide——TeO2 into the fluoroaluminate glass, a new oxyfluoride glass was obtained with better vitrification ability. Some physical properties were measured of the new glass with different TeO2 content(such as characteristic temperature, Abbe value, infrared light transmittance, damage threshold for DF laser ). The telluride fluoroaluminate with TeO2 content 15% had a maximum damage threshold up to 14.95 kW·cm-2. Analysis indicates that the main reason of the glass damage is thermal impact, which results from the absorbed laser energy for glass matrix and hydroxyl vibration. If the water content in the glass can be reduced, it will improve the property of the glass.
Jet singlet oxygen generator modeling
liu wan-fa, han xin-min, jin yu-qi, sang feng-ting
2005, 17.
Abstract:
The jet singlet oxygen generator (JSOG) is an efficient energy donor for a chemical oxygen-iodine laser (COIL). Using the trial-solution method under specific boundary conditions, the diffusion equations were derived of chlorine, singlet oxygen, and total oxygen in gas and liquid phases. The analytical solutions for the utilization of chlorine and the yield of singlet oxygen were obtained, which agree with the experimental results and are helpful for further improvement and optimization of the JSOG.
Effects of non-parallel grating pair on pulse space-time profiles
liu wen-bing, zhu qi-hua, feng guo-ying, wang xiao, wang fang
2005, 17.
Abstract:
The expressions of the first- to fourth-order dispersion change were derived when there was a small angle between the two gratings in the plane perpendicular to the grooves (diffracting plane). The field distribution of a pulsed super-Gaussian beam passing through a grating pair was derived. The relations between the misalignment and the space-time properties of the output pulse were analyzed. The results show that the pulse is distorted when it passes through the compressor. The misalignment and the lateral spectrum displacement co-make the pulse distortion more serious. When the pulse passes through the compressor twice, the effects of the lateral spectrum displacement is eliminated, but there are wings and the misalignment brings the pulse forward in time domain. The higher order disper
Frequency conversion of generating 193 nm laser by deep ultraviolet sum-frequency crystal CLBO
zhou cheng
2005, 17.
Abstract:
The properties of nonlinear frequency conversion in a new deep ultraviolet sum-frequency crystal CLBO were discussed. The data for sum-frequency CLBO crystal generating 193 nm laser of phase-matching angle, effective nonlinear coefficient, walk-off angle and maximum acceptance angle were calculated. According to those data and taking account of lasers commercialization requirements, several phase-matching projects were compared. At last, the phase-matching type of 2 100 nm(o)+213 nm(e)→193 nm(e) was selected. The phase-matching type of 2 100 nm(o)+213 nm(e)→193 nm(e) with large effective nonlinear coefficient of 0.97, small walk-off angle 3.7° and big acceptance angle 1.9×10-6 rad·mm was proved to be the optimum for generating 193 nm laser.
Vectorial nonparaxial cosh-Gaussian beams
gao zeng-hui, l bai-da
2005, 17.
Abstract:
The concept of vectorial nonparaxial cosh-Gaussian (ChG) beams is introduced and their free-space propagation equation is derived analytically by using the vectorial Rayleigh-Sommerfeld diffraction integrals. The on-axis and far-field expressions of vectorial nonparaxial ChG beams and the paraxial results are given as special cases of the general propagation equation. It is found that for vectorial nonparaxial ChG beams, the f parameter mainly determines their nonparaxiality, but the decentered parameter affects their transversal intensity profile and nonparaxial behavior.
Influences of SPM on compressed pulse with amplitude modulations and phase perturbations
ma zai-ru, feng guo-ying, zhu qi-hua, chen jian-guo
2005, 17.
Abstract:
Self phase modulation (SPM) plays an important role on the compressed pulse in chirped pulse amplification lasers systems. The influences of the SPM with amplitude modulations and phase perturbations on the compressed pulse is simulated. The simulations show that more amplitude modulations and phase perturbations lead to lower contrast of the compressed pulse, and bigger modulation cycle results in wider pre-pulse width.
Transform-circle graphic analysis of self-mode-locked laser cavity
zhang xiao-hua, zhang guang-yin, sun jing-hua, wei zhi-yi, yan cai-fan, gu xue-wen, wu ding-er
2005, 17.
