Active laser resonator performance: formation ofa specified intensity output
Tatyana Yu. Cherezova, Sergei S. Chesnokov, Leonid N. Kaptsov, Vadim V. Samarkin,and Alexis V. Kudryashov
We discuss the formation of a specified super-Gaussian intensity distribution of a fundamental mode bymeans of an intracavity controlled mirror, which is a water-cooled bimorph flexible mirror equipped withfour controlling electrodes. Analysis has confirmed the possibility to form fourth-, sixth-, and eighth-order super-Gaussian intensity distributions at the output of the stable resonators of industrial cw CO2
For laser applications in material processing andmanufacturing, nonlinear conversion of a beam witha uniform rectangular cross section is preferred.1,2
Examples of such beams are highly multimode,3 flat-tened Gaussian,4,5 and super-Gaussian.6,7
A specified laser intensity distribution can gener-ally be formed with either extracavity8 or intracavity9
mirrors. The main advantages of intracavity meth-ods are not only the possibility to form a desirableintensity structure but also to increase the power oflaser radiation. One of the well-known approachesis to apply graded reflectivity mirrors,7 but such mir-rors introduce sufficient intrinsic power losses suchthat they can be used only in lasers with large gain ofthe active medium �mostly with unstable resonators�.It was then suggested that graded-phase mirrors10,11
be used in stable laser cavities for specified intensityoutput formation. But such a mirror can only be
used for the specific applications for which they weredesigned. Each change in laser parameter wouldneed its own unique mirror. In contrast, with thehelp of just one flexible controlled mirror it would bepossible to form a number of given laser outputs. Itis also possible to compensate for different phase dis-tortions caused, for example, by thermal deformationof laser mirrors or by aberrations of the active me-dium. Such phase distortions could destroy thegiven laser output intensity distribution, and it is notpossible to predict them because some distortions de-pend, for example, on the pumping power and theinhomogeneity of the active medium, which is why itis more universal and prospective to use flexible con-trolled mirrors to perform different tasks.
2. Flexible Mirror Design
For the formation of a specified laser output we useda flexible mirror composed of a semipassive bimorphelement,12 designed and fabricated by the AdaptiveOptics Group of the Institute on Laser and Informa-tion Technologies of the �IPLIT� Russian Academy ofSciences. A bimorph element consists of two thinlayers of piezoceramic polarized normally to theirsurfaces. Applied voltage causes tension of the topplate and compression of the bottom plate, resultingin deformation of the reflective surface. The manu-facture of this type of flexible mirror proved that themost convenient to develop is a semipassive bimorphcorrectors.12 A traditional semipassive bimorphmirror consists of two plates: a comparatively thick
T. Yu. Cherezova, S. S. Chesnokov, and L. N. Kaptsov are withthe Department of Physics, Moscow State University, VorobyovyGory, Moscow 119899, Russia. V. V. Samarkin and A. V. Kudr-yashov �[email protected]� are with the Adaptive Optics for Industrialand Medical Applications Group, Institute on Laser and Informa-tion Technologies, Russian Academy of Sciences, Svyatoozerskya1, Shatura 140700, Russia.
Received 10 July 2000; revised manuscript received 26 June2001.
passive glass or metal substrate and a thin activepiezoceramic plate. The operation of a semipassivebimorph corrector is similar to that for a bimorphcorrector except that it is less sensitive.
For our research we designed the semipassiveadaptive mirror shown in Fig. 1. The mirror con-sists of a copper plate �Fig. 2� firmly glued to a planeactuator disk made from piezoelectric ceramic. Theactuator disk consists of two piezoceramic disks, sol-dered together and polarized normally to their sur-faces. The thickness of each piezoceramic disk is0.35 mm, and the thickness of the copper plate is 2.5mm. The interface between the two piezoceramicdisks contains a continuously conducting groundelectrode. Another continuously conducting elec-trode between the piezodisk and the copper plate, e1,was used to control the curvature of the whole mirror.Three controlling electrodes �one round, e2, and tworinglike, e3 and e4� were attached to the outer surfaceof the piezodisk. The mirror has a waffle-type cool-ing system inside the copper substrate.12
We measured the response function of each elec-trode of the bimorph mirror �the deformation of the
mirror surface that occurred while we applied voltageto each electrode� by using a modified Fizeau inter-ferometer13 with the procedure described in Section3.
