Fibre laser welding of dissimilar alloys of Ti-6Al-4V and Inconel 718 for aerospace application s

ORIGINAL ARTICLE

Fibre laser welding of dissimilar alloys of Ti-6Al-4V and Inconel 718for aerospace applications

Hui-Chi Chen &Andrew J.Pinkerton &Lin Li

Received:10February 2010/Accepted:15June 2010/Published online:30June 2010#Springer-Verlag London Limited 2010

Abstract Challenges in dissimilar materials welding are the differences of physical and chemical properties between welding materials and the formation of intermetallic brittle phases resulting in the degradation of mechanical properties of welds.However,dissimilar materials welding is increas-ingly demanded from the industry as it can effectively reduce material costs and improve the design.In aerospace applications,Ti-6Al-4V titanium alloy and Inconel 718nickel alloy have been widely used because of their superior corrosion resistance and mechanical properties.In this study,a single-mode continuous-wave fibre laser was used in butt welding of Ti-6Al-4V to Inconel 718.Investigations including metallurgical and mechanical examinations were carried out by means of varying processing parameters,such as laser power,welding speed and the laser beam offset position from the interface of the metals.Simple analytical modelling analysis was undertak-en to explain the phenomena that occurred in this process.Results showed that the formation of intermetallic brittle phases and welding defects could be effectively restricted at welding conditions produced by the combination of higher laser power,higher welding speed and shifting the laser beam from the interface to the Inconel 718alloy side.The amount of heat input and position of laser beam to improve the Ti-6Al-4V/Inconel 718weld quality are suggested.Keywords Fibre laser .Dissimilar material welding .Titanium alloy .Nickel alloy

1Introduction

Due to the excellent characteristics of good corrosion resistance,higher strength and creep resistance,titanium alloys like Ti-6Al-4V have been widely used in industry.One of the biggest applications of Ti-6Al-4V alloy is in the aerospace industries,for example as static and rotating components in the turbine engines [1].Meanwhile,Inconel 718nickel alloy,a high-temperature material,is also broadly used in the aerospace industries.Because of its superior mechanical properties and oxidation resistance at elevated temperatures,Inconel 718is particularly suitable for manufactured components in the high temperature regions of aero engines and gas turbines [2,3].

Today,the dissimilar materials welding process is increasingly attracting more attention in industry because it can reduce the material costs and improve the design flexibility.However,the formation of brittle phases,cracks and residual stresses still readily occur in a weld between dissimilar materials because their differences in physical and chemical properties,such as the melting and boiling points,thermal conductivity,density and coefficient of expansion [4].A limited amount of systematic research in this area has been carried out until now.They were welding of aluminium alloy to steel [5];aluminium alloy to titanium alloy [6];copper to steel [7];titanium alloy to stainless steel [8],dissimilar magnesium alloys [9]and dissimilar stainless steels [10].Schubert et al.[11]pointed out that controlling the diffusion mechanism appropriately by applying a lower heat input can reduce the formation of brittle intermetallic phases in dissimilar materials welds.They obtained a better weld with a combination of a higher laser power and a higher welding speed in welding aluminium-steel and aluminium-magnesium https://www.sodocs.net/doc/061803285.html,ing a high-energy density laser beam to restrict the amount of energy input was

H.-C.Chen (*):A.J.Pinkerton :L.Li

Laser Processing Research Centre,School of Mechanical,

Aerospace and Civil Engineering,The University of Manchester,Sackville Street,

Manchester M601QD,UK

e-mail:Hui-Chi.Chen@https://www.sodocs.net/doc/061803285.html,

Int J Adv Manuf Technol (2011)52:977–987DOI 10.1007/s00170-010-2791-3

another suggested method to control the heat diffusion and therefore minimise the thickness of the reactive interlayer and avoid the formation of brittle intermetallic phases especially in cases of welding steel-kovar,copper-steel and copper-aluminium joints[12].Regarding the issue of different conductivities between welding materials,apply-ing a backing block below welding samples has been pointed out as a method to control the heat flow and effectively suppress the thickness of the intermetallic layer in welding of steel to aluminium alloy[13].

Considering welding titanium and its alloys to nickel and its alloys:Seretsky and Ryba[14]used a Nd:YAG laser to investigate spot welding Ti to Ni with and without TiNi filler.Cracks and incompletely mixed liquids were ob-served in the welds.Chatterjee et al.[15,16]butt welded

Ti/Ni dissimilar materials using a CO2laser to investigate the solidification microstructure.They found that an asymmetric shape of weld,macrosegregation,and brittle intermetallic compounds,Ti2Ni and TiNi3,were readily generated within the weld with macroscopic cracks.

In the past10years,fibre lasers have been improved and developed intensively.Due to their advantages of good beam quality,low cost of maintenance and compact size, fibre lasers are suitable for most applications in laser materials processing and have been considered to compli-ment other types of laser systems,such as the Nd:YAG lasers and the CO2lasers[17].Nowadays,fibre lasers have been increasing used in welding similar materials.For instance,fibre laser welding of steels[18],aluminium alloy [19,20],stainless steel[21,22],magnesium alloy[23,24] and titanium alloy[25,26].Nevertheless,less work has been reported in this field related to fibre laser welding of dissimilar materials,such as welding of carbon steel to aluminium alloy[27]and titanium alloy to steel[28].The purpose of this study is to investigate the influence of processing parameters on the weld quality in fibre laser welding of Ti-6Al-4V and Inconel718.The melt pool shapes are modelled analytically using a two-dimensional model. 2Experimental investigation

Sheets of Ti-6Al-4V and Inconel718with2mm thickness were laser butt welded together by a single mode fibre laser operating in the continuous wave mode.The chemical compositions and physical properties of these two materials are shown in Tables1,2and Fig.1,respectively.

Figure2a shows the full setup of this experiment.An IPG1kW fibre laser with an emission wavelength of 1,070nm was used.The spot diameter of the focused laser beam was approximately72μm with a Gaussian intensity distribution.During welding,argon was supplied co-axially and laterally as the shielding gas.Both Ti-6Al-4V and Inconel718samples for welding were25×50×2mm,as shown in Fig.2b.The surface roughness of Ti-6Al-4V and Inconel718samples were,approximately, 4.66and 4.36Ra,respectively.Before welding,each sample was cleaned with acetone.The focal position of the laser beam was set at the top surface of the plates in this study.

A series of experiments was carried out to investigate the correlation of laser power,welding speed and the offset of the laser beam from the interface with the weld quality of full penetration welds.In Table3,the one variable at a time method was used.Each trail was conducted a total of three times to ensure repeatability.Firstly,four levels of the laser power,700,800,900and1,000W,were tested at a fixed welding speed when the laser beam was positioned on the interface of samples to investigate the influence of the laser power on the weld quality.Next,a study of the effect of welding speed was carried out by using different welding speeds,60,80and100mm/s at a fixed laser power of 1000W.In the final experiment,three different offset positions of the laser beam—on the interface of samples, offset from the interface of samples to the Ti-6Al-4V side 35μm and offset from the interface of samples to the Inconel718side35μm—were tested while other param-eters were kept constant to find the relation between the laser beam offset position and the weld quality.

After welding,all samples were sectioned across the weld,mounted in conductive resin,polished with diamond abrasives to1μm surface finish and etched with Krolls reagent for further examination.The weld bead shape including the weld width and depth were measured using optical microscopy with a personal computer running Solution DT software as shown in Fig.3.The mean diameter of porosity and length of crack in welds were also observed and calculated from the cross-section of welds by optical microscopy.Microstucture and phenomena of microsegregation within welds were observed by means of optical microscopy and scanning electron microscopy equipped with backscattered electron imaging and energy Table1Chemical composition(wt.%)of Ti-6Al-4V and Inconel718 [29,30]

Ti-6Al-4V Inconel718 Fe0.40a Balance

Al 5.5-6.750.20-0.80 V 3.5-4.5–

Cr–17.2-21.0 Nb+Ta– 4.75-5.50 Mo– 2.80-3.30 Ti Balance0.65-1.12 Ni–50.0-55.0 a The maximum limit

dispersive spectrometry.Profiles of microhardness includ-ing the base metals and the weld were tested using a Vickers microhardness machine with a100g load for10s. Figure3schematically illustrates evaluations of the weld dimension and the hardness distribution.