Abstract:
Using the propagation-circle and transform-circle graphic analysis, cavities with different configurations were analyzed and compared and a self-mode-locked cavity, a nearly symmetrical four-mirror cavity was obtained, which was more stable and easy to start. The operating performance of the nearly symmetrical cavity was ensured by experiment. A five-mirror mode-locked cavity was also analyzed.
Evaluating intermediate frequency error property of wavefront of optical components with PSD collapse
cheng xiao-feng, zheng wan-guo, jiang xiao-dong, ren huan, zhong wei, xu hua, jing feng
2005, 17.
Abstract:
Arithmetic of two-dimensional power spectral density (2-D PSD) of large optics wavefront was briefly described and PSD collapse was introduced to evaluate the intermediate frequency error property of wavefront. As the PSD collapse is radon transform projection of 2-D power spectral density at any angle, all valid data of wavefront of optics were used in calculation of the PSD collapse and the features of 1-D PSD were inherited in PSD collapse. Although the PSD collapse is the same as 1-D PSD in unit and behaving style, it is better in evaluating intermediate frequency error property of optics wavefront than 1-D PSD or 2-D PSD. As PSD collapse calculation uses all valid data of evaluated optics wavefront and can be directly perceived through its profile, the PSD collapse is possibly the sta
New analysis on laser-induced damage mechanism of array CCD device
li wen-yu, wang jin-bao, cheng xiang-ai, lu qi-sheng
2005, 17.
Abstract:
The SONY ICX055BL visible-light CCD was irradiated by 1 064 nm pulsed laser with the width of 5 ms. In the experiments the video signal was recorded by PC image acquisition card, at the same time the output of ICX055BL was recorded by oscillograph. The damaging mechanism analyses was not limited to MOS part of the CCD which work as the detector, stores and transferrs charge, but took the CCD as a function aggregate. Based on the experimental results and the characters of the CCD device circuit, the IC destruction was due to the circuit damage. That is to say the signal charge packages induced by the pulse laser damaged the reset-FET, which caused the device out of work for ever.
Influence of initially filled Ar gas density oncapillary discharge-pumped soft X-ray laser
peng hui-min, zheng wu-di, zhao yong-peng, cheng yuan-li, yang da-wei, wang qi
2005, 17.
Abstract:
In this paper the simulation of the influence of initially filled Ar density on the plasma conditions and the gain coefficient of 3p-3s transition of Ne-like Ar ions in capillary discharge pumped soft X-ray laser is presented. The parameters of discharge generator,which is located in Harbin Institute of Technology are used in the simulation. The temporal evolvement of spatial distributions of capillary discharge produced plasma conditions and gain coefficient are shown. The results shows that the extension of Ar gas density which the gain can be got is sufficiently wide and it is very useful for experiment. Choosing the initial pressure of 40~80 Pa in capillary is the best for getting good results.
Approximate computation model of clear sky spectral luminance
su yi, wan min, hu xiao-yang, yang rui, leng jie, zheng jie
2005, 17.
Abstract:
Based on radiative transfer equation, using the experiential formulae of air mass and atmospheric aerosol optical depth and atmospheric molecule parameters obtained by HITRAN database, an approximate algorithm for clear sky spectral luminance was given, which could be used generally. Clear sky spectral luminance was computed by the approximate algorithm model. Computation results indicate that there are distinct absorption lines of O2 and H2O on the curve of clear sky spectral luminance. The luminance of clear sky radiation is higher at shortwave band, while the spectrum for small sun angle shifts to longer waveband. The sky radiation luminance adjacent to horizon is higher.
Optical method for simultaneously measuring refractive-index structure parameter and inner scale of atmospheric turbulence
zhu wen-yue, zhao zhu-ling, ma xiao-shan, rao rui-zhong
2005, 17.
Abstract:
The principle is as follows: Supposing the inner scale has a specific value, the refractive-index structure parameters are equal for different wavelengths, which is based on the optical-propagation theory using the modified Hill spectrum with the inner scale effect. According to the proposed inversion principle, a three-wavelength scintillometer was designed for the reliability verification in the laser propagation trials. The results show that the inner scale near the land surface is generally between 2 and 10 mm, and it will vary accordingly as the refractive-index structure parameter changes. Moreover, some experiments also demonstrate that the method is reliable by the inverted values of any two wavelengths, of which the minimum correlation coefficient is 0.81.