3. Algorithm of a Specified Intensity Formation by useof an Intracavity Bimorph Flexible Mirror
The algorithm and numerical results are discussedon the basis of a stable laser cavity �Fig. 3�. Such acavity corresponds to an industrial fast axial flowcontinuous discharge CO2 laser, TLA-600, producedby the IPLIT of the Russian Academy of Sciences.14
The laser resonator �Fig. 3� consists of a plane outputcoupler, a CO2 tube, a convex mirror, a concave mir-ror, and a bimorph flexible mirror.
For the output corrector we determined the speci-fied field distribution, the so-called super-Gaussianfunction, and defined it as
�1�r1� � E0 exp���r1
�� �� , (1)
where E0 is the maximum value of the function �forsimplicity E0 � 1�, � is the scale factor, r1 is the radialcoordinate �we assume azimuthal symmetry�, is theorder of the super-Gaussian function related to therapidity of the transition from the maximum value tothe zero. For � 2 a super-Gaussian reduces to aGaussian function, whereas the higher the , the flat-ter the top of the profile.
To calculate the propagation of the beam Eq. �1��through all the elements of the laser resonator weused Huygens–Fresnel integral equations15–17 andtook into consideration that the beam in Eq. �1� sat-isfies all the necessary assumptions for validHuygens–Fresnel integrals.15 As is well known,15
the electromagnetic field could be presented by a sca-lar function ��r, �� representing the cross section ofthe field distribution. For azimuthal symmetry,such a function depends only on coordinate r, ��r��.
Fig. 1. Photograph of the mirror sample. Each of eight electrodesegments were connected to reproduce a ringlike electrode.
Fig. 2. Construction of the bimorph deformable mirror and aschematic of its electrodes.
Fig. 3. Experimental setup of the formation of the super-Gaussian TEM00 mode: 1, block of mirror electrode control; 2,semipassive bimorph mirror; 3, diaphragm; 4, concave mirror R �2200 mm; 5, convex mirror R � �800 mm; 6, active medium ofCO2; 7, ZnSe output mirror with a 69% coefficient of reflectivity; 8,LBA-2A �laser beam analyzer�; 9, oscilloscope; 10, computer; 11,lens f � 275 mm; 12, MAC-2 �mode analyzer computer�.
As a result we know the field distribution �2�r2� atthe position of the flexible mirror:
2�2�r2� � �0
b
K1�r1, r2��1�r1�r1dr1, (2)
where
K1�r1, r2� � 2�j
�BJ0�k
r1 r2
B �exp��jk2B
� Ar12
� Dr22��H�I�; (3)
2 is the eigenvalue; �1�r1� and �2�r2� are, respec-tively, the eigenmodes at the surface of the plane andthe flexible mirror; ri are the radial coordinates; indexi � 1 is related to the plane output mirror of diameter2b; i � 2 is related to the active mirror of diameter 2a;J0 is the Bessel function of zero order; k � 2���,where � is the laser wavelength; A, B, and D are theconstants determined by the ABCD ray matrix of thelaser resonator; H�I� is the additional multiplier18
that takes into account the saturation of an activemedium by an intensive beam:
H�I� � �1 �g0 Lam
2�1 �I�r�
Is�� , (4)
where g0 is the small-signal gain coefficient, g0 � 110cm�1, for this particular type of laser14; Lam is thelength of the active medium �Lam � 80 cm�; I�r� is thetransverse intensity distribution of the laser beam;and Is is the saturation intensity Is � 110 W�mm2.If the intensity of laser beam I�r� is comparable withIs �saturation intensity of the active medium�, theintensity of the complete laser beam is lower.
At the position of the flexible mirror the wave frontof the laser beam was extracted and was used todetermine the appropriate shape of the bimorph flex-ible mirror �mirror�r2�. Such a surface profile wasreconstructed with a minimal rms error when wecombined the experimentally measured responsefunctions of the mirror with appropriate weights.The weights correspond to the voltages to be appliedto each mirror electrode. We then found the stablefield distribution at the output mirror by iterativelysolving Eq. �2� together with the Huygens–Fresnelintegral equation,
1�1�r1� � �0
a
K2�r2, r1��2�r2�r2dr2, (5)
where
K2�r2, r1� � 2�j
�BJ0�k
r1 r2
B �� exp��
jk2B
� Ar12 � Dr2
2��� exp jk�mirror�r2��H�I�. (6)
Here �mirror�r2� is a phase shift added to the phase ofa beam reflected from the flexible mirror.
