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Variable reflectivity mirror unstable resonator with deformable mirror thermal compensation
cm .__
15 January
lli!l
1996
e
OPTICS COMMUNICATIONS
__
EISEVJER
Optics Communications
123 (1996)
115-120
Variable reflectivity mirror unstable resonator with deformable mirror thermal compensation N. Pavel, T. Dascalu, V. Lupei Institute
ofAtomic Physics, IFTAR-MAWRM
Department, P.O. Box MG-6, Bucharest RO-76900, Romania
Received 3 1 May 1995
Abstract
For thermal lensing compensation of a Nd:YAG rod, placed in different positive-branch unstable resonators with superGaussian reflectivity profile of the output mirror, a deformable thin glass plate was used as the rear mirror. Unstable resonators with magnifications of M= 1.5 and M= 1.8 were designed for 0.8 mm. mrad value of the beam quality. For unloaded resonators the output energies of a laser working at 10 Hz repetition rate and pump energies up to 50 J per pulse were close to those obtained for 1 Hz repetition rate.
1. Introduction Unstable resonators that use radial variable-reflectivity mirrors as output couplers have been demonstrated to be particularly successful for generation of high-energy diffraction limited beams with a smooth transverse profile [ l-71. By a suitable technology based on vacuum deposition of dielectric thin films on a transparent substrate, different reflectivity profiles such as: parabolic, super-parabolic and super-Gaussian were obtained [ 8-121. The mirror reflectivity profile can be designed to provide an optimum balance between the energy and the beam quality of the laser output. Due to the sensitivity of resonator properties to the thermal lensing of the active media, unstable resonators were initially used in single shot operation or in Qswitched systems with low average output power. However, recently it has been demonstrated that the unstable resonators can be used in high power solidstate lasers if the resonator is properly designed. These new unstable resonator configurations are: (i) the “rod 0030-4018/96/$12.00 0 1996 Elsevier Science B.V. All rights reserved SSD10030-4018(95)00468-8
imaging unstable resonator” [ 131 and (ii) the “nearconcentric unstable resonator” [ 141. From a pulsed Nd:YAG laser, output beams with divergence about twenty times lower than that obtained with a multimode stable resonator at an average power of 200 W have been obtained in first configuration. The second configuration is characterised by a much lower sensitivity to thermal lensing as compared to other unstable resonator schemes: a maximum output power of 420 W and beam parameter products below 3 mm. mrad have been reported on a pulsed Nd:YAG laser [ 141. In this paper the results on output beam characteristics obtained from Nd:YAG positive-branch unstable resonators with super-Gaussian reflectivity profile of the output mirrors and thermal lens compensated by a deformable rear mirror are presented. This method of thermal lens compensation was used before in CO, stable resonator [ 151 and in Nd:YAlO, stable and unstable configuration [ 161. Here we report the results on this thermal lens compensation method in unstable resonators with output mirror of super-Gaussianreflectivity profile. This technique proves suitable for the
116
N. Pave1et al. /Optics
Communications
resonator configurations used in our experiments: plane output mirror and convex totally reflectivity rear mirror. The possibility of obtaining concave radius of the deformable membrane is also discussed.
2. Resonator design The schematic unstable configuration used in investigation is presented in Fig. 1. The resonator with an internal variable lens with refractive power D has the same mode properties across the mirrors as the equivalent resonator with stability parameters g* and length L* given by gi”=gi-Ddj(l-di/pi),
i,j=l,
2
i#j,
L*=dl+d2-Ddldz,
(1) (2)
where gi = 1 - ( dl + d2) /pi is the stability parameter for an empty resonator (D = 0)) pi is the curvature radius of mirror i, di is the distance between mirror i and the adjacent principal planes of the rod and D is the refractive power of the rod. The magnification M of the unstable resonator (Fig. 1) can be calculated from the equivalent parameters gT using the relation:
M=12g$g:-lI+~4g:g~(g~g~-l).
