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ISSN1001-3806 CN51-1125/TN Map

2008 Vol. 32, No. 4

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Study of bandwidth for suppressing seawater backscattering based on frequency filtering
JI Hang, MA Yong, LIANG Kun, WANG Hong-yuan
2008, 32(4): 337-339,356.
Abstract:
In the application of using lidar to detect undersea targets,a kind of signal processing technology based on frequency filtering is proved to be able to suppress the seawater backscattering effectively.The bandwidth of the filter in the receiving system doesn't only suppress the backscattering,but also supresses the target signal.In order to estimate the range of the bandwidth,the seawater transport model of the modulated-pulse lidar signal,and the frequency characteristic of the seawater backscattering signal and target reflecting signal were studied.After simulating the received signal on frequency domain,the optimum design method on the bandwidth of the filter in the receiving system was found and the optimum signal-to-noise ratio of the system could be established by this result.
Study on the densification of SiO2-TiO2 sol-gel films by laser irradiation
LI Ai-kui, WANG Ze-min, LIU Jia-jun, ZENG Xiao-yan
2008, 32(4): 343-345,349.
Abstract:
In order to study the application of laser direct writing technology in the area of thin film elements rapid fabrication,the densification of SiO2-TiO2 porous sol-gel films on SiO2/Si wafer was performed by means of a continuous fiber laser with the wavelength of 1.07μm.The effect of laser power density on the shrinkage of the film was investigated.The thresholds of laser power density and the change of thickness of films under different preheated temperatures were discussed.Finally,the mechanism of laser densification of the SiO2-TiO2 films was also analyzed.The experimental results demonstrate that the shrinkage of films increases with the laser power density.The thresholds of laser power density will increase with increasing temperature in the process of laser densification.The energy of induced laser beam is absorbed by Si substrate instead of Sol-Gel film.The mechanism of laser densification of the SiO2-TiO2 films is mainly based on the shrinkage of nanon-scale pore due to the energy transfer from Si wafers.
Application of modulated lidar on optical carrier for ocean exploration
MA Yong, JI Hang, LIANG Kun, LIN Hong
2008, 32(4): 346-349.
Abstract:
A method of lidar for ocean exploration was presented,where microwave signal was modulated on laser pulses and the modulated optical pluses were transmitted into water.At the receiver,the modulated optical carrier was examined from a frequency filter to render target detection.Compared with other methods which could restrain the backscattering signal,characteristics and current study situation of modulated lidar on optical carrier for ocean exploration were overviewed.
Study surface emission mechanism of La2O3-Mo cathode by laser deposition
HAO Shi-ming, NIE Zuo-ren
2008, 32(4): 357-359,409.
Abstract:
In order to study the surface emission mechanism of La2O3-Mo cathode,film cathodes were studied by using a set of equipment,specially designed for cathode research,with which film cathode can be prepared by pulse laser deposition.In order to gain insight into the relation between cathode emission properties and the cathode surface La/O ratio,electron emission properties and surface compositions(lanthanum and oxygen) of the cathodes were investigated experimentally.Experiment results indicate that the emission current densities descent gradually along with surface lanthanum film thickness attenuation;the cathode emission properties are determined intensively by the surface atomic La/O ratios.The higher the La/O ratio gets,the better the emission property reaches.Then the theory of La2O3-Mo cathode emission mechanism was discussed.It indicates that the theory of monoatomic layer can't explain perfectly emission mechanism of La2O3-Mo cathode;the excess active lanthanum is crucial element to the improvement of thermionic emission.
Time interval measurement of laser ranging based on CPLD & microchip
CHEN Jia-yi, YI Xiao-su
2008, 32(4): 363-365,369.
Abstract:
In order to improve the precision of time interval measurement in pulsed laser ranging,several interpolation methods are used.Analog interpolation time-interval measurement has advantages of high precision,small blind area,long measurement range and good linearity.Ananalog interpolation measurement method using complex programmable logic device(CPLD) and microchip was presented.Benefiting from the use of CPLD,the circuit became simplified.Furthermore,the time-interval measurement system adapted extraordinarily to high performance portable pulsed laser rangefinder for its compactness,simple structure and high reliability.
Study of Raman spectrum in detecting mineral substance concentration of drinking water
YANG Chang-hu, SHI Xiang-hua, LIU Xiao-bing, LIAO Jia-xin
2008, 32(4): 366-369.