3Experimental results

3.1The weld geometry

As shown in Fig.4,each full penetration weld has near-parallel sides under all the values of the laser power, welding speed and the laser beam offset position used in the experiments.In each case,the weld profile on the Ti-6Al-4V side is straighter than on the Inconel718side.The weld geometries were obvious different between three different laser beam offset positions when laser power and welding speed were800W and100mm/s as shown in Fig.4a,b and c, respectively.The weld with a bigger fusion zone was obtained when the laser beam was positioned on the Inconel 718side,as shown in Fig.4c.Meanwhile,in Fig.4b,the weld with a clear undercut and a smaller fusion zone was obtained when the laser beam was positioned on the Ti-6Al-4V

side.

Fig.1Material properties of Ti-6Al-4V[31]and Inconel718[35]

(Cp and k mean specific heat and thermal conductivity,respectively)

Ti-6Al-4V[31,33]Inconel718[32,34]

Hardness(Hv)353404

Melting point(°C)1,6551,260-1,336

Boiling point(°C)3,3152,917

Density(g/cm) 4.428.91

Specific heat(J/kg°C)610435

Coefficient of expansion(10?6°C?1)8.013.0

Latent heat(kJ/kg)290272

Solidus temperature(°C)1,6051,260

Liquidus temperature(°C)1,6551,336

Thermal conductivity(W/m°C)

at20°C 5.811.4

at～T m/217.521.3

Thermal diffusivity(m2/s)

at20°C 2.15×10?6 2.94×10?6

at～T m/2 6.49×10?6 5.50×10?6

Table2Physical properties of

Ti-6Al-4V and inconel

718

Fig.2Setup for the fibre laser welding of dissimilar materials process:

(a)diagram of the full setup,(b)illustration of the clamped system

When the laser beam was positioned on the interface of samples,the relationship between the weld geometry,welding speed and laser power was shown in Fig.5.When welding speed was kept at 80and 100mm/s,results show that,in both cases,the weld width randomly varied when laser power increased from 700to 1,000W as shown in Fig.5a .Meanwhile,the influence of welding speed on the weld width with the constant laser power of 1,000W was shown in Fig.5b .The weld width decreased from 564to 351μm when welding speed was increased from 60to 100mm/s.The relationship between the laser beam offset position and the weld width is shown in Fig.6.When the laser power and welding speed were 900W and 80mm/s,respectively,a wider weld width of 603μm was obtained when the laser beam was positioned on the interface.Meanwhile,the weld width with the laser beam offset to the Ti-6Al-4V side and the Inconel 718side was around 495and 458μm,respectively.When laser power increased to 1,000W,a narrower weld was found when the laser beam was positioned on the interface.A slightly wider weld was obtained when the laser beam was offset to the Ti-6Al-4V side.

3.2The weld defects

The relationship between the formation of porosity,laser power,welding speed and the laser beam offset position is shown in Fig.7.Porosity was produced at a wide range of parameter combinations,as shown in Fig.7.The offset position of the laser beam probably was not the main factor to determine the formation of porosity.The diameter of

micro-porosities observed from this work ranged from 15to 172μm.Figure 8shows the relationship between the formation of crack,laser power,welding speed and the laser beam offset position.Cracks were produced at a wide range of parameter combinations as shown in Fig.8.However,crack-free welds were more readily obtained at a higher laser power and a higher welding speed.As previously,the offset position of the laser beam was not a key factor to influence the formation of crack in the weld.The mean crack length in each weld was between 63and 663μ

m.

Fig.4Macrostructure of cross sections produced at 800W and 100mm/s when the laser beam was (a )positioned on the interface,(b )offset on the Ti-6Al-4V side,(c )offset on the Inconel 718

side

Fig.3Schematic diagram of the weld dimension and hardness tests

Table 3Experimental matrix Welding speed (mm/s)Laser power (W)60700,1,000b

80700,800,900b ,1,000b 100

700,800b ,900,1,000b

b

Three different laser beam offset positions —on the interface,offset from the interface to the Ti-6Al-4V side 35μm and offset from the interface to the Inconel 718side 35μm —were carried out individually with these combinations of welding parameters

3.3Hardness distribution of the weld

Figure9a shows the relationship between hardness distri-butions and laser power when the laser beam was positioned on the interface.It indicates that higher hardnesses occurred near the fusion zone in comparison with the parent materials.No clear trend was found between laser power and hardness variations.When laser power and the laser beam offset position were700W and on the interface,respectively,the influence of welding speed on hardness variations is shown in Fig.9b.Results show that less hardness variations between the fusion zone and parent metals was obtained with the welding speed of 60mm/s while more significant hardness variations were found at a higher welding speed of80or100mm/s.

Figure10displays the relationship between the laser beam offset position and hardness variations when laser power and welding speed were900W and80mm/s, respectively.Hardness variations near the fusion zone were clear when the laser beam were positioned on the interface or offset to the Ti-6Al-4V side as shown in Fig.10a and b, respectively.On the other hand,in Fig.10c,the hardness variation near the fusion zone was minimal when the laser beam was offset to the Inconel718side.

3.4Microsegregation of the weld

Welds produced at different welding conditions are shown in Fig.11.Figure11a is a partial cross-sectioned

area Fig.8Relationship between the formation of crack,laser power, welding speed and the laser beam offset position.(Centre,Ti side and Ni side mean the laser beam was positioned on the interface,offset to the Ti-6Al-4V side and offset to the Inconel718side,

respectively) Fig.7Relationship between the formation of porosity,laser power, welding speed and the laser beam offset position.(Centre,Ti side and Ni side mean the laser beam was positioned on the interface,offset to the Ti-6Al-4V side and offset to the Inconel718side,

respectively) Fig.6Relationship between the weld widths and the laser beam

offset position when welding speed was kept at80

mm/s

Fig.5Relationship between the weld width of full penetration welds

and a different laser powers;b different welding speeds at a constant

laser power of1,000W.(The laser beam was positioned on the

interface of the welding materials)

observed under an optical microscope when welding conditions were 800W,60mm/s and the laser beam was offset on the Inconel 718side.It is likely that vortices occurred in the weld producing different microstructures.Hardness and chemical compositions of points A-G are tabulated in Tables 4and 5,respectively.Higher hardnesses were obtained at points B,F and G.According to the Ni-Ti phase diagram [36]and their chemical compositions in Table 5,points B and G could be identified as the TiNi 3phase.Meanwhile,point D with 814.1Hv was classified as the TiNi phase and point A (263.5Hv)and point E (375.4Hv)are the hardness of unwelded Ti-6Al-4V and Inconel 718,respectively.

When welding conditions were 700W,80mm/s and the laser beam was offset on the Ti-6Al-4V side,a back-scattered electron image near the top area of weld was taken and is shown in Fig.11b .Because atomic number of Ni is higher than Ti,Ti-6Al-4V and Inconel 718can be easily identified as the black and grey colour,respectively,in Fig.11b .Several metal mixes were found within the weld.The molten material near the Ti-6Al-4V side was under-standably richer in this alloy than that near the Inconel 718side and clear vortices were found in the weld.Hardness at

points H-M is listed in Table 4.A high hardness of 389.2Hv occurred at point I.

4Discussion

Usually,the formation of cracking can be discussed in terms of metallurgical and mechanical factors and previous research [15,16]has highlighted two factors that could influence the formation of cracks within a Ti/Ni or Ti

alloy/

Fig.10Hardness distributions of welds produced at different laser beam offset positions when laser power and welding speed were 900W and 80mm/s,respectively,a on the interface,b offset to the Ti-6Al-4V side,c offset to the Inconel 718

side

Fig.9Hardness distributions of welds produced at a the constant welding speed of 80mm/s;b the constant laser power of 700W

Ni alloy weld.Firstly,two intermetallic brittle phases,Ti 2Ni and TiNi 3,which are readily produced within the weld during welding of a titanium alloy and a nickel alloy,can increase the susceptibility to failure at relatively low stresses.Secondly,the large differences of thermo-physical properties between Ti-6Al-4V and Inconel 718can generate the stresses that actually cause the formation of cracks within the weld.