Damage effect on CCD detector irradiated by 500 fs laser pulse
huang shao-yan, zhang yong-sheng, tang ben-qi, zhang yong, wang zu-jun, xiao zhi-gang
2005, 17.
Abstract:
A 250 μJ, 500 fs ultra-short laser pulse was used to radiate linear array CCD detector. The whole responding from linear, saturation, cross talk and totally damaged was observed. Theoretical analyses were made to explain the damage mechanism. The experiment shows that the saturated energy threshold of CCD element is 0.45 μJ/cm2. The CCD is damaged by six pulses with energy density of 0.14 J/cm2 and the damage is due to lattice heat and evaporation with plasma. When the laser energy density is 1.41 J/cm2, the output waveform of CCD detector is unrecognizable for single pulse and there is no output for two pulses. The damage mechanism is considered to be Coulomb force of electric field from charge separation.
ICF与激光等离子体
Preparation of ultra-thin freestanding polyimide films with sequential evaporation technique
qi tong-fei, wu yong-gang, wang yong, zhang li, lin xiao-yan, tian guo-xun, jiao hong-fei, chen ling-yan
2005, 17.
Abstract:
Ultra-thin freestanding polyimide(PI) films of 100 nm thickness were formed by sequential evaporation of 4,4'-diaminodiphenyl ether(ODA) and pyromellitic dianhydride(PMDA) precursor monomers followed by a thermal treatment of 150 ℃ 1 h and 350 ℃ 2 h. The chemical structures of the PI films were investigated using FTIR spectroscopy and the degree of imidization was calculated. Results show that the PI film has a fully imidization. The surface morphology of the films, compared with co-deposited PI films, was observed using AFM, the surface morphology of the PI films would be better by depositing ODA first.
Spectroscopy diagnosis of hydrogen plasma excited by helicon-wave
wang jia-kou, wu wei-dong, sun wei-guo, deng hong-yan, cheng xin-lu, tang yong-jian
2005, 17.
Abstract:
The hydrogen plasma was excited by using the technology of helicon-wave plasma chemical vapor deposition (HWP-CVD). The characteristics of the plasma were investigated by using the vacuum ultraviolet-visible emission spectroscopy. The influence of experiment parameters on the relative density of the excited hydrogen atoms was analyzed through the analysis of the hydrogen Balmer lines, and that on the vibrational temperature of hydrogen was studied through the analysis of the hydrogen Fulcher band lines. The electron temperature, the electron density and the relative rate coefficient were analyzed. The experimental results indicate that the state of a low pressure hydrogen plasma can be diagnosed by the corona model and the density of the excited hydrogen atoms increases with the increas of
Influence of different kinds of evaporation sources on films uniformity
dong lei, zhao yuan-an, yi kui, shao jian-da, fan zheng-xiu
2005, 17.
Abstract:
Several evaporation sources, including the plane and spherical source, and their influence on film uniformity were studied. It is found that when the ratio between the radius of the source surface and the height of the substrate is less than 1/17, the area of the source surfaces can be ignored, and when it is greater than 1/10, the area of the source surface should be considered. When the ratio between the depth of the spherical surface and the radius of the source surface is less than 0.5, the spherical source has little effect on films uniformity compared with the plane source, and when it is greater than 0.6, the influence of spherical surface source on films uniformity should be considered. Based on the study, the relation between the emission characteristic of sources and film uniform
Physical analysis for designing nested-wire arrays on Z-pinch implosion
yang zhen-hua, liu quan, ding ning, ning cheng
2005, 17.