(3)
For the laser performances the sensitivity of the resonator magnification M to the variation of the rod
123 (1996) 115-120
refractive power is important. With the increasing of the rod refractive power D the magnification M decreases and the unstable resonator might become stable; in these conditions a decrease of the laser beam quality takes place. The output energy E,,, is related to the input energy Ei” by relation (4) :
r-l=
[eU--l+exp(-eU) s
lU-l+exp(-eU) X
S
(4)
EU
where E= E,,/Eti is the pump energy normalised to the threshold pump energy Eth; E= 2crE,,,,/ ylhv is the normalised output energy with u the stimulated emission cross section and yr = -ln(R,/M2) the logarithmic losses of the output mirror; lJ( r) is the square of the mode amplitude of the resonator and dS is the surface element of the laser rod. Eq. (4) is valid for any mode profile U(r), not only for the super-Gaussian. Due to the decrease of the resonator magnification M the mode volume in the active rod and the output energy decreases, too. Moreover the logarithmic losses of the output mirror are changed and this leads to an inefficient energy extraction from the laser resonator. planeVRM
mirror Nd:YAG laser rod with refractive power D
_L 2% .---se
I-Fig. 1. The super-Gaussian output mirror unstable resonator with the Nd:YAG lenslike active media. dI and d2 are the distances between the mirrors and the adjacent principal planes of the Nd:YAG rod and M=aT/al is the resonator magnification.
N. Pave1 et al. /Optics
Communicarions
Fig. 2. The reflectivity profile of the output mirror is described by the relation R(r) = R,, exp [ - 2( r/w,)“] where r is the radial coordinate and Ra is the peak reflectivity, w,,, is the mirror spotsize and n denotes the order of the mirror.
123 (1996) I IS-120
117
one with M = 1.5 made by a total reflectivity convex mirror of - 8 m radius, and (ii) the other with M = 1.8 using a rear mirror of -5 m radius. The results on output beam characteristics obtained on these configurations are comparatively presented with those determined by using a classical plane-plane resonator of 30 cm length and 39% output mirror reflectivity. The output energies and beam quality obtained at 1 Hz repetition rate and different pumping levels are presented in Fig. 3. The output energies obtained from unstable resonators were fitted with relation (4). A output energy was obtained in lower (with -25%) unstable resonators as compared with the stable one, but with an improved beam quality. The beam quality was defined by 9~14 where 8 is the beam divergence (determined as 86.5% encircled energy in the focal plane of a 1000 mm focal lens) and w is the beam parameter, calculated from the near-field intensity dis-
A positive thermal lens inside the laser resonator modifies its optical configuration and the output beam characteristics. In order to keep the beam quality stable, without any decrease of the output energy, the equivalent resonator configuration must be stabilised; a possibility to maintain the magnification M insensitive to the variation of D is to modify, accordingly the rear mirror radius. The rear mirror radius and the resonator parameters for a given magnification M are related by the relation: 1
1 -= P2
(d,
+d2--DW2)
l-&j
1
_ _1. (M+‘)* g; 4M
. (3
This equation was used in order to maintain constant magnification of the unstable resonators by modifying the radius of the rear mirror function of the refractive power D of the rod.
3. Experimental results and discussion A Nd:YAG laser rod (a 5 X 56 mm) placed in a cylindrical silver coated cavity was optically pumped in a repetitive regime with a ILC 6F2 lamp. A plane super-Gaussian mirror of order n = 5, with mirror spotsize of w, = 1.7 mm and peak reflectivity of R,= 35% (Fig. 2) has been used in two unstable resonators: (i)
Fig. 3. Output energy and beam quality at 1 Hz repetition rate. For unstable configurations the experimental energies are close to those predicted by relation (4).
118
N. Pave1 et al. /Optics Communications 123 (1996) 115-120
Fig. 4. Output energy and beam quality obtained at 10 Hz repetition rate for the stable and unstable resonators. Comparatively with the 1 Hz repetition rate a decrease of the output energy and an alteration of the beam quality were observed.
tribution (obtained by scanning the laser beam near the output with a pinhole and a photodiode). At 10 Hz repetition rate the laser beam characteristics are presented in Fig. 4. With the increasing of the pump power a decrease of the output energies and an alteration of the beams quality was observed. To explain this behaviour, the position of the unstable resonators in the stability diagram has been studied. At 10 Hz repetition rate the laser rod was considered as equivalent to a thick lens with the refractive power D, function of the pumping level, and determined by the method described in [ 171 that ensure a 5% precision of the results. The variations of the g,? stability parameters for the investigated resonators are presented in Fig. 5, function of the pump level. Due to the decrease of the magnification M the unstable configuration can become stable and a decrease of the output energy and beam quality is expected.