Abstract:
In order to assay the quality of drinking water,several kinds of brand drinking water on the market and the distilled water offered in the laboratory were studied.By using laser Raman spectrum method,the samples' full width at half maximum(FWHM) and depolarization ratio of laser Raman spectrum at stretching vibration were measured.The study showed that as the samples' mineral substance concentration increased,its FWHM at stretching vibration decreased,but its depolarization ratio of laser Raman spectrum at stretching vibration increased.This results provides us a simple and effective way to assay the quality of drinking water.
Research and development of the optical model of human eyes
KONG Mei-mei, GAO Zhi-shan, CHEN Lei, LI Xin-hua
2008, 32(4): 370-373.
Abstract:
Human eyes are the important sense organ that can gain the outside information by the light stimulation primarily.In fact,human eyes are complex optical systems including many interfaces.Each interface has the complex geometric properties and optical characteristics.The optical model of human eyes can be established with the data obtained by different kinds of tools,such as optical measurements or anatomical methods.It can be used to study the optical properties of each interface,which is of great significance in the field of ophthalmology and optometry.The optical structures and properties of the several representative eye models were summarized.And the trend of development of the optical model of human eye,i.e.,individuation and precision was presented.
Study about the temperature effect of the retaroation of quartz wave-plates
KONG Qing-dian, SONG Lian-ke, KONG Li-hua
2008, 32(4): 374-376.
Abstract:
The precision of wave-plate is often influenced by temperature.In order to get the relationship between the retardation of quartz wave-plate and temperature so as to reduce the error generated by temperature,the factors affecting the retardation of the wave-plate were theoretically analyzed.At the same time,the error was analyzed under different conditions.The result shows that the retardation of the wave-plate reduces with the increase of temperature.The result is useful for the wave-plate properly used at different temperature.
Optimization of laser peening parameters using Taguchi method
SUN Yue-qing, ZHOU Jian-zhong, LIANG Qing-lei, CHEN Yi-bin, HUANG Shu
2008, 32(4): 377-379,386.
Abstract:
In order to make a comprehensive evaluation of process parameters of laser peening,a Taguchi experimental method was adopted here.Laser peening of the 12mm thick 6061-T6 aluminum alloy sheet was studied by changing the laser power,laser shot diameter and pulse width.The objective of the study was to assess the impact of laser parameters on residual compressive stress and the interaction of parameters.The finite element software ABAQUS was applied to simulate the laser peening process.The Taguchi method was used to formulate the experimental layout and establish the order of predominance among the identified critical parameters,and predict the optimal setting for each process parameter.The results obtained were analyzed using the software MINITAB.The results show that three parameters related to the magnitude of compressive residual stress imply different effects.Laser shot diameter ranks first,followed by pulse width and laser power.The best combination of levels is A3B3C2.The optimal result is confirmed with a superior ultimate surface residual compressive stress of 125MPa.
Optimization of grazing-incidence angle in high repetition rate acousto-optical Q-switched grazing-incidence lasers
HE Fa-hong, HUANG Lei, GONG Ma-li, LIU Qiang, WANG Qi, YAN Xing-peng
2008, 32(4): 380-382.
Abstract:
The grazing-incidence angle in grazing-incidence lasers was optimized for high repetition rate acousto-optical Q-switch by calculating the equivalent pump mode cross-section area.High repetition rate(2MHz) acousto-optically Q-switched TEM00 output was obtained.It is shown from the results that there is an optimum grazing-incidence angle which is beneficial to high repetition rate operation in grazing-incidence laser.
The optimal model reconstruction of Hartmann-Shack wavefront sensor
TONG Gui, LIAO Wen-he, LIANG Chun
2008, 32(4): 387-389,392.
Abstract:
Reconstruction modes of Hartmann-Shack wavefront sensor have direct influence on the precision of sensing and reconstruction of incident wavefront.Because reconstruction modes of Zernike polynomials based on Hartmann-Shack wavefront sensor were easy to be influenced by the gradient sensing noise,optimal reconstruction modes according to the wavefront sensing noise were put forward by the correlation analysis and decoupling transform of wavefront reconstruction matrix.Furthermore,the error of wavefront model reconstruction thanks to the wavefornt sensing noise can be reduced by filtering the portion of the optimal modes.By Monte-Carlos' random experiment,the antinoise level of Hartmann-Shack wavefront sensor whose subapertures distributes at a square was verified.As a result,the reconstruction error reduced from 0.0212λ to 0.0048λ after getting rid of the part of optimal reconstruction.The way to analyze the optimal reconstruction modes has an effect on filtering the wavefront gradient sensing and improve the sensing precision of wavefront sensor.