In order to clearly realise the relevance between processing parameters and the weld quality particularly in the formation of intermetallic brittle phases and cracks in welds,a simple two-dimensional analytical model was developed and compared with the experimental results.The model focuses on the relationships between laser power,welding speed,the laser beam offset position and the melt

pool properties and behaviours,including the melt area,melt ratio and cooling rate.

4.1Analytical model for welding dissimilar materials The thermal distribution in both Ti-6Al-4V and Inconel 718welding plates were modelled individually according to Rosenthal ’s equation for two dimensional flow of heat [37]as shown in Eq.1:

T x ;y eTàT 0?q 02p k

e àl vx

K 0l vr eT

e1T

where T (x ,y )is the temperature at point (x ,y ;°C),T 0is the original sample temperature (20°C),q ′is the rate of heat per unit length (W/m),k is the thermal conductivity (W/m °C),1is the thermal diffusivity (m 2/s),v is welding speed (m/s),K 0is the modified Bessel function of the second kind and

zero order,and r ?x 2ty 2eT12

=is the distance from the heat source (m ).In order to increase the precision of modelling results,values of thermal conductivity and thermal diffu-sivity at around half of the melting point of each material are used,as shown in Table 2and Fig.3.Heat transfer across the interface of the two welding materials is ignored at this stage.From results of the thermal distribution,the melt pool size is defined according to the melt points of Ti-6Al-4V (1,655oC)and Inconel 718(1,260oC)as shown in Fig.12a and b .In Fig.12a ,on the Ti-6Al-4V side,the melt pool width,the melt pool length in the forward direction and the melt pool length in the rear direction are presented as W Ti ,L 1Ti and L 2Ti ,respectively.Meanwhile,in Fig.12b ,W Ni ,L 1Ni and L 2Ni are the melt pool width,the melt pool length in the forward direction and the melt pool length in the rear direction on the Inconel 718side,respectively.

The Ti-6Al-4V and Inconel 718melt pools are then taken as ellipses;one ellipse represents the area in front

of

Fig.11Microsegregation of Ti-6Al-4V/Inconel 718welds produced at a 800W,60mm/s and the laser beam was offset to the Inconel 718side (optical microscope image),b 700W,80mm/s and the laser beam was offset to the Ti-6Al-4V side;SEM backscattered electron image

Table 4Hardness of points A-M in Fig.9

Hardness (Hv)

A 263.5

B 889.0

C 319.1

D 814.1

E 375.4

F 906.2

G 909.1

H 251.2

I 389.2

J 344.7

K 353.0

L 367.0M

368.6

the beam axis and one is the area behind the beam axis.The mean length of the separate melt pools in the forward and

rear directions is L 1?L 1Ti tL 1Ni eT2and L 2?L 2Ti tL 2Ni eT

2

,respec-tively.This is taken as the length of the combined pool.The melt pool is described in Eqs.2a –2d and Fig.12c :On the Ti-6Al-4V side (y >0):For x >0:

x 2L 12ty 2

W 2Ti ?1e2a T

For x <0:

x 2L 22ty 2

W 2Ti

?1e2b T

On the Inconel 718side (y <0):For x >0:

x 2L 12ty 2

W 2Ni ?1e2c T

For x <0:

x 2L 22ty 2

W 2Ni

?1e2d T

After that,the melt pool area (mm 2),the melt ratio and the cooling rate of the melt pool (°C/mm)[38]are calculated as shown in Eqs.3,4,5,respectively.The melt pool area:

Melt pool area ?

p ?W Ti L 1tL 2eTt

p ?W Ni L 1tL 2eT

e3T

The melt ratio:Melt ratio ?V Ni

V Ti

?

p ?W Ni L 1tL 2eT

4

?t Ni p ?W Ti L 1tL 2eT

4

?t Ti

e4a T

where,V Ni ,V Ti ,t Ni and t Ti mean the melt volume in the Inconel 718side and Ti-6Al-4V side,and the thickness of the Inconel 718and Ti-6Al-4V plates,respectively.Due

to

Table 5Chemical composition (wt.%)of points A-G in Fig.9a

A

B C D E

F G Ti –19.127.7855.4290.2933.4020.85Al –––– 5.50 2.31–V ––– 3.50 4.21––Ni 55.2744.3950.6225.05–35.0645.59Cr 21.3617.2318.72 6.00–12.7218.26Nb – 4.84 4.72––––Fe 17.4214.4216.187.28–11.2315.30Hg 5.95––

––

5.28–S –– 1.98––––Tm –

––

3.74–

–

–Phase

Inconel 718

TiNi 3

Inconel 718

TiNi

Ti-6Al-4V

Unknown

TiNi 3

the same thickness of the Ti-6Al-4V and Inconel 718plates,Eq.4a can be rewritten to Eq.4b .Melt ratio ?

W Ni W Ti

e4b T

According to Hofmeister et al.[31],the cooling rate of a melt pool at the conductive cooling is related to the length of the pool by an expression of the form as shown in Eq.5.The cooling rate (T

):Log T

?à2?log L 1tL 2eTt3

e5TFrom the models it can be seen that when laser power

and welding speed are kept at 1,000W and 80mm/s,a longer and bigger melt pool is obtained when the laser beam is offset to the Inconel 718side as shown in Fig.13a .Similar lengths of melt pool are obtained whether the laser beam is positioned on the interface or offset to the Ti-6Al-4V side.The melt area in the Inconel 718side is slightly wider than in the Ti-6Al-4V side when the laser beam is positioned on the interface.A bigger melt area is found in the Ti-6Al-4V side when the laser beam is offset to the Ti-6Al-4V side.Similar trends are observed when welding speed increases from 80to 100mm/s,as shown in Fig.13b .

Relationships between the formation of cracks and the melt pool behaviours including the melt pool area,the melt ratio and the cooling rate are shown in Table 6and Fig.14.The cooling rate increases as the melt pool area decreases.There is a higher possibility to produce crack-free welds when the melt pool area and the cooling rate are in the range of 0.45～0.95mm 2and 1,142～3,423°C/sec,respec-tively.Welds with crack readily occur when the heat input is higher than 16J/mm or lower than 9J/mm.Crack-free welds with the smaller melt ratio (symbol “○”)are observed within a very small processing window (the melt pool area and the cooling rate are around 0.44～0.59mm 2and 1,946～2,930°C/sec,respectively).4.2Discussion on experimental results

The amount of heat input can determine the degree of dilution and chemical composition in the weld [39].It also determines the cooling rate,which is inversely proportional to the square of the melt pool length [38].Thermal strains caused by high cooling rates can increase the crack initiation rate,but a higher thermal gradient resulting in a rapid cooling rate in the weld can also reduce the grain size to increase solidification crack resistance [40].Additionally,a rapid cooling rate may induce non-equilibrium solidifica-tion in the weld and thus amount of segregation in the solidified pool [12,41].Modelled results (Fig.14)indicate that crack-free welds were produced at a wide range of cooling rates so together these effects do not seem to be dominant in determining if cracking will occur in the fibre laser welding of Ti-6Al-4V to Inconel 718process.