Abstract:
Z-pinch experiments have demonstrated that the X-ray power increases 40% with a nested-wire array compared with that with a single-layered wire array. The design of the nested-wire array on Z accelerator is studied through the implosion dynamics and the growth of RT instabilities. The analysis shows that the nested-wrie array does not produce more total X-ray radiation energy than the single-layered wire arrya, but it obviously increases the X-ray power. The radius of the outer array of the nested-wire array could be determined based on the radius of the optimized single-layered wire array. The masses of the outer and inner arrays could be determined by the implosion time of the nested-wire array, which is roughly the same as that of the single-layered wire array. Some suggestions are put
Research on the neutral native point defects in KDP crystals using first-principles theory
wang kun-peng, zhang jian-xiu, fang chang-shui, yu wen-tao, wang sheng-lai, gu qing-tian, sun xun
2005, 17.
Abstract:
The formation energies and concentrations at room temperature of various neutral native point defects in KDP crystals were studied using first-principles theory. The calculation results show that Hi may be the dominant point defect at room temperature in KDP. The formation energy of O vacancy (5.25 eV) is much higher than that of O interstitial (0.60 eV). Optical absorption center may be formed due to the O vacancy and may be responsible for the lowering of the damage threshold in KDP. K vacancy enlarges the volume of cavity surrounded by the eight O atoms by about 3.2%. K-vacacy(VK) defect may increase ionic conductivity and therefore laser-induced damage threshold decrease.
Output energy stability of four-pass amplification system
xu lan, su jing-qin, peng han-sheng, jing feng, ang wen-yi, peng zhi-tao, li qiang, hu dong-xia, he shao-bo, ding lei, li ming-zhong
2005, 17.
Abstract:
In accordance with the built-up structure of the main amplifier in technical integration experiment line (TIL), the effects of the injected energy, amplifier gain and transmission on the output energy stability were calculated. Experimental results show that the greater the injected energy, the weaker the effect of the injected energy on the output energy. The effect of the small gain coefficient was greater than that of the injected energy. And the effect of the loss component transmission on the output energy stability in amplification cavity was more obvious than the effect on the output energy stability out of amplification cavity. The level of the output energy stability of TIL was analyzed according to the experimental data. For the 3 ns temporally flat pulse, to meet the requirement
Preparation of cone-shell target for fast ignition experiment
du kai, luo xuan, zhou lan, wan xiao-bo, xiao jiang
2005, 17.
Abstract:
The preparation of cone-shell target used in fast ignition experiment was investigated. Polystyrene(PS) microshells with less wall thickness and diameter distribution were prepared with monodisperse PS. The dependence of the quality of Au cone on the parameters such as the composition, the pH of electroplating bath, the current density and the tip effect was discussed. A hole with a diameter about 120 μm on PS microshell was drilled. An Au cone-shell target was produced.
粒子束及加速器技术
Effect of cathode and anode plasma motion on current characteristics of pinch diode
yang hai-liang, qiu ai-ci, sun jian-feng, li jing-ya, he xiao-ping, tang jun-ping, li hong-yu, wang hai-yang, huang jian-jun, ren shu-qing, yang li, zou li-li
2005, 17.
Abstract:
The preliminary research results for the effect of cathode and anode plasma motion on current characteristics of the pinch ion diode on FLASH Ⅱ accelerator are reported. The structure and principle of pinch reflex ion beam diode are introduced. The time dependent evolution of electron and ion flow in large aspect-ratio relativistic diodes is studied by analytic models. The equation of Child-langmuir, weak focused-flow, strong focused-flow and parapotential flow are corrected to reduce the diode A-C gap caused by the motion of cathode and anode plasma. The diode current and ion current are calculated with these corrected equations, and the results are consistent with the experimental data. The methods of increasing ion current and efficiency are also presented. The high power ion beam peak
Survey control network of HIRFL-CSR
cai guo-zhu, wang shao-ming, man kai-di, yang sheng-li, guo yi-zhen
2005, 17.
Abstract:
Setup of survey control network for CSR and method of data analysis were described. Bundle’s principle and arithmetic of program was explained in detail. Junior control network was set up by Total Station firstly, computation which was densified to form final survey control network for CSRm(main ring of Cooler Storage Ring). The survey control network comprises 168 network points, and it is surveyed by using laser tracker with its software Insight. The accuracy of network points’ position reached 0.08 mm. According to this result devices of CSRm were aligned, and accuracy of quadruple magnets reached 0.15 mm in transverse direction, reaching the design requirement. It is proved that this control network is feasible for setup of circular accelerator.