Impact of XPM on the microwave photonic switching with NOLM
YUAN Ming-hui, WU Chang-feng, SUN Xiao-han
2008, 32(4): 390-392.
Abstract:
In order to obtain the impact of cross-phase modulation(XPM) on the microwave photonic switching with nonlinear optical loop mirror(NOLM) the numeric analysis platform with XPM is established by the split-step Fourier method that can solve the coupled nonlinear SchrÖdinger equation,and the impact of XPM on the carrier signal modulated by the microwave and the power transmission function of NOLM Tm is obtained.The simulation results showed that XPM induced the distortion of waveforms and the leak of side lobes.And the larger the modulation bandwidth was,the larger the leak of side lobes.Furthermore,Tm was distorted because of the XPM-induced nonreciprocity:Tm decreased when the splitting ratio of the coupler f∈(0,0.5) and increased when f∈(0.5,1).
Diffraction of Bessel-Gaussian beam passing through annular and circular apertures
QU Jun, MENG Kai, WANG Liu-san, DING Pei-hong, CUI Zhi-feng
2008, 32(4): 393-395.
Abstract:
From the Collins formula,the diffraction of Bessel-Gaussian beam passing through circular and annular apertures was studied based on numerical simulation.The results indicate that the axial intensity of Bessel-Gaussian beam through a circular aperture changes with the Fresnel number F periodically;the axial intensity of Bessel-Gaussian beam through an annular aperture attenuates with the F at the function of vibration.When F is the same,the transversal intensity of Bessel-Gaussian beam through a circular aperture distributes more smooth than an annular aperture.The smaller the annular aperture,more obvious is the modulation of transversal intensity;when the annular aperture is equal to the waist of the beam,the transversal intensity is independent of the Fresnel number F.
Design of drive circuit for continuously adjustable ns pulse LD
ZHANG Shou-qi, LOU Qi-hong, ZHOU Jun, DONG Jing-xing
2008, 32(4): 396-398.
Abstract:
In order to meet the need of single-mode pigtailed pulse LD and its later optical amplification,a ns pulse LD drive circuit with variable pulse,frequency and power was designed by using metal oxide semiconductor field effect transistor(MOSFET) as switch.By analyzing the drive characteristic of MOSFET,a suitable grid drive circuit was used,so the pulse width and the ability to bring loads were improved.A protect circuit was designed to protect the expensive LD from over shot,sharps,arcs etc.It is concluded that the drive circuit works stably and is suitable for driving the LD.
Effect of linear polarized CO2 lasers on cut kerfs of nonmetallic material
XIE Xiao-zhu, WEI Xin, HU Wei
2008, 32(4): 399-401,416.
Abstract:
Highly absorptive nonmetallic material,die-board,was cut by linear polarized CO2 lasers through eight different directions.Effect of laser power,cutting speed and assisted air on the width of the cut kerfs of the die-board was also discussed by contrast with that of lower carbon steel.The results indicate that the difference between the top and the bottom kerfs width of the die-board along eight directions is not sensitive to linear polarization with altering laser power and cutting speed,while the kerf width difference of steel is on the contrary.Assisted gas such as N2 and air has little effects on the kerf,therefore air should be selected in view of lower cost.Uniform cut kerfs can be achieved with lower cutting speed under certain laser power or higher laser power at a certain cutting speed.
Near-field analysis of misaligned CO2 laser of two-dimension axisymmetric-fold combination cavity
YAN Ting-guang, LI Yu-de, XIAO Feng-xia, LIU Xian-kui, GAO Ke, FENG Tao
2008, 32(4): 402-405,444.
Abstract:
Under the condition of small angle misalignment,the effecton output beam's near-field distribution of CO2 lasers with two-dimensional axisymmetric-fold combination cavity was ascertained after analyzing and simulating beams combination output based on the axis determination of misaligned plano-concave and concave-plano-concave cavity resonator.The results showed that at small angle misalignment,the effect on near-field within 4cm was un-conspicuous and the light intensity was still at Gaussian distribution,and that out of the 4cm area,the effect became obvious with the misalignment angle.These results showed that the effect on near-field with 4cm was more practically.