The melting ratio of fused materials is another important factor that determines the formation of defects in dissimilar materials welds [12].Producing a bond similar to a brazed joint,by melting one material to induce another one to melt,has been suggested as a method to avoid the formation of intermetallic phases within the weld [4].Perhaps because of this mechanism,the majority of the crack-free welds were produced at a higher melt ratio in Table 6and Fig.14.It is possible that when the beam was positioned on the Inconel 718side,the lower melting point and higher thermal conductivity of Inconel 718meant the heat could dissipate more quickly resulting in the lower thermal gradient and a wider fusion zone (Fig.4c )than when on the Ti-6Al-4V side.Accordingly,the influence of the Marangoni forces on the melt pool surface could be less when the laser beam was positioned on the Inconel 718side.For these reasons,the smaller hardness variation that occurred (Fig.10c )indicates less formation of Ti-Ni intermetallics,which can increase strength and hardness but decrease ductility.Due to Ti-6Al-4V having a lower thermal conductivity than Inconel 718,when the laser beam was offset to the Ti-6Al-4V side,more heat

could

Fig.13The melt pool curves in fibre laser welding of Ti-6Al-4V to Inconel 718obtained at three different laser beam offset positions with laser power of 1,000W and welding speed of a 80mm/s,b 100mm/s

accumulate in the Ti-6Al-4V side.This could have caused a narrower fusion zone (Fig.4b ),a higher thermal gradient and hence a strong Marangoni fluid flow,assisting the formation of the brittle intermetallic phases and increasing hardness variations,as indicated in Fig.10b .

For optimum properties,it is important to avoid the formation of these intermetallic phases in the welds [42,43].In this case,it is possible to achieve this by appropriately restricting the size and extent of the melt pool and the solidification time.When the laser beam is offset to the Inconel 718side,the significant reduction of the melt area in the Ti-6Al-4V side and the wider melt area

in the Inconel 718side (Fig.13)may cause less vigorous convective flow in the molten zone around the keyhole,avoiding the formation of intermetallic phases in the weld because most of heat input can be lost quickly on the Inconel 718side before enough heat is transferred into the Ti-6Al-4V side to induce severe microsegregation [44].Crack-free welds were also readily observed at higher welding speed,as shown in Fig.8.Although higher speed is normally related to higher cooling rate,any direct relation between cracking and cooling rate has already been considered.It is therefore likely that other factors apart from cooling rate and intermetallic formation played a secondary role in determining the final state of a weld.Melt pool geometry (elongation at higher speeds),keyhole geometry and stability effects and slight difference beam absorption at different traverse velocities may have contributed.

5Conclusions

The effects of three processing parameters,laser power,welding speed and offset distance of the laser beam from the interface,were investigated individually during fibre laser welding of Ti-6Al-4V to Inconel 718.Experimental results indicated that when welding 2mm thick sheets

of

Fig.14Relationship between the formation of crack,the melt pool area,melt ratio and cooling rate

Table 6Detailed values from the analytical modelling with different welding parameters Speed (mm/s)Power (W)Laser beam position c Heat input (J/mm)Melt pool area (mm 2)

Melt ratio Cooling rate (°C/sec)The formation of crack 60700Centre 11.670.39 1.274,625.16Crack 601,000Ti side 16.670.950.701,021.69Crack 601,000Centre 16.67 1.05 1.601,061.33Crack 601,000Ni side 16.67 1.35 3.60689.49Crack 80700Centre 8.750.21 1.269,268.46Crack 80800Centre 10.000.30 1.465,405.81Crack-free 80900Ti side 11.250.440.552,930.67Crack-free 80900Centre 11.250.46 1.253,139.48Crack-free 80900Ni side 11.250.59 2.981,860.01Crack-free 801,000Ti side 12.500.590.561,946.53Crack-free 801,000Centre 12.500.64 1.241,983.89Crack-free 801,000Ni side 12.500.83 2.761,142.71Crack-free 100700Centre 7.000.16 1.241,0711.01Crack-free 100800Centre 8.000.21 1.217,800.86Crack-free 100800Ti side 8.000.220.506,055.21Crack 100800Ni side 8.000.24 4.165,267.95Crack 100900Centre 9.000.29 1.265,077.40Crack-free 1001,000Centre 10.000.39 1.303,423.88Crack-free 100

1,000

Ni side

10.00

0.51

2.85

1,933.88

Crack-free

c

Centre,Ti side and Ni side mean the laser beam was positioned on the interface,offset to the Ti-6Al-4V side and offset to the Inconel 718side,respectively

Ti-6Al-4V to Inconel718with an IPG1kW fibre laser, crack-free welds could be readily obtained by a higher laser power and welding speed.A better quality weld with less hardness variations and less chance of cracks can be generated by offsetting the laser beam approximately 35μm from the interface to the Inconel718side and using a combination of a higher laser power and a higher welding speed.This is attributed to this method suppressing the formation of Ti-Ni intermetallic brittle phases. Acknowledgement The UK Engineering and Physical Sciences Re-search Council(EPSRC)is acknowledged for grant EP/C013352/1,which allowed the purchase of the single mode,high-power fibre laser used here.

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Publication

激光原理与应用课试卷试题答案

激光原理及应用[陈家璧主编] 一、填空题（20分，每空1分） 1、爱因斯坦提出的辐射场与物质原子相互作用主要有三个过程，分别是（自发辐射）、（受激吸收）、（受激辐射）。 2、光腔的损耗主要有（几何偏折损耗）、（衍射损耗）、（腔镜反射不完全引起的损耗）和材料中的非激活吸收、散射、插入物损耗。 3、激光中谐振腔的作用是（模式选择）和（提供轴向光波模的反馈）。 4、激光腔的衍射作用是形成自再现模的重要原因，衍射损耗与菲涅耳数有关，菲涅耳数的近似表达式为（错误！未找到引用源。），其值越大，则衍射损耗（愈小）。 5、光束衍射倍率因子文字表达式为（错误！未找到引用源。）。 6、谱线加宽中的非均匀加宽包括（多普勒加宽），（晶格缺陷加宽）两种加宽。 7、CO2激光器中，含有氮气和氦气，氮气的作用是（提高激光上能级的激励效率），氦气的作用是（有助于激光下能级的抽空）。 8、有源腔中，由于增益介质的色散，使纵横频率比无源腔频率纵模频率更靠近中心频率，这种现象叫做（频率牵引）。 9、激光的线宽极限是由于（自发辐射）的存在而产生的，因而无法消除。 10、锁模技术是为了得到更窄的脉冲，脉冲宽度可达（错误！未找到引用源。）S，通常有（主动锁模）、（被动锁模）两种锁模方式。 二、简答题（四题共20分，每题5分） 1、什么是自再现？什么是自再现模？ 开腔镜面上的经一次往返能再现的稳态场分布称为开腔的自在现摸 2、高斯光束的聚焦和准直，是实际应用中经常使用的技术手段，在聚焦透镜焦距F一定的条件下，画出像方束腰半径随物距变化图，并根据图示简单说明。 3、烧孔是激光原理中的一个重要概念，请说明什么是空间烧孔？什么是反转粒子束烧孔？ 4、固体激光器种类繁多，请简单介绍2种常见的激光器（激励方式、工作物质、能级特点、可输出光波波长、实际输出光波长）。 三、推导、证明题（四题共40分，每题10分）

08激光原理与技术试卷B

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10. 均匀加宽指的是引起加宽的物理因素对各个原子是 等同的, 。 11. 入射光强和饱和光强相比拟时，增益随入射光强的增加而减少，称 增益饱和 现 象。 12．方形镜的mnq TEM 模式沿x 方向有 m 条节线，没y 方向有 n 条节线. 二.单项选择题（每题2分，共10分） 1. 关于高斯光束的说法，不正确的是（ ） (A)束腰处的等相位面是平面； (B)无穷处的等相位面是平面； (C)相移只含几何相移部分； (D)横向光强分布是不均匀的。 2. 下列各模式中，和圆型共焦腔的模q n m TEM ,,有相同频率的是（A ） (A)1,,2-+q n m TEM ； (B) q n m TEM ,,2+； (C) 1,,1-+q n m TEM ； (D) 1,1,2-++q n m TEM 。 3. 下列各种特性中哪个特性可以概括激光的本质特性（C ） (A)单色性； (B)相干性； (C)高光子简并度； (D)方向性。 4. 下列加宽机制中，不属于均匀加宽的是（B ） (A)自然加宽； (B)晶格缺陷加宽； (C)碰撞加宽； (D)晶格振动加宽。 5. 下列方法中，不属于横模选择的是（D ） (A)小孔光阑选模； (B) 非稳腔选模； (C) 谐振腔参数N g ,选择法； (D)行波腔法。 三、简答题（每题4分，共20分）