In order to maintain the magnification of the unstable resonators invariable, the radius of the rear mirror was modified function of the rod refractive power according to relation (5). The deformable optical mirror was made from a 0.65 mm thick BK7 glass membrane with 22 mm diameter and fixed in a metallic mount. This base was constructed in such a way that the accuracy of the mirror contour is insensitive to the mounting and the pressure on the mirror was obtained by a water column. The experimental points on the mirror curvature, function of the pressure on the mirror are presented in Fig. 6a where, for comparison, the theoretical curve is also plotted. This dependence is almost linear in the 1.04 to 0.16 bar pressure range. This deformable mirror was used in the unstable resonators in order to maintain invariable its magnification. The variation of the curvature radius of the membrane function of the pumping level is presented in Fig. 6b. The beam quality and the output energies obtained from these resonators are presented in Fig. 7. By this procedure the beam quality was maintained constant at N 0.8 mm. mrad, characteristic for unloaded resonators. The output energies were close to those obtained for 1 Hz repetition rate. During the laser operation no degradation of the membrane total reflecting film was observed. The pump level used was not high but we estimate that this method can be successfully used for thermal compensation for high power unstable lasers. If a concave radius for the rear mirror would be necessary, new schemes to extent
:
Fig. 5. The equivalent stability diagram of the resonators for a variation of the rod refractive power D between 0 and 0.21 m-l. Due to the refractive power of the rod the unstable resonators pass in the stable region.
N. Pave1 eral. /Optics Communications 123 (1996) 115-120
-0.4 7
- ~
q
I
I
I
I
experimental points theory
.E-
0.0
I
I
I
I
I
I
1.04
1.08
1.12
1.16
I
pressure (bar) -012
I
I
I
I I 10 Hz repetition rate
-7
E
v-016
-024
Fig. 6. The dependence of the curvature radius of the glass plate function of pressure is presented in (a). The experimental points are close to the theoretical values. (b) The rules of variation for the rear radius mirror function of the pumping level at 10 Hz repetition rate.
119
method of thermal lens compensation by a deformable rear mirror was recently used for a diode-side pumped Nd:YAG laser [ 181 and the pressure on the membrane was obtained by a simple screw, placed in the centre of the plate. By fixing this screw on the thin plate glass, a concave profile of the mirror could be also obtained. In our experiments the laser rod was considered as a thick lens with refractive power D, without taking into account any type of intracavity distortions. To compensate for these effects a bimorph mirror with control electrodes [ 191 can be used but with a substantial cost increase of the laser system. In conclusion, a deformable thin glass plate was used as the rear mirror in different positive branch unstable resonators with super-Gaussian reflectivity profile of the output mirror. By this mean thermal lensing in a Nd:YAG rod was compensated. For unstable resonators with magnification of 1.5 and 1.8 the beam quality was maintained at a value of 0.8 mm mrad. For these resonators the output energies of laser working at 10 Hz repetition rate and pump energies up to 50 J per pulse were close to those obtained for 1 Hz repetition rate.
References [l] A. Parent, N. McCarty and P. Lavigne, IEEE J. Quantum Electron. QE-23 (1987) 222.
[ 21 S. De Silvestri, P. Laporta, V. Magni, 0. Svelto, C. Arnone, C.
O”I’/‘I’I
10
*’
Pump3~nergy (Jy
50
Fig. 7. Beam quality and output energy for thermal compensated unstable resonators. A constant value of -0.8 mm.mrad for the beam quality was maintained with the output energies close to those obtained at 1 Hz repetition rate.