Design of YAG laser welders controlled with pulse wave shaping and laser power feedback
NIU Zeng-qiang, PENG Wen-da, NIU Han-ben
2008, 32(4): 406-409.
Abstract:
In order to improve the stability of the output power of the laser welder,a rear optical detector was installed to feedback the output laser power signal to the control unit,making a closed loop control system.Also,a phase compensation signal was added to the laser power signal to increase the control accuracy.In addition,the control function of pulse wave shaping was used to extend the application of the laser welder.Experiments showed that the laser power fluctuation was less than 3%.Compared with 8% laser power fluctuation of the traditional laser welder,the control accuracy was improved greatly.The actual welding experiment has verified that the welding quality can be improved by changing the waveform of the laser power.
Simulation of the temperature field in rapid prototyping of selective laser melting
SHI Wen-qing, YANG Yong-qiang, HUANG Yan-lu, CHENG Da-wei
2008, 32(4): 410-412.
Abstract:
In order to implement rapid prototyping of Cu-P alloy powder based on selective laser melting,the temperaturefield was simulated by the finite element analysis software——ANSYS before fabrication so that its distribution could be obtained.During the process of simulation,the thermal physical parameters of material at certain temperature were obtained throughinterpolation method,an unequal meshing method was adopted and the thermal enthalpy could be used to replace the latent heat offusion.It shows that the temperature field distribution likes an ellipse and the parameters selected by simulation(a laser power of100W,a scanning speed of 0.25m/s and a beam spot radius of 0.1mm were selected when the layer thickness was 0.22mm) canbe used in selective laser melting.
Comparison for coherent combining and spectrum combining of fiber lasers
ZHOU Pu, HOU Jing, CHEN Zi-lun, LIU Ze-jin
2008, 32(4): 413-416.
Abstract:
Significant progress has been recently reported on beam combination of fiber laser arrays using coherent combining and spectrum combining technology.Analyzing the basic requirement for the fiber laser,key technology,number scalability,beam quality,system stability and beam steering comes to a comparative study on these two technologies.The results show coherent combining using master oscillator power-amplifierfiber arrays configuration and spectrum combining cannot give high power laser beam with good beam quality at the same time that we have to balance the pros and cons of each technology for different application.
The research progress in data processing algorithm of satellite laser ranging
FANG Qing-hai, ZHAO Yong-li
2008, 32(4): 417-419,423.
Abstract:
The research background and development states of satellite laser ranging(SLR) systems were summarized.The data processing algorithm played an important part in the development of the SLR technique.So the applied aspects and research development states of the widespread and some advanced data processing algorithms at home and abroad were reviewed,including screen processing technique,Poisson statistic filter algorithm and correlation detection algorithm et al.Finally the research progress and developmental direction in data processing algorithms of SLR were also presented.
Study on fiber laser with China-made Yb3+-doped double-clad fiber
ZHANG Jun, CHEN Shuang, FENG Ying
2008, 32(4): 420-423.
Abstract:
High power fiber laser has important application in the directed energy domain.In order to find the laser output characteristic under different fiber length and back-cavity mirrors,numerical simulation and experiment method were used.With home-made large-core Yb-dopped fiber,double-clad fiber laser system was constructed.And the signal laser with a central wavelength of 1092nm and the maximum output power of 1.6W was obtained.It was shown that optimum fiber length had important contact with back-cavity and pump power.The maximum output could be obtained with the optimum R2.It is found that the output characteristics of the fiber laser can be better by design the reflectivity ratio of the back-cavity mirror.
Effect of the aperture on the on-axis polarization properties of partially coherent light
ZHAO Ting-jing
2008, 32(4): 424-426,433.
Abstract:
Based on the beam coherence-polarization matrix and Collins formula,the on-axis polarization property ofGaussian-Schell model beam diffracted through an aperture was studied numerically.Simulation results showed that,due todiffraction effect,the polarization distribution of Gaussian-Schell model beam became non-uniform,there was oscillation of the on-axial polarization distribution,and that with increasing of the truncation parameter and decreasing of the spatial coherenceparameters and the transmission distance,oscillations strengthened gradually.While when the beams transmit on axis in freespace,polarization distribution in the near field is uniform,with increasing of the transmission distance and decreasing of thespatial coherence parameters,the on-axial polarization distribution increased.Thus the on-axial polarization distribution can becontrolled by apertures,which is useful for the application of partially coherent light.