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2 .光子简并度指光子处于、 、、。（4分） 3．激光器的基本结构包括三部分，即、 和。（3分） 4．影响腔内电磁场能量分布的因素有、 、。（3分） 5．有一个谐振腔，腔长L=1m，在1500MHｚ的范围内所包含的纵模个数为个。（2分） 6．目前世界上激光器有数百种之多，如果按其工作物质的不同来划分，则可分为四大类，它们分别是、、 和。（4分） 三、计算题（42分） 1．（8分）求He-Ne激光的阈值反转粒子数密度。已知＝6328?，1/f( ) ＝109Hz，＝1，设总损耗率为，相当于每一反射镜的等效反射率R＝l－L ＝98.33％，＝10—7s，腔长L＝0.1m。 2．（12分）稳定双凹球面腔腔长L＝1m,两个反射镜的曲率半径大小分别为R 1＝1.5m,R ＝3m求它的等价共焦腔腔长，并画出它的位置。 2 3．（12分）从镜面上的光斑大小来分析，当它超过镜子的线度时，这样的横模就不可能存在。试估算在L＝30cm, 2a=0.2cm 的He-Ne激光方形镜共焦腔中所可能出现的最高阶横模的阶次是多大？ 4．4．（10分）某高斯光束的腰斑半径光波长。求与腰斑相距z=30cm处的光斑及等相位面曲率半径。 四、论述题（8分） 1．（8分）试画图并文字叙述模式竞争过程

激光原理与技术试题

2006-2007学年第1学期《激光原理与技术》B卷试题答案 1 .填空题（每题4分）[20] 1.1激光的相干时间T和表征单色性的频谱宽度△V之间的关系 为 1/ c 1.2 一台激光器的单色性为5X10-10,其无源谐振腔的Q值是_2x109 1.3如果某工作物质的某一跃迁波长为100nm的远紫外光，自发跃迁几率A10等于105S1，该跃迁的受激 辐射爱因斯坦系数B10等于6x1010 m3^2^ 1.4设圆形镜共焦腔腔长L=1m，若振荡阈值以上的增益线宽为80 MHz判断可能存在两个振荡频率。 1.5对称共焦腔的1（A D）_1_,就稳定性而言，对称共焦腔是稳定______________ 空。 2.问答题（选做4小题，每小题5分）[20] 2.1何谓有源腔和无源腔？如何理解激光线宽极限和频率牵引效应？ 有源腔：腔内有激活工作物质的谐振腔。无源腔：腔内没有激活工作物质的谐振腔。 激光线宽极限：无源腔的线宽极限与腔内光子寿命和损耗有关: 九'；有源腔由于受到自发辐射影响，净损耗不等于零，自发辐射的随机相位造成输出激光的线宽极限 n2t 2 ( C)h 0 ------------------- 。 n t Rut 频率牵引效应：激光器工作物质的折射率随频率变化造成色散效应，使得振荡模的谐振频率总是偏离无源腔 相应的模的频率，并且较后者更靠近激活介质原子跃迁的中心频率。这种现象称为频率牵引效应。 2.2写出三能级和四能级系统的激光上能级阈值粒子数密度，假设总粒子数密度为n阈值反转粒子数密 度为n t. 三能级系统的上能级阈值粒子数密度n 2t n n ——-;四能级系统的上能级阈值粒子数密度2 n2t n t 。 2.3产生多普勒加宽的物理机制是什么？ 多普勒加宽的物理机制是热运动的原子（分子）对所发出（或吸收）的辐射的多普勒频移。 2.4均匀加宽介质和非均匀加宽介质中的增益饱和有什么不同？分别对形成的激光振荡模式有何影响? 均匀加宽介质：随光强的增加增益曲线会展宽。每个粒子对不同频率处的增益都有贡献，入射的强光不仅使自身的增益系数下降，也使其他频率的弱光增益系数下降。满足阀值条件的纵模在振荡过程中互相竞争，结果总是靠近中心频率的一个纵模得胜，形成稳定振荡，其他纵模都

《激光原理》本科期末考试试卷及答案

系、班 姓 名 座 号 ………………密……………封……………线……………密……………封……………线………………… 华中科技大学2012年《激光原理》期末试题(A) 题 号 一 二 三 四 总分 复核人 得 分 评卷人 一. 填空: （每孔1分，共17分） 1. 通常三能级激光器的泵浦阈值比四能级激光器泵浦阈值 高 。 2. Nd:Y AG 激光器可发射以下三条激光谱线 946 nm 、 1319 nm 、 1064 nm 。其 中哪两条谱线属于四能级结构 1319 nm 、 1064 nm 。 3. 红宝石激光器属于 3 几能级激光器。He-Ne 激光器属于 4 能级激光器。 4. 激光具有四大特性，即单色性好、亮度高、方向性好和 相干性好 5. 激光器的基本组成部分 激活物质、 激光谐振腔 、 泵浦源 。 6. 激光器稳态运转时，腔内增益系数为 阈值 增益系数,此时腔内损耗激光光子的速率和生成激光的光子速率 相等. 7. 调Q 技术产生激光脉冲主要有 锁模 、 调Q 两种方法。 二、解释概念：（共15分，每小题5分）(选作3题) 题 号 一 二 三 合计 得 分 1. 基模高斯光束光斑半径： 激光光强下降为中心光强21 e 点所对应的光斑半径. 2. 光束衍射倍率因子 光束衍射倍率因子= 角 基膜高斯光束远场发散基膜高斯光束束腰半径实际光束远场发散角 实际光束束腰半径?? 3. 一般稳定球面腔与共焦腔的等价关系： 一般稳定球面腔与共焦腔的等价性：任何一个共焦腔与无穷多个稳定球面腔等价； 任何一个稳定球面腔唯一地等价于一个共焦腔。 三、问答题：（共32分，每小题8分） 题 号 一 二 三 四 合计 得 分 1. 画出四能级系统的能级简图并写出其速率方程组 ()()()()　Rl l l l l N N n f f n dt dN n n n n n A n W n s n dt dn S n S A n N n f f n dt dn A S n W n dt dn τυννσυννσ-???? ??-==++++-=++-???? ??--=+-=02111220321303001010 3232121202111 222313230303 ,, W 03 A 03 S 03 S 32 S 21 A 21 W 21 W 12 E 3 E 2 E 1 E 0

激光原理与激光技术习题

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激光原理试卷

激光原理试卷

广东工业大学考试试卷( A ) 课程名称: 激光原理与技术 试卷满分100 分 考试时间: 2007年6月18日 (第16周 星期 一) 一、 选择题（每题3分，共30分） 1.世界上第一台激光器是 （ ） (A)氦氖激光器． (B)二氧化碳激光器． (C)钕玻璃激光器． (D)红宝石激光器． (E)砷化镓结型激光器． 2.按照原子的量子理论，原子可以通过自发辐射和受激辐射的方式发光，它们所产生的光的特点是：（ ） (A)两个原子自发辐射的同频率的光是相干的，原子受激辐射的光与入射光是 不相干的． (B)两个原子自发辐射的同频率的光是不相干的，原子受激辐射的光与入射光 是相干的． (C)两个原子自发辐射的同频率的光是不相干的，原子受激辐射的光与入射光 是不相干的． (D)两个原子自发辐射的同频率的光是相干的，原子受激辐射的光与入射光是 相干的． 3．氦-氖激光器属于典型的（ ）系统 （A ）二能级（B ）三能级（C ）四能级（D ）多能级 4．体积3 cm 1=V ，线宽nm 10=?λ，中心波长60nm ，模式数目为（ ） 20 201012104 (D) 102 (C) 104 (B) 102 )A (???? 5．多普勒加宽发生在（ ）介质中 6．半共心腔在稳定图上的坐标为（d ） （A ）（-1，-1） （B ） （0，0） （C ）（1，1） （D ）（0，1） 7．对于均匀增宽介质，中心频率处小信号增益系数为)00 (v G ，当s I I =时 ， 饱和显著，非小信号中心频率增益系数为：（c ） （A ） )00 (v G （B ） )00 (2v G （C ） )00(21v G （D ） )00 (3 1v G 8．.一平凹腔,其凹面镜的半径R 等于腔长L,它是(b ) （A ）稳定腔 （B ）临界腔 （C ）非稳腔 9.能够完善解释黑体辐射实验曲线的是( c ) （A ）瑞利-金斯公式 （B ）维恩公式 （C ）普朗克公式 （D ）爱因斯坦公式