the pressure on the membrane can be used (for example a pneumatic cell). The variation of the concave membrane radius can be necessary in construction of stable resonators for fundamental mode selection. The
Cali, S. Sciortino and C. Zizzo, Optics Comm. 67 ( 1988) 229. [3] S. de Silvestri, P. Laporta, V. Magni and 0. Svelto, IEEE J. Quantum Electron. QE-24 (1988) 1172. [4] S. de Silvestri, V. Magni, 0. Svelto and G. Valentini, IEEE J. Quantum Electron. QE-26 (1990) 1500. [5] S. De Silvestri, V. Magni, S. Taccheo and G. Valentini, Optics Lett. 16 (1991) 642. [6] A. Caprara and G.C. Reali, Optics Lett. 17 (1992) 414. [7] M.R. Perrone, F. Mezzolla, C. Cali and C. Pace, Appl. Phys. L&t. 59 (1991) 1153. [S] P. Lavigne, N. McCarthy and J.G. Demers, Appl. Optics 24 (1985) 2581. [9] P. Lavigne, N. McCarthy, A. Parent and K.J. Snell, Can. J. Physics 66 (1988) 888. [lo] G. Emiliagni, A. Piegari, S. De Silvestri, P. Laporta and V. Magni, Appl. Optics 28 (1989) 2832. [ 1 l] G. Duplain, P.G. Verly, J.A. Dobrowolski, A. Waldorf and S. Bussiere, Appl. Optics 32 (1993) 1145. [ 121 M.R. Perrone, A. Piegari and S. Scaglione, IEEE J. Quantum Electron. QE-29 (1993) 1423. [ 131 V. Magni, S. De Silvestri, Lie-Jia Qian and 0. Svelto, Optics Comm. 94 (1992) 87.
120 [ 141 N. Hodgson,
IV. Pave1 et al. /Optics Communications
G. Bostanjoglo and H. Weber, Optics Comm. 99 (1993) 75. [ 151 Kerning Ku, P. Loosen and H. Koechner, Optics Comm. 106 (1994) 269. [ 161 S.A. Chetkin and G.V. Vdovin, Optics Comm. 100 (1993) 159.
123 (1996) 115-120
[ 171 N. Subhash and K. Sathianadnan, IEEE .I. Quantum Electron. QE-20 (1984) 111. [ 181 U.J. Greiner and H.H. Klingenberg, Optics Lett. 19 (1994) 1207. [ 191 A.V. Kudryashov and V.Ya. Panchenko, Proc. IBEE 94THO614-8 (1994) 209.
15 January
lli!l
1996
e
OPTICS COMMUNICATIONS
__
EISEVJER
Optics Communications
123 (1996)
115-120
Variable reflectivity mirror unstable resonator with deformable mirror thermal compensation N. Pavel, T. Dascalu, V. Lupei Institute
ofAtomic Physics, IFTAR-MAWRM
Department, P.O. Box MG-6, Bucharest RO-76900, Romania
Received 3 1 May 1995
Abstract
For thermal lensing compensation of a Nd:YAG rod, placed in different positive-branch unstable resonators with superGaussian reflectivity profile of the output mirror, a deformable thin glass plate was used as the rear mirror. Unstable resonators with magnifications of M= 1.5 and M= 1.8 were designed for 0.8 mm. mrad value of the beam quality. For unloaded resonators the output energies of a laser working at 10 Hz repetition rate and pump energies up to 50 J per pulse were close to those obtained for 1 Hz repetition rate.
1. Introduction Unstable resonators that use radial variable-reflectivity mirrors as output couplers have been demonstrated to be particularly successful for generation of high-energy diffraction limited beams with a smooth transverse profile [ l-71. By a suitable technology based on vacuum deposition of dielectric thin films on a transparent substrate, different reflectivity profiles such as: parabolic, super-parabolic and super-Gaussian were obtained [ 8-121. The mirror reflectivity profile can be designed to provide an optimum balance between the energy and the beam quality of the laser output. Due to the sensitivity of resonator properties to the thermal lensing of the active media, unstable resonators were initially used in single shot operation or in Qswitched systems with low average output power. However, recently it has been demonstrated that the unstable resonators can be used in high power solidstate lasers if the resonator is properly designed. These new unstable resonator configurations are: (i) the “rod 0030-4018/96/$12.00 0 1996 Elsevier Science B.V. All rights reserved SSD10030-4018(95)00468-8
imaging unstable resonator” [ 131 and (ii) the “nearconcentric unstable resonator” [ 141. From a pulsed Nd:YAG laser, output beams with divergence about twenty times lower than that obtained with a multimode stable resonator at an average power of 200 W have been obtained in first configuration. The second configuration is characterised by a much lower sensitivity to thermal lensing as compared to other unstable resonator schemes: a maximum output power of 420 W and beam parameter products below 3 mm. mrad have been reported on a pulsed Nd:YAG laser [ 141. In this paper the results on output beam characteristics obtained from Nd:YAG positive-branch unstable resonators with super-Gaussian reflectivity profile of the output mirrors and thermal lens compensated by a deformable rear mirror are presented. This method of thermal lens compensation was used before in CO, stable resonator [ 151 and in Nd:YAlO, stable and unstable configuration [ 161. Here we report the results on this thermal lens compensation method in unstable resonators with output mirror of super-Gaussianreflectivity profile. This technique proves suitable for the
116
N. Pave1et al. /Optics
Communications
resonator configurations used in our experiments: plane output mirror and convex totally reflectivity rear mirror. The possibility of obtaining concave radius of the deformable membrane is also discussed.