Spatial laser beam shaping using aspheric Galilean beam expansion system
LI Dian-jun, LIANG Si-yuan, CAO Jian-jian
2008, 32(4): 427-429.
Abstract:
It's desirable to design a set of aspheric Galilean laser beam expansion system which can reshape high power TEA CO2 laser beam with waist of 8mm to a diameter of 25mm.Based on the mathematical model and the Romberg numerical integrating algorithm,an array with 40 sets of data was obtained to describe the aspheric surfaces.By fitting the data with the method of the nonlinear least square,the sag's analytical equations of aspheric surfaces were obtained.Using the optical design software package,ZEMAX,the Gaussian beam with beam waist 8mm was emulated passing through the designed beam reshaping system.The results show that the designed system can reshape the entrance Gaussian beam,the peak-valley wavefront error of the flat-top output with a diameter of 25mm is about 25 waves,which proves it being collimated.It makes necessary preparation for further applications.
Calculating the coupling efficiency of the laser diode to the semi-tapered multimode fiber by ray-tracing method
WANG Chao, FENG Guo-ying, YANG Hao, ZHOU Qing, LI Wei, SU Juan
2008, 32(4): 434-436,440.
Abstract:
In order to analyze the factors which affect the coupling efficiency between LD and the semi-tapered multimode fiber,considering the multi-reflection on the tapered surface,using improved ray-tracing algorithm,the coupling efficiency of LD to the semi-tapered multimode fiber without cladding was calculated in different cases separately,such as different semi-tapered angle or different semi-tapered width,or different relative shift and incline.The results indicated that when semi-tapered width value was appropriate,the influence of the tapered angle on the coupling efficiency was unconspicuous;The coupling efficiency was sensitive to the relative shift,while it was inertial to the relative incline.
Study of laser beam deflection tolerance of divergent sphere Gaussian wave
ZHANG Xin-bao, LI Shou-ke
2008, 32(4): 437-440.
Abstract:
Because of the large beam diameter and special characteristics of the non-diffracting beam produced by an axicon,the non-diffracting beam can tolerate the eccentricity of the incident laser beam's axis to the axicon.For studying the additional tolerance property to the incident light beam's deflection,adopting a kind of incident divergent sphere Gaussian wave,it is proved that the divergent sphere Gaussian wave can tolerate the eccentricity of the incident laser beam's axis through theoretical analysis and practical tests.The obtained conclusion is that the axis of the non-diffracting beam produced by an axicon is very stable and can be adopted as the datum line to measure the spatial straightness error in continuous working distance,which may be short,medium or long.
A new method to study laser propagation in inhomogeneous medium
LIU Jun-guo, WANG Yu-lei
2008, 32(4): 441-444.
Abstract:
In order to study laser propagation in inhomogeneous medium,Collins formula was improved by using time inversion characteristic of optic phase conjugation wave.Based on the new method,beam transmission in medium was calculated.It was proved that the new method was correct and effective in dealing with near field calculation and it was helpful for simulation and parameter optimization of beam transmission.
Effect of cross talk on multichannel chaotic optical communication systems
LI Feng, PAN Wei, LUO Bin, TAO Yuan, JIANG Ning, SHAO Yu-ting
2008, 32(4): 445-448.
Abstract:
In order to study the effect of the cross talk on synchronization and decoding,a multichannel chaotic optical communication system was established based on vertical-cavity surface-emitting lasers(VCSELs).Based on the corresponding rate equations,similarity index was used to evaluate the synchronization performance,and 2.5Gbit/s message coding/decoding of chaotic masking method was numerically analyzed.The results show that the system can get better synchronization quality with less relative injection strength and more channel interval.The synchronization performance of dual-channel system decreases obviously compared with master-slave single channel system,and changes little when the channel number increases.The signals can be correctly recovered when the synchronization is good enough.
论文
Time-dependent characteristics of pulsed Er-doped superfluorescent fiber amplifiers
CHAO Xing, YANPing, GONG Ma-li
2008, 32(4): 340-342,352.