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2006-2007学年 第1学期 《激光原理与技术》B 卷 试题答案 1． 填空题(每题4分)[20] 激光的相干时间τc 和表征单色性的频谱宽度Δν之间的关系为___1c υτ?= 一台激光器的单色性为5x10-10，其无源谐振腔的Q 值是_2x109 如果某工作物质的某一跃迁波长为100nm 的远紫外光，自发跃迁几率A 10等于105 S -1，该跃迁的受激辐射爱因斯坦系数B 10等于_____6x1010 m 3s -2J -1 设圆形镜共焦腔腔长L=1m ，若振荡阈值以上的增益线宽为80 MHz ，判断可能存在_两_个振荡频率。 对称共焦腔的 =+)(2 1 D A _-1_，就稳定性而言，对称共焦腔是___稳定_____腔。 2. 问答题(选做4小题，每小题5分)[20] 何谓有源腔和无源腔如何理解激光线宽极限和频率牵引效应 有源腔：腔内有激活工作物质的谐振腔。无源腔：腔内没有激活工作物质的谐振腔。 激光线宽极限：无源腔的线宽极限与腔内光子寿命和损耗有关：122' c R c L δ υπτπ?= = ；有源腔由于受到自发辐射影响，净损耗不等于零，自发辐射的随机相位造成输出激光的线宽极限 220 2()t c s t out n h n P πυυυ?= ?。 频率牵引效应：激光器工作物质的折射率随频率变化造成色散效应，使得振荡模的谐振频率总是偏离无源腔相应的模的频率，并且较后者更靠近激活介质原子跃迁的中心频率。这种现象称为频率牵引效应。 写出三能级和四能级系统的激光上能级阈值粒子数密度，假设总粒子数密度为n ，阈值反转粒子数密度为 n t. 三能级系统的上能级阈值粒子数密度22 t t n n n += ；四能级系统的上能级阈值粒子数密度2t t n n ≈。 产生多普勒加宽的物理机制是什么 多普勒加宽的物理机制是热运动的原子（分子）对所发出（或吸收）的辐射的多普勒频移。 均匀加宽介质和非均匀加宽介质中的增益饱和有什么不同分别对形成的激光振荡模式有何影响 均匀加宽介质：随光强的增加增益曲线会展宽。每个粒子对不同频率处的增益都有贡献，入射的强光不仅使自身的增益系数下降，也使其他频率的弱光增益系数下降。满足阀值条件的纵模

激光原理试卷集锦

1：腔模，横模，纵模。 腔模：在具有一定边界条件的腔内，电磁场只能存在于一系列分立的本征状态之中。将谐振腔内可能存在的电磁场的本征态称为腔的模式。 横模：在垂直于腔轴的横截面内的稳定场分布称为谐振腔的横模。镜面上各点场的振幅按同样的比例衰减,各点的相位发生同样大小的滞后。这种在腔反射镜面上形成的经过一次往返传播后能自再现的稳定场分布称为自现模或横模。 纵模：腔模沿腔轴线方向的稳定场分布称为谐振腔的纵模。在腔的横截面内场分布是均匀的，而沿腔的轴线方向(纵向)形成驻波，驻波的波节数由q决定。通常将由整数q所表征的腔内纵向场分布称为腔的纵模。 2：频率牵引。 答：有源腔中的纵模频率总是比无源腔中同序列纵模频率更接近工作物质的中心频率，这种现象称为频率牵引。 3：光学谐振腔的作用是什么？ 答：①提供轴向光波模的光学正反馈。②控制振荡模式的特性。 4：对称共焦腔镜面上基模的特点是什么？ 答： ①基模为高斯分布,镜面中心光最大,向边缘平滑降落。 ②光斑的大小与反射镜的横向尺寸无关, 与波长和腔长有关(是共焦腔的一个重要特性。当然,这一结论只有在模的振幅分布可以用厄米-高斯函数近似表述的情况下才是正确)。 ③高斯光束的能量主要集中在束腰内部。 5：LD半导体的PN结实现粒子数目反转分布条件是什么？LD激光器的泵浦方式有哪些？答：①掺杂浓度足够高，使准Fermi能级分别进入导带和价带。 ②正向偏压V足够高，使eV>E g,从而E C F —E v F =eV>hv。 电注式，光泵浦，高能电子束 6：固体激光器激活介质的激光性质主要指什么？它们分别在固体激光设计时，决定什么？答：能级结构，吸收光谱，荧光光谱①能级结构：晶体的激光性质主要取决于Cr3+。Cr的外层电子组态为3d5 4s1 ,掺入Al2 O3 后失去3个电子,剩下3d壳层上3个外层电子(3d3 )。 ②吸收光谱：由于红宝石死各向异性晶体，故其吸收特性与光的偏振状态有关。 ③荧光光谱： 红宝石晶体有两条强荧光谱线,分别称为R1线和R2线。 R1 线中心波长为694.3nm,对应于E→4 A2 能级的自发辐射跃迁。 R2 线中心波长为692.9nm,对应于2A→ 4A2 能级的自发辐射跃迁。 7：常见的临界腔有哪些？其判定条件分别是什么？ 答： 8：简并能级，简并度 答：简并能级：电子可以有两个或两个以上的不同运动状态具有相同的能级. 简并度：同一能级对应不同的电子状态的数目（处于同一光子太、态的光子数称为光源的光子简并度） 9：He—Ne激光器放电毛细管内径要很小的主要原因是什么？ 答：Ne原子激光下能级2p和3p向基态的跃迁为选择定则所禁戒，粒子只能通过字发辐射跃迁到1s能级。由于1s能级向基态的跃迁也属禁戒，因此1s能级的Ne原子只有扩散到放电管管壁，通过与管壁碰撞释放能量后方能返回基态，称为“管壁效应”。激光下能级如不能被较快抽空，将会造成粒子的堆积，形成“瓶颈效应”。

2009-2010《激光原理与技术》课程试题B 试卷试题答案

一、填空题（20分，每空1分） 1、爱因斯坦提出的辐射场与物质原子相互作用主要有三个过程，分别是（自发辐射）、（受激吸收）、（受激辐射）。 2、光腔的损耗主要有（几何偏折损耗）、（衍射损耗）、（腔镜反射不完全引起的损耗）和材料中的非激活吸收、散射、插入物损耗。 3、激光中谐振腔的作用是（模式选择）和（提供轴向光波模的反馈）。 4、激光腔的衍射作用是形成自再现模的重要原因，衍射损耗与菲涅耳数有关，菲涅耳数的近似表达式为（错误！未找到引用源。 ），其值越大，则衍射损耗（愈小）。 5、光束衍射倍率因子文字表达式为（错误！未找到引用源。 ）。 6、谱线加宽中的非均匀加宽包括（多普勒加宽），（晶格缺陷加宽）两种加宽。 7、CO2激光器中，含有氮气和氦气，氮气的作用是（提高激光上能级的激励效率），氦气的作用是（有助于激光下能级的抽空）。 8、有源腔中，由于增益介质的色散，使纵横频率比无源腔频率纵模频率更靠近中心频率，这种现象叫做（频率牵引）。 9、激光的线宽极限是由于（自发辐射）的存在而产生的，因而无法消除。 10、锁模技术是为了得到更窄的脉冲，脉冲宽度可达（错误！未找到引用源。）S ，通常有（主动锁模）、（被动锁模）两种锁模方式。 二、简答题（四题共20分，每题5分） 1、什么是自再现？什么是自再现模？ 开腔镜面上的经一次往返能再现的稳态场分布称为开腔的自在现摸 2、高斯光束的聚焦和准直，是实际应用中经常使用的技术手段，在聚焦透镜焦距F 一定的条件下，画出像方束腰半径随物距变化图，并根据图示简单说明。 3、烧孔是激光原理中的一个重要概念，请说明什么是空间烧孔？什么是反转粒子束烧孔？ 4、固体激光器种类繁多，请简单介绍2种常见的激光器（激励方式、工作物质、能级特点、可输出光波波长、实际输出光波长）。 三、推导、证明题（四题共40分，每题10分） 1、短波长（真空紫外、软X 射线）谱线的主要加宽是自然加宽。试证明峰值吸收截面为π λσ22 = 。