2. Resonator design The schematic unstable configuration used in investigation is presented in Fig. 1. The resonator with an internal variable lens with refractive power D has the same mode properties across the mirrors as the equivalent resonator with stability parameters g* and length L* given by gi”=gi-Ddj(l-di/pi),
i,j=l,
2
i#j,
L*=dl+d2-Ddldz,
(1) (2)
where gi = 1 - ( dl + d2) /pi is the stability parameter for an empty resonator (D = 0)) pi is the curvature radius of mirror i, di is the distance between mirror i and the adjacent principal planes of the rod and D is the refractive power of the rod. The magnification M of the unstable resonator (Fig. 1) can be calculated from the equivalent parameters gT using the relation:
M=12g$g:-lI+~4g:g~(g~g~-l).
(3)
For the laser performances the sensitivity of the resonator magnification M to the variation of the rod
123 (1996) 115-120
refractive power is important. With the increasing of the rod refractive power D the magnification M decreases and the unstable resonator might become stable; in these conditions a decrease of the laser beam quality takes place. The output energy E,,, is related to the input energy Ei” by relation (4) :
r-l=
[eU--l+exp(-eU) s
lU-l+exp(-eU) X
S
(4)
EU
where E= E,,/Eti is the pump energy normalised to the threshold pump energy Eth; E= 2crE,,,,/ ylhv is the normalised output energy with u the stimulated emission cross section and yr = -ln(R,/M2) the logarithmic losses of the output mirror; lJ( r) is the square of the mode amplitude of the resonator and dS is the surface element of the laser rod. Eq. (4) is valid for any mode profile U(r), not only for the super-Gaussian. Due to the decrease of the resonator magnification M the mode volume in the active rod and the output energy decreases, too. Moreover the logarithmic losses of the output mirror are changed and this leads to an inefficient energy extraction from the laser resonator. planeVRM
mirror Nd:YAG laser rod with refractive power D
_L 2% .---se
I-Fig. 1. The super-Gaussian output mirror unstable resonator with the Nd:YAG lenslike active media. dI and d2 are the distances between the mirrors and the adjacent principal planes of the Nd:YAG rod and M=aT/al is the resonator magnification.
N. Pave1 et al. /Optics
Communicarions
Fig. 2. The reflectivity profile of the output mirror is described by the relation R(r) = R,, exp [ - 2( r/w,)“] where r is the radial coordinate and Ra is the peak reflectivity, w,,, is the mirror spotsize and n denotes the order of the mirror.