For infinity mirrors and for a flexible mirror thatideally reproduces the phase of the desired beam, wedo not need to make such numerical calculations ofthe resultant field distribution formed by our intra-cavity flexible mirror because it is a super-Gaussianprofile see Eq. �1��. But inasmuch as the mirrors ofa laser resonator are finite and flexible mirrors re-produce the phase of the beam with some error, theoutput distribution might differ from the initialsuper-Gaussian function and we must find it by iter-atively solving Eqs. �2�–�5�.
4. Formation of a Super-Gaussian Output Beam with aCO2 Laser
A. Results of the Numerical Calculations
The main parameters of the laser resonator of the CO2laser shown in Fig. 3 are Fresnel numbers, N1 � b2��B � 0.66 and N2 � a2��B � 6.47, and the stabilityfactor G � 0.51. �Here b � 8 mm is the radius of theplane output coupler, a � 25 mm is the radius of theactive bimorph mirror, � � 10.6 �m is the wavelength,and B � 9104 mm is the effective length of the reso-nator.� Parameters of the super-Gaussian functionEq. �1�� were chosen as E0 � 1, � � 4.8 and 5.1 mm for � 4 and 6, respectively. The particular beam waistswere chosen according to the theory of moments andare well-described in Ref. 19. For this laser we canassume that H�I� � const, because the intensity of thebeam is much smaller than the saturation intensity Isof the active medium. According to the algorithm de-scribed in Section 3 we were able to calculate the volt-ages to be applied to the mirror electrodes to form thesuper-Gaussian beams �see Table 1�.
Figure 4 shows the evolution of a fourth-order super-Gaussian beam at the surface of an output mirror aftera number of round-trip calculations. Curve 1 repre-sents the initial beam; curves 2–11 represent the beamprofiles after the corresponding number of even passes�round trips� calculated with Eqs. �2�–�5�. To achievethe parameters of the resonator mentioned above, weneed to make approximately 130 iterations to gain anaccuracy of 10�7 for the calculations. Figure 5 showsthe main results of the calculations: curve 1, Gauss-ian mode; curve 2, super-Gaussian fundamental modeintensity distributions of the fourth order and the sixthorder of the plane output mirror. Far-field pattern ofthe calculated super-Gaussian beam is shown in Fig.6�a�. As one can see it is possible to increase the peakvalue of the intensity in the far field by 1.6 times in
Table 1. Voltages Applied to Electrodes of Flexible Mirrors to FormSuper-Gaussian Beams
comparison with the Gaussian TEM00 mode of the res-onator. At the same time the sidelobes of the inten-sity distribution appear in the far field. But as can beseen from curve 1 in Figs. 7�a� and 7�b�, the sidelobesare not significant so that the M2 factor of the fourth-
order super-Gaussian mode is M2 � 1.36. Note that,for an ideal fourth-order super-Gaussian beam withthe same near-field beam waist of � � 4.8 mm, the M2
factor is generally higher, M2 � 1.46, as illustrated bycurve 2 in Fig. 7, which also shows that the wholewidth of the beam in the far field increases because ofthe sidelobes. For sixth-order super-Gaussian beamsthe difference is higher, that is, for the beam formed bya flexible mirror it is M2 � 1.38, for an ideal beam it isM2 � 1.8. Therefore, the fact that our corrector doesnot reproduce an ideal super-Gaussian function in thenear field �Fig. 4� results in a positive effect in far-fieldreduction of sidelobes and improves the M2 factor.We define the M2 factor based on the InternationalStandard20 ISO 11146, which is M2 � �d0���4��,where � is the wavelength, d0 is the near-field waistdiameter calculated as a second-moment intensity dis-tribution at the waist location �in our case at the planeof the output resonator mirror�,
d0 � 2�2�� r2I�r, z�rdrd�
�� I�r, z�rdrd�
;
Fig. 4. Evolution of the fourth-order super-Gaussian beam at thesurface of an output mirror: 1, initial beam; 2, beam after oneround trip; 3, beam after two round trips; 4, beam after three roundtrips, etc.; 11, beam after ten round trips.
Fig. 5. �a� Formation of the fourth-order super-Gaussian fundamental mode: 1, Gaussian; 2, theoretically obtained; 3, experimentallyobtained. �b� Formation of the sixth-order super-Gaussian fundamental mode: 1, Gaussian; 2, theoretically obtained; 3, experimentallyobtained.