激光原理试题

物理专业2006级本科《激光原理及应用》期末试题（A卷答案） 一、简答题 1.激光器的基本结构包括三个部分，简述这三个部分 答：激光工作物质、激励能源（泵浦）和光学谐振腔； 2.物质的粒子跃迁分辐射跃迁和非辐射跃迁，简述这两种跃迁的区别。 答：粒子能级之间的跃迁为辐射跃迁，辐射跃迁必须满足跃迁定则；非辐射跃迁表示在不同的能级之间跃迁时并不伴随光子的发射或吸收，而是把多余的能量传给了别的原子或吸收别的原子传给他的能量。 3.激光谱线加宽分为均匀加宽和非均匀加宽，简述这两种加宽的产生机理、谱线的基本线 型。 答：如果引起加宽的物理因数对每一个原子都是等同的，则这种加宽称为均匀加宽。自然加宽、碰撞加宽及晶格振动加宽均属均匀加宽类型。 非均匀加宽是原子体系中每一个原子只对谱线内与它的表观中心频率相应的部分有贡献。多普勒加宽和固体晶格缺陷属于非均匀加宽。 4.简述均匀加宽的模式竞争 答：在均匀加宽的激光器中，开始时几个满足阈值条件的纵模在振荡过程中相互竞争，结果总是靠近中心频率的一个纵模获胜，形成稳定的振荡，其他的纵模都被抑制而熄灭。 这种情况叫模式竞争。 5.工业上的激光器主要有哪些应用为什么要用激光器 答：焊接、切割、打孔、表面处理等等。工业上应用激光器主要将激光做热源，利用激光的方向性好，能量集中的特点。 6.说出三种气体激光器的名称，并指出每一种激光器发出典型光的波长和颜色。 答：He-Ne激光器，（红光），Ar+激光器，（绿光），CO2激光器，μm（红外） 7.全息照相是利用激光的什么特性的照相方法全息照相与普通照相相比有什么特点 答：全息照相是利用激光的相干特性的。全息照片是三维成像，记录的是物体的相位。 二、证明题：（每题6分，共18分） 1.证明：由黑体辐射普朗克公式 3 3 81 1 h KT h c e νν πν ρ= - 导出爱因斯坦基本关系式： 3 21 3 21 8 A h n h B cν πν ν== 三、计算题 1．由两个凹面镜组成的球面腔，如图。凹面镜的曲率半径分别为2m、3m，腔长为1m。发光波长600nm。 （1）求出等价共焦腔的焦距f；束腰大小w0及束腰位置； （2）求出距左侧凹面镜向右米处的束腰大小w及波面曲率半径R； 解: (0) 激光腔稳定条件

08激光原理与技术试卷B

08激光原理与技术试卷B

2 华南农业大学期末考试试卷（B 卷） 2008～2009学年第一学期 考试科目：激光原理与技术 考试类型：（闭卷） 考试时间：120分钟 姓名 年级专业 学号 题号 一 二 三 四 总分 得分 评阅人 一.填空题（每空2分，共30分） 1. 设小信号增益系数为0g ，平均损耗系数为α，则激光器的振荡条件为 g o > α 。 2. 相格 是相空间中用任何实验所能分辨的最小尺度。 3. 四能级系统中，设3E 能级向2E 能级无辐射跃迁的量子效率为1η，2E 能级向1E 能 级跃迁的荧光效率为2η，则总量子效率为 。。 4. 当统计权重21f f =时，两个爱因斯坦系数12B 和21B 的关系为 B 12=B 21 。 5. 从光与物质的相互作用的经典模型，可解释 色散 现象和 物质对光的 吸收 现象。 6. 线型函数的归一化条件数学上可写成 。 7. 临界腔满足的条件是 g1g2=1 或 g1g2=0 。 8. 把开腔镜面上的经过一次往返能再现的稳态场分布称为开腔的 自再现模 。 9. 对平面波阵面而言，从一个镜面中心看到另一个镜面上可以划分的菲涅耳半周期 带的数目称为 菲涅耳数 。

3 10. 均匀加宽指的是引起加宽的物理因素对各个原子是 等同的, 。 11. 入射光强和饱和光强相比拟时，增益随入射光强的增加而减少，称 增益饱和 现 象。 12．方形镜的mnq TEM 模式沿x 方向有 m 条节线，没y 方向有 n 条节线. 二.单项选择题（每题2分，共10分） 1. 关于高斯光束的说法，不正确的是（ ） (A)束腰处的等相位面是平面； (B)无穷处的等相位面是平面； (C)相移只含几何相移部分； (D)横向光强分布是不均匀的。 2. 下列各模式中，和圆型共焦腔的模q n m TEM ,,有相同频率的是（A ） (A)1,,2-+q n m TEM ； (B) q n m TEM ,,2+； (C) 1,,1-+q n m TEM ； (D) 1,1,2-++q n m TEM 。 3. 下列各种特性中哪个特性可以概括激光的本质特性（C ） (A)单色性； (B)相干性； (C)高光子简并度； (D)方向性。 4. 下列加宽机制中，不属于均匀加宽的是（B ） (A)自然加宽； (B)晶格缺陷加宽； (C)碰撞加宽； (D)晶格振动加宽。 5. 下列方法中，不属于横模选择的是（D ） (A)小孔光阑选模； (B) 非稳腔选模； (C) 谐振腔参数N g ,选择法； (D)行波腔法。 三、简答题（每题4分，共20分）

激光原理试题

1） CO2激光器的腔长L=100cm ，反射镜直径D=，两镜的光强反射系数分别为r1=,r2=。求由衍射损耗及输出损耗分别引起的c c Q υτδ?,,，。(设n=1) 2） 红宝石调Q 激光器中有可能将几乎全部的Cr+3激发到激光上能级，并产生激光巨脉冲。设红宝石棒直径为1cm ，长为，Cr+3的浓度为39cm 102-?2 ， 脉冲宽度10ns ，求输出激光的最大能量和脉冲功率。 3） 氦氖激光器放电管长l=，直径d=，两镜反射率分别为100%、98%，其它单程损耗率为，荧光线宽MHz 1500d =?υ。求满足阈值条件的本征模式数。（d G 1 1034 m -?=） 4） 入射光线的坐标为r1=4cm ，1=弧度,求分别通过焦距大小都为F=的凸、凹透镜后的光线坐标。 5） 有一个凹凸腔，腔长L=30cm ，两个反射镜的曲率半径大小分别为R1= 50cm 、R2=30cm ，如图所示，使用He-Ne 做激光工作物质。①利用稳定性 条件证明此腔为稳定腔 ②此腔产生的高斯光束焦参数 ③此腔产生的高斯 光束的腰斑半径及腰位置 ④此腔产生的高斯光束的远场发散角。 6） 某激光器（m 9.0μλ==）采用平凹腔，腔长L=1m ，凹面镜曲率半径R=2m 。求①它产生的基模高斯光束的腰斑半径及腰位置②它产生的基模高斯光束的焦参数③它产生的基模高斯光束的远场发散角 答案