123 (1996) I IS-120
117
one with M = 1.5 made by a total reflectivity convex mirror of - 8 m radius, and (ii) the other with M = 1.8 using a rear mirror of -5 m radius. The results on output beam characteristics obtained on these configurations are comparatively presented with those determined by using a classical plane-plane resonator of 30 cm length and 39% output mirror reflectivity. The output energies and beam quality obtained at 1 Hz repetition rate and different pumping levels are presented in Fig. 3. The output energies obtained from unstable resonators were fitted with relation (4). A output energy was obtained in lower (with -25%) unstable resonators as compared with the stable one, but with an improved beam quality. The beam quality was defined by 9~14 where 8 is the beam divergence (determined as 86.5% encircled energy in the focal plane of a 1000 mm focal lens) and w is the beam parameter, calculated from the near-field intensity dis-
A positive thermal lens inside the laser resonator modifies its optical configuration and the output beam characteristics. In order to keep the beam quality stable, without any decrease of the output energy, the equivalent resonator configuration must be stabilised; a possibility to maintain the magnification M insensitive to the variation of D is to modify, accordingly the rear mirror radius. The rear mirror radius and the resonator parameters for a given magnification M are related by the relation: 1
1 -= P2
(d,
+d2--DW2)
l-&j
1
_ _1. (M+‘)* g; 4M
. (3
This equation was used in order to maintain constant magnification of the unstable resonators by modifying the radius of the rear mirror function of the refractive power D of the rod.
3. Experimental results and discussion A Nd:YAG laser rod (a 5 X 56 mm) placed in a cylindrical silver coated cavity was optically pumped in a repetitive regime with a ILC 6F2 lamp. A plane super-Gaussian mirror of order n = 5, with mirror spotsize of w, = 1.7 mm and peak reflectivity of R,= 35% (Fig. 2) has been used in two unstable resonators: (i)
Fig. 3. Output energy and beam quality at 1 Hz repetition rate. For unstable configurations the experimental energies are close to those predicted by relation (4).
118
N. Pave1 et al. /Optics Communications 123 (1996) 115-120
Fig. 4. Output energy and beam quality obtained at 10 Hz repetition rate for the stable and unstable resonators. Comparatively with the 1 Hz repetition rate a decrease of the output energy and an alteration of the beam quality were observed.
tribution (obtained by scanning the laser beam near the output with a pinhole and a photodiode). At 10 Hz repetition rate the laser beam characteristics are presented in Fig. 4. With the increasing of the pump power a decrease of the output energies and an alteration of the beams quality was observed. To explain this behaviour, the position of the unstable resonators in the stability diagram has been studied. At 10 Hz repetition rate the laser rod was considered as equivalent to a thick lens with the refractive power D, function of the pumping level, and determined by the method described in [ 171 that ensure a 5% precision of the results. The variations of the g,? stability parameters for the investigated resonators are presented in Fig. 5, function of the pump level. Due to the decrease of the magnification M the unstable configuration can become stable and a decrease of the output energy and beam quality is expected.
In order to maintain the magnification of the unstable resonators invariable, the radius of the rear mirror was modified function of the rod refractive power according to relation (5). The deformable optical mirror was made from a 0.65 mm thick BK7 glass membrane with 22 mm diameter and fixed in a metallic mount. This base was constructed in such a way that the accuracy of the mirror contour is insensitive to the mounting and the pressure on the mirror was obtained by a water column. The experimental points on the mirror curvature, function of the pressure on the mirror are presented in Fig. 6a where, for comparison, the theoretical curve is also plotted. This dependence is almost linear in the 1.04 to 0.16 bar pressure range. This deformable mirror was used in the unstable resonators in order to maintain invariable its magnification. The variation of the curvature radius of the membrane function of the pumping level is presented in Fig. 6b. The beam quality and the output energies obtained from these resonators are presented in Fig. 7. By this procedure the beam quality was maintained constant at N 0.8 mm. mrad, characteristic for unloaded resonators. The output energies were close to those obtained for 1 Hz repetition rate. During the laser operation no degradation of the membrane total reflecting film was observed. The pump level used was not high but we estimate that this method can be successfully used for thermal compensation for high power unstable lasers. If a concave radius for the rear mirror would be necessary, new schemes to extent
:
Fig. 5. The equivalent stability diagram of the resonators for a variation of the rod refractive power D between 0 and 0.21 m-l. Due to the refractive power of the rod the unstable resonators pass in the stable region.
N. Pave1 eral. /Optics Communications 123 (1996) 115-120
-0.4 7
- ~
q
I
I
I
I
experimental points theory
.E-
0.0
I
I
I
I
I
I
1.04
1.08
1.12
1.16
I
pressure (bar) -012
I
I
I
I I 10 Hz repetition rate
-7
E
v-016
-024
Fig. 6. The dependence of the curvature radius of the glass plate function of pressure is presented in (a). The experimental points are close to the theoretical values. (b) The rules of variation for the rear radius mirror function of the pumping level at 10 Hz repetition rate.