Fig. 6. Far-field patterns of a laser beam: �a� theory of the fourth-order super-Gaussian modes, �b� experimental results of the GaussianTEM00 mode, �c� experimental results of the super-Gaussian fourth-order TEM00 mode.
� is the divergence angle defined as � � df�f, with f asthe focal length of the lens in the focal plane for whichwe calculate the beam width df as the second-ordermoment of the focal plane intensity distribution
If�r, z�,
df � 2�2�� r2If�r, z�rdrd�
�� If�r, z�rdrd�
.
B. Experimental Results
The experimental setup to form super-Gaussianbeams is shown in Fig. 3. To apply voltages to theelectrodes of a flexible mirror we used the mirrorcontrol block, 1 in Fig. 3. The near-field intensitydistribution was achieved with the laser beam ana-lyzer, LBA-2A, �8 in Fig. 3� and the far-field patternin the focal plane of lens f � 275 mm �11 in Fig. 3� wasanalyzed with the mode analyzer computer, MAC-2,�12 in Fig. 3�. The result of the experimental forma-tion of a fourth-order super-Gaussian beam is pre-sented as curve 3 in Fig. 5�a�. The super-Gaussianintensity distribution appeared when we applied thevoltages listed in Table 1. The power of the super-Gaussian beam was approximately 10% higher thanfor the Gaussian beam and the waist widened by asmuch as 1.26 � 0.05. The calculations indicatedthat the beam waist should have increased by asmuch as 1.29 times. In the focal plane of the lens �11in Fig. 3� the far-field peak intensity value of theGaussian mode is shown in Fig. 6�b�. The amplitudeof the far-field intensity distribution of a fourth-ordersuper-Gaussian beam Fig. 6�c�� increases by 1.6times compared with a Gaussian beam, which is ingood agreement with the theory; see Fig. 6�a�. Theshape of the far-field pattern becomes narrower, butthe sidelobes that should exist are not visible at noiselevel. The experimental formation in the near-field
of the sixth-order super-Gaussian beam is shown inFig. 5�b�, curve 3. In this case we had a 12% powerincrease in comparison with that of a Gaussian fun-damental mode. We obtained a far-field pattern ofthe super-Gaussian mode that is similar to a fourth-order mode.
5. Formation of a super-Gaussian Output Beam with aYAG:Nd3� Laser
Here we report the results of our investigation of thepossibility of forming a specified intensity output of astable resonator with a YAG:Nd3� laser. All the ac-tive mirrors have a large aperture with diameters of20 mm or larger. It is difficult to use such deform-able mirrors in the cavities of industrial cw solid-state lasers because of the relatively small aperturesin stable resonator beams. We suggest expansion ofthe beam inside a laser cavity to a diameter of theadaptive mirror by using a meniscus on one end of theactive element21 �Fig. 8�. At the same time the ac-tive mirror would have a concave spherical profile.Such a laser resonator allows us to use wide aperturemirrors without supplementary optical elements andtherefore without undesirable loss. We consideredthe possibility of forming a super-Gaussian laser out-put with this type of laser resonator with the follow-ing parameters: Fresnel numbers of N1 � b2\B� �0.3 and N2 � a2\B� � 12.3 and a geometric factor ofG � 0.58. Here 2a � 20 mm is the diameter of thebimorph deformable mirror, 2b � 6 mm is the diam-eter of the plane output mirror, � � 1.06 �m is thewavelength, B � 6200 mm is the effective length of
Fig. 7. Normalized far-field intensity distributions: �a� 1, fourth-order super-Gaussian formed by a flexible mirror �with near-field waist� � 4.8 mm�; 2, ideal fourth-order super-Gaussian mode �� � 4.8 mm�; 3, Gaussian beam �� � 4.8 mm�. �b� Fragment of the intensitydistributions in �a�.
Fig. 8. Layout of a telescope-type stable resonator of a YAG:Nd3�
laser with a wide-aperture mirror: 1, output coupler; 2, activemedium; 3, thermal lens; 4, meniscus; 5, bimorph flexible mirror.
the telescope-type resonator �Fig. 8�; and A, B, and Dare the elements of the ABCD ray matrix of the laserresonator.