1）解： 衍射损耗: 188.0)1075.0(1 106.102 262=???==--a L λδ s c L c 8 81075.110 3188.01-?=??== δτ 6 86 81011.31075.1106.1010314.322?=??????==--c Q πντ MHz Hz c c 1.9101.91075.114.321 2168 =?=???= = ?-πτν 输出损耗: 119.0)8.0985.0ln(5.0ln 212 1=??-=-=r r δ s c L c 881078.210 3119.01 -?=??== δτ 6 86 8 1096.41078.2106.1010314.322?=??????==--c Q πντMHz Hz c c 7.5107.510 78.214.32121 6 8 =?=???= = ?-πτν 2）解： 10 8 34 152210694310310 6.631020.0750.0053.14--??? ??????===ν?πν?h L r V h W J 9103.4-?= W t W P 34.010 10104.39 9 =??==-- 3)解：025.0015.02 02.0015.02 =+=+=T δ mm l G t /1105500 025.05-?===δ mm d G m /11025 .110310344 4 ---?=?=?= 410 510254 =??==--t m G G α MHz D T 21212 ln 4 ln 15002ln ln =?=?=?α νν MHz L c q 3005 .0210328=??==?ν 8]1300 2121 []1[ =+=+??=?q T q νν

激光原理与技术习题一

《激光原理与技术》习题一 班级 序号 姓名 等级 一、选择题 1、波数也常用作能量的单位，波数与能量之间的换算关系为1cm -1 = eV 。 （A ）1.24×10-7 (B) 1.24×10-6 (C) 1.24×10-5 (D) 1.24×10-4 2、若掺Er 光纤激光器的中心波长为波长为1.530μm ，则产生该波长的两能级之间的能量间 隔约为 cm -1。 （A ）6000 (B) 6500 (C) 7000 (D) 10000 3、波长为λ=632.8nm 的He-Ne 激光器，谱线线宽为Δν=1.7×109Hz 。谐振腔长度为50cm 。假 设该腔被半径为2a=3mm 的圆柱面所封闭。则激光线宽内的模式数为 个。 （A ）6 (B) 100 (C) 10000 (D) 1.2×109 4、属于同一状态的光子或同一模式的光波是 . (A) 相干的 (B) 部分相干的 (C) 不相干的 (D) 非简并的 二、填空题 1、光子学是一门关于 、 、 光子的科学。 2、光子具有自旋，并且其自旋量子数为整数，大量光子的集合，服从 统计分布。 3、设掺Er 磷酸盐玻璃中，Er 离子在激光上能级上的寿命为10ms ，则其谱线宽度为 。 三、计算与证明题 1．中心频率为5×108MHz 的某光源，相干长度为1m ，求此光源的单色性参数及线宽。 2．某光源面积为10cm 2，波长为500nm ，求距光源0.5m 处的相干面积。 3．证明每个模式上的平均光子数为 1 )/exp(1 kT hv 。

《激光原理与技术》习题二 班级 姓名 等级 一、选择题 1、在某个实验中，光功率计测得光信号的功率为-30dBm ，等于 W 。 （A ）1×10-6 (B) 1×10-3 (C) 30 (D) -30 2、激光器一般工作在 状态. (A) 阈值附近 (B) 小信号 (C) 大信号 (D) 任何状态 二、填空题 1、如果激光器在=10μm λ输出1W 连续功率，则每秒从激光上能级向下能级跃迁的粒子数 是 。 2、一束光通过长度为1m 的均匀激励的工作物质。如果出射光强是入射光强的两倍，则该物 质的增益系数为 。 三、问答题 1、以激光笔为例，说明激光器的基本组成。 2、简要说明激光的产生过程。 3、简述谐振腔的物理思想。 4、什么是“增益饱和现象”？其产生机理是什么？ 四、计算与证明题 1、设一对激光能级为2E 和1E (设g 1=g 2)，相应的频率为ν(波长为λ)，能级上的粒子数密度分 别为2n 和1n ，求 (a) 当ν=3000MHz ，T=300K 时，21/?n n = (b) 当λ=1μm ，T=300K 时，21/?n n = (c) 当λ=1μm ，21/0.1n n =时，温度T=？ 2、设光振动随时间变化的函数关系为 （v 0为光源中心频率）， 试求光强随光频变化的函数关系，并绘出相应曲线。 ???<<=其它,00),2exp()(00c t t t v i E t E π

不得不看的激光原理试题测验必备

不得不看的激光原理试题测验必备

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激光原理复习题(页码是按第五版书标注的，黄色底纹的页码是按第六版书标注的) 填空 6424''?= 简答 6636''?= 计算 121527'''+= 论述 11313''?= 1.什么是光波模式和光子态？什么是相格？Page5 答：光波模式(page5):在一个有边界条件限制的空间V 内，只能存在一系列独立的具有特定波矢k 的平面单色驻波。这种能够存在于腔内的驻波（以某一波矢k 为标志）称为光波模式。 光子态(page6):光子在由坐标与动量所支撑的相空间中所处的状态,在相空间中，光子的状态对应于一个相格。 相格(page6):在三维运动情况下，测不准关系为3 x y z x y z P P P h ??????≈，故在六位相空间中，一个光子态对应（或占有）的相空间体积元为3x y z x y z P P P h ??????≈，上述相空间体积元称为相格。 2.如何理解光的相干性？何谓相干时间、相干长度、相干面积和相干体积？Page7 答：光的相干性(page7):在不同的空间点上、在不同的时刻的光波场的某些特性的相关性。 相干时间(page7)：光沿传播方向通过相干长度c L 所需的时间，称为相干时间。 相干长度：相干光能产生干涉效应的最大光程差，等于光源发出的光波的波列长度。 ?相干面积： 相干体积(page7)：如果在空间体积c V 内各点的光波场都具有明显的相干性，则c V 称为相干体积。 3.何谓光子简并度，有几种相同的含义？激光源的光子简并度与它的相干性什么联系？Page9 答：光子简并度(page9)：处于同一光子态的光子数称为光子简并度。 光子简并度有以下几种相同含义(page9)：同态光子数、同一模式内的光子数、处于相干体积内的光子数、处于同一相格内的光子数。 联系：激光源的光子简并度决定着激光的相干性，光子简并度越高，激光源的相干性越好。 4.什么是黑体辐射？写出Planck 公式,并说明它的物理意义。Page10 答：黑体辐射(page10)：当黑体处于某一温度T 的热平衡情况下，它所吸收的辐射能量应等于发出的辐射能量，即黑体与辐射场之间应处于能量（热）平衡状态，这种平衡必然导致空腔内存在完全确定的辐射场，这种辐射场称为黑体辐射或平衡辐射。 Planck 公式(page10)：33 81 1 b h k T h c e ννπνρ=- 物理意义(page10)：在单位体积内，频率处于ν附近的单位频率间隔中黑体的电磁辐射能量。 5.描述能级的光学跃迁的三大过程，并写出它们的特征和跃迁几率。Page10 答：(1)自发辐射 过程描述(page10)：处于高能级2E 的一个原子自发的向1E 跃迁，并发射一个能量为h ν的光子，这种过程称为自发跃迁，由原子自发跃迁发出的光波称为自发辐射。 特征：a) 自发辐射是一种只与原子本身性质有关而与辐射场νρ无关的自发过程,无需外来光。b) 每个发生辐射的原子都可看作是一个独立的发射单元，原子之间毫无联系而且各个原子开始发光的时间参差不一，所以各列光波频率虽然相同，均为ν，各列光波之间没有固定的相位关系，各有不同的偏振方向，而且各个原子所发的光将向空间各个方向传播，即大量原子的自发辐射过程是杂乱无章的随机过程，所以自发辐射的光是非相干光。 自发跃迁爱因斯坦系数：211 s A τ= (2)受激吸收 过程描述(page12)处于低能态1E 的一个原子，在频率为ν的辐射场作用（激励）下，吸收一个能量

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