Abstract:
After solving time-dependent rate equations,the transient performance of superfluorescent fiber amplifiers wasstudied and the system's output characteristics and response to different modulation frequency were obtained.As long as modulationrate is within a certain range,high-peak-power pulses would be generated.For 1m Er-doped fiber pumped by 0.1W and the seedmodulated in nanosecond range with duty cycle of 50%,the amplifier outputs pulses with declining peaks,and stabilizes after about 200ns.Characteristics of the amplified signal could be controlled by monitoring the seed's pulse and spectral properties.The studysuggests possible means to produce high power pulses with ampeified spowtaneous emission fiber source whose mean wavelength andspectral width are manipulable,and has practical value in long-distance application within 1.5μm atmospheric window.
Character analysis and development of metal material for microscale laser shock processing
CHE Zhi-gang, XIONG Liang-cai, SHI Tie-lin, YANG Li-kun
2008, 32(4): 350-352.
Abstract:
The microscale effect,elastic-plastic theory and material nonlinearity of laser shock processing were analyzed and discussed.The rotation ellipsoid model was put forward according to the physical development and space profile of plasma,which lay a theory foundation for plasma three dimension model.The development of microscale laser shock processing was presented.
An improved algorithm for estimating parameters of semiconductor lasers
YAN Yan-xia, YU Yan-guang
2008, 32(4): 353-356.
Abstract:
For the sake of accurately estimating linewidth enhancement factor of semiconductor lasers with external cavity,optical feedback self-mixing interferometric technology and gradient-based optimization algorithm were introduced to achieve best data-theoretical fitting.In addition,an iterate formula was improved with alterable steps introduced.Simulation and experiment data were obtained.The accuracy of algorithm was higher and antinoise capability was better.The simulation result showed that the relative standard deviation of linewidth enhancement factor was less than 2.55% when signal-to-noise ratio was 20dB.Experiment data result showed that the relative standard deviation of linewidth enhancement factor was less than 5.1%.
Gain-switched Nd3+:YVO4+KTP green laser at high repetition rate
WANG Jin-ding, WANG An-bang, WANG Yun-cai
2008, 32(4): 360-362.
Abstract:
A compact green laser,which can emit continuous wave or laser pulse trains respectively,was reported.With utilizing a laser diode end-pump Nd3+:YVO4+KTP gluing crystal,19% optical-optical conversion efficiency was achieved in continuous output.Adjusting the waveform of the laser power supply to gain-switch the laser diode,the corresponding output waveform of square,sine,or triangle green laser pulses were obtained.The intensity and pulsewidth of the laser pulses could be varied with the amplitude and duty circle of the injecting current pulses.Meanwhile,by changing the injecting current pulses repetition rates,the laser pulse trains repetition rates could be tuned from 0.5Hz to as high as 2MHz.A green laser pulse train,with 74ns pulsewidth,285mW peak power and amplitude noise less than 3%,was obtained at 560kHz.The research showed that green laser pulse of high repetition rates and narrow pulsewidth could be obtained by gain-switched technique.
Derivation of the Lamb coefficients in four frequency ring laser
YANG Jian-qiang
2008, 32(4): 383-386.
Abstract:
In order to study the laser multi-modes coupling effects,theoretical deduction of four frequency ring laser at Ja=1→Jb=2 transition was conducted with the third-order perturbation method from the Lamb semi-classical self-consistent theory.The Lamb coefficients in the non-Doppler limit general case including the population pulsation effects were derived.The analysis shows that the conclusion drawn can be generally applied,which is helpful to the quantitative study on the laser multi-modes coupling fine effects.
Numerically modeling and optimizing pulse-shape of Cr4+:YAG Q-switched lasers
XIONG Ji-chuan, LAN Ge, WAN Yong
2008, 32(4): 430-433.
Abstract:
In order to study the symmetry property of a single pulse for passively Q-switched lasers,the coupled rate equations were solved numerically and the temporal profile of laser pulse was obtained.The relationship between the symmetry property of a single pulse and the parameters of absorber and output coupler was presented and the pulsewidth was recalculated accounting for the asymmetry property of laser pulse.The relationship between pulsewidth and parameteres of absorber and output coupler was presented also.Conclusion was drawn that the pulse was symmetric when the variable b=0.6 and that the pulsewidth was minimal when b=0.78.This provides a method to optimize the pulse shape and pulsewidth by adjusting the value of b.