Figure 9 shows the main results of the diffractioncalculations. Curve 1 represents the Gaussian fun-damental TEM00 mode on the resonator output, andcurve 2 shows a fourth-order super-Gaussian beamprofile. Our calculations show that the mode vol-ume of the super-Gaussian beams increases by a fac-tor of 2.1–2.2, the diffraction losses decrease by 1.1–1.2 times and the far-field peak intensity increases bya factor of 2 in comparison with the Gaussian TEM00mode. The mode volume was estimated as the inte-gral from a transverse intensity distribution overtransverse coordinates at five places inside the cavityand at the mirrors as well. Power losses were cal-culated as � � 1 � 1 2. The voltages necessary forthe formation of super-Gaussian beams are listed inTable 2.
6. Influence of Thermal Deformation of a ResonatorMirror on the Formation of a Specified Laser Output
We now present the results of our investigation of theself-consistent problem of the influence of output�passive� mirror thermal deformation on the forma-tion of a specified transverse field distribution of alaser beam. We also discuss the active correctiontechnique to compensate for beam distortions.
Output beams are known to depend on differentphase distortions inside a laser cavity, which is whyit is necessary to control all the aberrations that candegrade beam formation performance. One of themost important sources of phase aberration is ther-
mal deformation of a mirror surface caused by theabsorption of laser radiation.
Because of the significant difference between ther-mal expansion coefficients of a piezoceramic and thesubstrate material an uncooled bimorph mirror has aconsiderable amount of thermal deformation. Toavoid this problem we used a bimorph mirrorequipped with a cooling system.12 The interferomet-ric measurements of a cooled mirror illuminated by alaser beam with 2.5-kW�cm2 power density showedno thermal deformation.12 That is why we take intoaccount only the output �passive� noncooled mirrorfor the numerical simulations of thermal deformationon the formation of a specified transverse field distri-bution.
First, we calculated the temperature distributionof a mirror illuminated by a specified beam. Weused a round glass plate mirror warmed by a beamwith azimuthal symmetry and formed by an intra-cavity active mirror. The analysis was based on thefollowing hypotheses: the laser beam is partially ab-sorbed only by the dielectric reflective coatings of themirror; the thermal flux on the border between coat-ings and air is neglected because the thermal conduc-tivity of glass is greater than ten times that of thethermal conductivity of air; the reflective coatings donot influence the elastic properties of the mirror; themirror substrate is not affected by any forces; ther-mal conductivity coefficient �, the linear thermal ex-pansion coefficient �, the Poisson coefficient � for thematerial of the mirror substrate are all independentof temperature; deformation does not influence thetemperature; the temperature of the side borders ofthe substrate is constant and is equal to the roomtemperature �for simplicity room temperature waszero�; and the temperature is stable. According tothese assumptions we can use the steady-state heatconduction equation:
�T � 0, (7)
with boundary conditions of
��T
�z
z�z0�2
� k1 I�r�, (7a)
T�r0, z� � 0, (7b)
T�r0, �z0�2� � 0. (7c)
Here k1 is the absorption coefficient of reflective mir-ror coatings. �The coefficient was measured experi-mentally and equals 5.6 � 10�4 for the output mirrorwith a 99.8% reflectivity coefficient.� I�r� is the in-cident specified intensity distribution formed by aflexible mirror �the intracavity power of the laserbeam is 160 W�, � is the thermal conductivity �1.36W�m�K for the quartz glass at 300 K�, r0 � 2 mm isthe radius of the mirror, z0 � 1 cm is the mirrorthickness, z � z0�2 corresponds to the front surface ofthe mirror and z � z0�2 corresponds to the rear of themirror.
Equation �7a� shows that the thermal flux though
Fig. 9. Formation of the super-Gaussian fundamental modes atthe output of a YAG:Nd3� laser stable resonator: 1, Gaussianmode; 2, fourth-order super-Gaussian mode.
Table 2. Voltages Applied to Electrodes of Flexible Mirrors to FormSuper-Gaussian TEM00 Modes at the Output of a YAG:Nd3� Laser
Type ofBeam Exp��r�0.94�4� Exp��r�0.98�6� Exp��r�1.1�8�
the exposed surface is equal to the intensity k1I�r�absorbed by the reflective coatings of the mirror.Equations �7b� and �7c� determine the constant tem-perature on the side and rear surfaces of the mirror.The solution for Eq. �7� is given by
T�r, z� � �k�1
�
J0��k0r�Ak sh� k z� � Bk ch� k z��, (8)
where coefficients Ak and Bk are determined from theboundary conditions; J0 is the zero-order Bessel func-tion, k � �k
0z0�r0, and �k0 is the root of the equation
J0��k0� � 0. All the coordinates in Eq. �8� were nor-
malized on radius r0 and thickness z0 of the mirrorsubstrate.