Design of end magnetic structures for Shanghai DUV-FEL hybrid undulators
cai gen-wang, jia qi-ka
2005, 17.
Abstract:
Design of end magnetic structures for a hybrid undulator is very complicated. In this article, magnetic field calculation was carried out using the "Radia" code, aimed to optimize the end magnetic structures for the Shanghai DUV-FEL hybrid undulator with a fixed gap. Without electromagnet correction, the first and second field integrals of the hybrid undulator were almost zero by reducing sizes of the two final magnets and positioning the two end poles. After the shield was added outside the final magnet, the fringe fields were lower than 5×10‑4 T off 10 mm to the final magnet.
Basic study on destruction of tantalum target bombarded by high energy flux pulse electron beam
zhu jun, zhang lin-wen, long ji-dong, li jing, yu hai-jun, shi jin-shui
2005, 17.
Abstract:
A MonteCarlo program MCNP is used to simulate the energy deposition of high energy flux pulse electron beam in the target material. According to the simulation results and the size and the character of the hole on the tantalum target by electron beam bombardment, the basic physical destruction mechanism of structuredifferent tantalum targets is presented. Due to the difference of the energy deposition in different targets, the shock wave in the 1 mm solid target will develop and compress the target in both radial and axial directions, while the compression in the foil target is inapparent, the size of the hole on the 1 mm solid target almost doubles that of the foil target. The melt ejection and spallation in the theoretical model are in accordance with the experiment result.
Optimization design of axial dielectric of DC high-voltage accelerating tube
yang xiao, mao ben-jiang, he xiao-hai
2005, 17.
Abstract:
Axial insulation structure was optimized to reduce potential gradient in DC high-voltage accelerating tubes of 500 mA. At first, both principle of surface flashover and axial insulation structure of accelerating tubes were analyzed. Then, it was found that electric field aberration at the junction of triple junction causes high electric field intensity through numerical simulation in terms of theory of SEEA. Optimal structure is ascertained by analyzing four types of insulation structure respectively and it has such features as angle of +45° between the insulator surface and the cathode, a metal electrode ring embedded evenly in flutes at both ends of insulator and the insulator embedded evenly in the anode.
Performance of plasma opening switch with different driven-current and geometric scale of electrodes
chen lin, dai ying-min, jiang wei, wu shou-dong, li ye, xu min
2005, 17.
Abstract:
The plasma opening switch (POS) performance was investigated with different driven current and different POS cathode diameters (f20 mm and f40 mm). The results show that the rise time of the load current decreases and the voltage multiplication factor of POS increases when the driven current increases. In the case of larger cathode diameter, lengthened conduction time and longer rise time of load current are obtained, meanwhile the POS voltage and current transfer efficiency decrease. The maximal voltage multiplication factor and current transfer efficiency obtained in experiments are about 4.9 and 97%, respectively. The rise time of load current is less than 100 ns.
Design and stability analysis of tuning system for new beam buncher B1 at HIRFL
xu zhe, shi ai-min, wang chun-xiao, ren hong-wen
2005, 17.
Abstract:
In order to synchronize the extracted ion beam from the Sector Focusing Cyclotron (SFC) with the accelerating RF phase of the Separated Sector Cyclotron (SSC), a new beam buncher is designed in IMP. This paper is mainly devoted to a automatic frequency tuning system which is one of the most important parts of the buncher. The system has been put into operation and it is possible to stabilize the inherent resonant frequency of the cavity on the frequency of input signal (22~54 MHz), consequently avoid the voltage drop down and get higher RF voltage on the accelerated gap in cavity. The safe and effective operation of the beam buncher is ensured.
Experimental study of piezoelectric coefficient of ferroelectric materials
guo shu-guang, zhang shu-ren, cheng zhong-dao
2005, 17.
Abstract:
The ferroelectric cathode material is a new kind of functional material. A new electron emission phenomena was observed by chance. With the increase of emission times, the piezoelectric coefficient decreased to zero firstly and then gradually approached to a given inverse value, whose absolute value was less than that of the initial value. Surprisingly, it was found that the current emission density had not changed during the course of the change of the piezoelectric coefficient. It is found that the experiment is repeatable.It is difficult to explain the observed phenomena using the existing electron emission theory.