119
method of thermal lens compensation by a deformable rear mirror was recently used for a diode-side pumped Nd:YAG laser [ 181 and the pressure on the membrane was obtained by a simple screw, placed in the centre of the plate. By fixing this screw on the thin plate glass, a concave profile of the mirror could be also obtained. In our experiments the laser rod was considered as a thick lens with refractive power D, without taking into account any type of intracavity distortions. To compensate for these effects a bimorph mirror with control electrodes [ 191 can be used but with a substantial cost increase of the laser system. In conclusion, a deformable thin glass plate was used as the rear mirror in different positive branch unstable resonators with super-Gaussian reflectivity profile of the output mirror. By this mean thermal lensing in a Nd:YAG rod was compensated. For unstable resonators with magnification of 1.5 and 1.8 the beam quality was maintained at a value of 0.8 mm mrad. For these resonators the output energies of laser working at 10 Hz repetition rate and pump energies up to 50 J per pulse were close to those obtained for 1 Hz repetition rate.
References [l] A. Parent, N. McCarty and P. Lavigne, IEEE J. Quantum Electron. QE-23 (1987) 222.
[ 21 S. De Silvestri, P. Laporta, V. Magni, 0. Svelto, C. Arnone, C.
O”I’/‘I’I
10
*’
Pump3~nergy (Jy
50
Fig. 7. Beam quality and output energy for thermal compensated unstable resonators. A constant value of -0.8 mm.mrad for the beam quality was maintained with the output energies close to those obtained at 1 Hz repetition rate.
the pressure on the membrane can be used (for example a pneumatic cell). The variation of the concave membrane radius can be necessary in construction of stable resonators for fundamental mode selection. The
Cali, S. Sciortino and C. Zizzo, Optics Comm. 67 ( 1988) 229. [3] S. de Silvestri, P. Laporta, V. Magni and 0. Svelto, IEEE J. Quantum Electron. QE-24 (1988) 1172. [4] S. de Silvestri, V. Magni, 0. Svelto and G. Valentini, IEEE J. Quantum Electron. QE-26 (1990) 1500. [5] S. De Silvestri, V. Magni, S. Taccheo and G. Valentini, Optics Lett. 16 (1991) 642. [6] A. Caprara and G.C. Reali, Optics Lett. 17 (1992) 414. [7] M.R. Perrone, F. Mezzolla, C. Cali and C. Pace, Appl. Phys. L&t. 59 (1991) 1153. [S] P. Lavigne, N. McCarthy and J.G. Demers, Appl. Optics 24 (1985) 2581. [9] P. Lavigne, N. McCarthy, A. Parent and K.J. Snell, Can. J. Physics 66 (1988) 888. [lo] G. Emiliagni, A. Piegari, S. De Silvestri, P. Laporta and V. Magni, Appl. Optics 28 (1989) 2832. [ 1 l] G. Duplain, P.G. Verly, J.A. Dobrowolski, A. Waldorf and S. Bussiere, Appl. Optics 32 (1993) 1145. [ 121 M.R. Perrone, A. Piegari and S. Scaglione, IEEE J. Quantum Electron. QE-29 (1993) 1423. [ 131 V. Magni, S. De Silvestri, Lie-Jia Qian and 0. Svelto, Optics Comm. 94 (1992) 87.
120 [ 141 N. Hodgson,
IV. Pave1 et al. /Optics Communications
G. Bostanjoglo and H. Weber, Optics Comm. 99 (1993) 75. [ 151 Kerning Ku, P. Loosen and H. Koechner, Optics Comm. 106 (1994) 269. [ 161 S.A. Chetkin and G.V. Vdovin, Optics Comm. 100 (1993) 159.
123 (1996) 115-120
[ 171 N. Subhash and K. Sathianadnan, IEEE .I. Quantum Electron. QE-20 (1984) 111. [ 181 U.J. Greiner and H.H. Klingenberg, Optics Lett. 19 (1994) 1207. [ 191 A.V. Kudryashov and V.Ya. Panchenko, Proc. IBEE 94THO614-8 (1994) 209.