The displacements of the mirror substrate in theaxial W�r, z� and radial U�r, z� directions were deter-mined from the following system of equations22,23:
�U �Ur2 �
11 � 2�
�E�r
�2�1 � ��
1 � ��
�T�r
� 0,
�W �1
1 � �
�E� z
�2�1 � ��
1 � 2��
�T� z
� 0, (9)
where
E ��U�r
�Ur
��W� z
.
An approximate solution of Eq. �9� is given by23
W�r, z� � �z0�1 � �� �k�1
�
J0��k0r�
� Bk sh� k z� � Ak ch� k z��� k
� 6�r0�1 � ���1 � r2� �k�1
�
J1��k0�
� Ak k ch� k�2� � 2sh� k�2��� k3. (10)
The calculated displacement of mirror W�r, z� is thenused as an additional multiplier of the kernel Eq. �3��� t�r� � exp2jkW�r��.
To calculate the influence of the output �passive�mirror thermal deformation on the formation of aspecified transverse field distribution of a laser beam,we proceeded with the following steps:
�a� Calculation of the specified laser output in theresonator with a deformable mirror according to theprocedure described in Section 3.
�b� Determination of the thermal deformation ofthe output mirror of the laser resonator warmed bythe beam calculated in �a�.
�c� Calculation of the steady-state field distributionof the resonator with the thermally distorted outputmirror and active mirror �shaped to form a super-Gaussian beam� according to the Fox and Li meth-od.16,17
Steps �b� and �c� are repeated until the stationaryfield distribution is obtained.
To examine a possible compensation for the distor-
tion of a specified intensity distribution caused bythermal deformation of the output mirror we re-peated �a� and �b� as listed above and then proceededwith the following:
�c� Calculation of the propagation of a specifiedlaser beam back through all the elements �includingthe thermally deformed mirror� to the position of aflexible corrector.
�d� Extraction and compensation of the shape of thewave front of the beam and simultaneous reproduc-tion of the necessary wave-front shape of the beamwith a bimorph mirror;
�e� Calculation of the stationary field distributionformed in the resonator with the new shape of de-formable mirror and a thermally deformed outputcoupler.
Steps �b�–�e� are repeated until the stationary fielddistribution of a laser mode is reached.
The main results of the calculations are given inFig. 10. Curve 1 represents a fourth-order super-Gaussian beam formed by a flexible corrector at theoutput coupler without thermal deformation. Curve2 shows the distortions of the intensity distributioncaused by thermal deformation of the output mirror.Curve 3 illustrates the intensity distribution withphase aberration compensation caused by thermaldeformation of the output coupler with the help of abimorph deformable mirror. One can see that thedeformable mirror could partially compensate for thedistortions caused by intensity distribution.
6. Conclusion
We have shown that it is possible to form super-Gaussian intensity output of a laser resonator withYAG:Nd3� and CO2 lasers with an intracavity flexi-ble mirror. The experiment with a cw CO2 lasershowed that, by remaining in the TEM00 regime, wewere able to increase the total power by 10–12% and
Fig. 10. Super-Gaussian TEM00 mode at the plane output couplerof a telescope-type YAG:Nd3� laser stable resonator: 1, withoutthermal deformations of the output coupler; 2, with distortions ofthe intensity distribution caused by thermal deformation of theoutput mirror; 3, with phase aberration corrections caused by ther-mal deformations with a bimorph flexible mirror.
to enlarge the peak intensity value in the far field byas much as 1.6 times compared with the Gaussianfundamental mode. We studied the influence ofthermal deformations of the output mirror on theshape of the given intensity distribution. We havereported the possible partial compensation of the dis-tortion of a given laser beam caused by thermal de-formation of the output coupler with an intracavitybimorph mirror. We believe that an opportunitynow exists for the creation of intelligent flexible la-sers to generate intensity distributions specified bythe user.
The authors thank P.-A. Belanger and C. Pare ofLaval University, Quebec, Canada, for their helpfuldiscussions with regard to this study. This researchwas partly supported by grant DERA-NICTL ELM1158.
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