高功率微波
Truncation of open boundary of 3D rectangular waveguide by CPML
wang yue, wang jian-guo, zhang dian-hui
2005, 17.
Abstract:
The requirement for truncating the open boundary of waveguide used in the simulation of high power microwave (HPM) sources was discussed. The characteristics of different types of perfectly matched layer (PML) was analyzed, and the convolutional PML was chosen to truncate open boundary of the dispersive waveguide device. The unsplit-field PML was constructed using the split-field PML and the plane-wave solution of electromagnetic field in free space. By applying the convolutional theorem of Fourier transform, the discrete iterative equations of electromagnetic field in the CPML media in the rectangular coordinate system was presented. The performance of CPML was simulated when it was used to truncate the rectangular waveguides excited by the sources with different frequencies and modes. Th
Coupling effects of LEMP on aerial multiconductor power lines
ren he-ming, zhou bi-hua, yu tong-bin, wang zhao
2005, 17.
Abstract:
Based on the transmission line model, this paper proposes a method that integrates the lightning return stroke channel, the earth and the overhead lines together for calculating the lightning-induced voltages on overhead lines. The finite-difference time-domain (FDTD) method is used to obtain the electromagnetic field values near a cloud-to-ground lightning return stroke channel, and then these field values are put into the discretized transmission line equations to calculate the induced voltage at the end of overhead lines. Analyses show that the induced voltage on one conductor of the multi-conductor loaded lines is affected by the presence of other lines, and the voltages induced on each of the line conductors are generally 10%~20% lower than those corresponding to a single conductor l
Simulation analysis on input cavity of 8 mm gyroklystron
wang hui, li hong-fu, luo yong, xu yong
2005, 17.
Abstract:
Modulator cavity of multi-cavity Gyroklystron transforms the TE411 mode in out cavity to TE011 mode in inner resonant cavity through 4 slots. TE011 mode is used to modulate the transverse velocity of gyroelectron beam. In this paper, an analysis of cold cavity is presented. HFSS code is used to simulate couple of structure variety accurately and revise approximate analysis. It shows that the ratio of the energy storage of the inner cavity to that of the outer cavity is 41.65, when the angle between coupling slots' midline and waveguide axis is 45°. Length of slots affects Q factor greatly while resonance frequency is insensitive to it. Moreover, Q factor is more sensitive to length of slots than to width of them. Energy storage in coaxial cavity is calculated. Based on a large number of c
Study on the region of instable beam-wave interaction in a relativistic backward wave oscillator
HUANG Feng, WANG Dong, XING Qing-zi, DENG Jing-kang
2005, 17.
Abstract:
A theoretical research was developed for relativistic backward wave oscillators (RBWO) composed of a thin annular electron beam guided by a strong magnetic field through a slow wave structure (SWS) consisting of a cylindrical waveguide with a sinusoidally varying wall radius. Firstly, the analytic expressions of dispersion relations were derived from Swegle's analytic theory of RBWO. Then one code written by Matlab was used to solve the dispersion equations. Through drawing contour lines in the complex plane, the whole dispersion curves of SWS with electron beams were obtained and detailed study on the region of instable beam-wave interaction was carried out. The microwave growth rate and energy efficiency were calculated too. The simulation results illustrate that this interaction, which
Analysis on coupling effects of EMP into lapped joints in conducting screens
yang ling-xia, ge de-biao, wei bing
2005, 17.
Abstract:
In this paper, the coupling and penetration of electromagnetic pulse through lapped joints in conducting screen are simulated by the finite difference time domain (FDTD) method. Equivalent electromagnetic current sheets on the aperture and the transmission field are computed. For obtaining the far zone transmission field easily, the radiation of equivalent electromagnetic current sheets in a quarter-space is replaced by the radiation of equivalent electromagnetic current sheets and their images in free space based on the equivalence principle. This equivalent scheme avoids the difficulty of computing the Green’s function with the boundaries of lapped joints. During extrapolating, sub-area extrapolation is applied which saves much computing time. Finally, by analyzing the variation of coup