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Confocal positive branch-filtering unstable resonator for Nd:YAG-laser
Volume 74, n u m b e r 1,2
OPTICS COMMUNICATIONS
1 December 1989
CONFOCAL P O S I T I V E B R A N C H - F I L T E R I N G U N S T A B L E R E S O N A T O R F O R N d : Y A G - L A S E R Li Ho M I N a n d K. V O G L E R Friedrich-Schiller-University Jena, Department of Physics, 6900 Jena, GDR Received 6 June 1989
We have developed a positive branch unstable Nd:YAG laser resonator producing a nearly gaussian beam in the far as well as in the near field. The output of the laser oscillator is characterized by an energy of 500 to 600 mJ in free-runningoperation and 200 to 300 mJ in Q-switchedoperation with a pulse duration of 20 to 30 ns. Within the full angle of divergenceof 0.2 mrad the beam contains about 85% of the output energy. This new resonator configuration fits very well the demands of various applications in research and technology.
1. Introduction Unstable resonator ( U R ) configurations have been extensively investigated [ 1-3 ] and have shown to be successfully applied to high gain gas [4,5] and solid state lasers [ 6 - 8 ], delivering a much greater output energy, better energy extraction a n d lower beam divergence than stable resonators (SR) in TEMoo-mode operation. On the other hand they are more compact and easier to handle than SR with internal telescope, a scheme which tries to overcome the drawbacks of small mode volume and unsatisfactory divergence of c o m m o n TEMoo SR [9]. U n f o r t u n a t e l y the output beam quality of most unstable configurations in the near field c o m m o n l y suffers from strong intensity modulations within the beam. Thus the near field output beam of a diffraction coupled resonator usually possesses in the centre a zero intensity a n n u l u s [ 10 ]. Even polarization coupled [ 11 ] or self-imaging resonators (SLUR) [ 12] show strong irregular Fresnel diffraction or several diffraction rings of the fundamental transversal mode in the near field. From these points there originate serious prejudice against the uncontested application of U R in small extended laboratory experiments or for material processing in industry [ 13 ], because it is very u n c o n v e n i e n t to obtain good beam quality only after several meters in the far field distance. There are some efforts to improve the near field beam pattern of U R [ 14,15 ] and great success was achieved by G o b b i et al. [ 16,17 ]
introducing a novel self-filtering U R ( S F U R ) (fig. 1 ). However suitable conditions for self-filtering are not restricted to the necessity of the use of a negative branche U R ( N B U R ) , as suggested. We have established a positive branch U R ( P B U R ) which also utilizes the self-filtering condition. With this type of much more compact resonator we also get a very smooth central Airy-function-like intensity distribution of the beam in the near field while m a i n t a i n i n g the other unique properties of an UR. We describe the function of this resonator and give an example of experimental realization.
2. Description of function Generally in the S F U R configuration (fig. 1 ) the
2o M1
Q
P
Nd:YAG
~14
M2
Fig. 1. Negative branche unstable resonator (NBUR) with selffiltering commonly labeled as SFUR (or better NB/SFUR). M~, M2 - concave mirrors both with radii of curvature r~, r2>0, (rt < rz), 2a - diameter of the diffraction aperture at the common focus location of both mirrors length, P - polarizing output coupler, A/4 - quarter-wave plate, Q - switch unit, optionally.
0030-4018/89/$03.50 © ElsevierScience Publishers B.V. (North-Holland)
79
Volume 74, n u m b e r 1,2
OPTICS COMMUNICATIONS
diffraction from a suitable dimensioned aperture (diameter 2a) in combination with the mirror M1 generates a central Airy-disk-like laser cavity mode. In contrast to the usual cavity modes of an UR obtained in the geometric limit of small diffraction influence with N = a 2/(),f~ ) >> l, (where fl is the focal length of the mirror M, with minor radius of curvator and 2 is the wavelength), the SFUR conditions deeply involves diffraction from the aperture edge which determines the cavity field distribution, for a Fresnel number N < 1. Thus the small aperture produces a strong diffraction of the plane wave comming from the mirror ME which is counterbalanced by the focusing action of M 1 working together with the aperture as a low-pass spatial frequency filter during the mode build-up time by blocking all outer rings of the diffraction pattern as well as all higher spatial frequencies of the radiation field. In this way the cleaning up from Fresnel modulations and smoothing of the beam profile usually occuring on the way of propagation to the far field distance already takes place during multipass cavity transists. For this special operation regime the basic design condition is [ 17 ] a = r k = 1.222fl/2a,
ora=
( 0 . 6 1 2 f l ) 1/2 ,
which means to choose the aperture radius, a, so that a plane wave incident on it is focused by the mirror M~ to an Airy-disk having the same radius rA=a. As seen from this expression the aperture dimension is only determined by the radius of curvature of the mirror M ~, v~= 2f~, whereas the magnification M of the U R is appointed by the ratio M=r2/h =2D/2a ( r 2 radius of mirror M 2 ) and has to be adapted to the laser rod dimension ( ~ output beam diameter 2D), the small signal gain and the cavity losses for optimum energy extraction [ 19 ]. Up to now self-filtering condition is realized only in NBUR configurations (see also refs. [4,5] ) though we found it is also possible for PBUR installation [ 18 ]. In the case of a PBUR design there is also a well predestinated demand for the aperture diameter (2a) allowing the UR to operate in the self-filtering condition (fig. 2). This diameter is again determined by the shorter mirror focal length fz --r~/2, which is a now a convex mirror, acting together with a virtual diffraction aperture. Using a real object diaphragm 2A at a certain distance/A, which is the real counterpart of that vir80
1 December 1989
tual aperture image 2a, forces a new self-filtering laser oscillation. We have proved that both U R the N B / SFUR and the PB/SFUR, possessing an equal magnification and corresponding mirror parameters deliver almost identical output values of the laser beam. The only remarkable difference of both resonator designs is the overall optical length L, which is much shorter for the P B / S F U R configuration, L a B = r E - f l This might be of great practical importance for the construction of a small compact laser cavity. Another advantage is the relatively free decision over the position lg and the size 2A of the aperture used inside of the laser resonator. This facilitates not only the adjustment of the laser cavity but also the installation of further resonator elements.
3. Experimental findings The schematic configuration of our P B / S F U R is shown in fig. 2. The laser head used for our resonator contains a laser rod of a 6 m m × 90 m m dimension doped by a Nd-concentration of N ( N d 3+ ) = l × 1020 cm-3, and equiped with an anti-reflection coating on both front faces (Monocrystaly Turnov, CSSR). The rod is pumped by one linear xenon flashlamp which is situated together with the rod in an elliptically formed silver coated glass reflector. The Nd-YAG laser head is characterized by a pump efficiency of 2K=0.38 J-~ and a loss coefficient of a = 0 . 0 0 4 cm -1 as defined in ref. [20], whereas the overall resonator losses containing the thin film plate polarizer P and the quarterwave plate 2/4 in a SR configuration are about 25% in a full roundtrip. In the P B / S F U R configuration the resonator con-
. . . . . .
"
2a 20
M1
Q
2A
P
Nd:YAG
~/4 M 2
Fig. 2. Positive branche unstable resonator ( P B U R ) with selffiltering P B / S F U R . Mj - convex m i r r o r h < 0 , M2 - concave m i r r o r r2 > 0, ]rl I < [ r2 I, LpB = If21 -- If~ I, the other denotations as in fig. I.
Volume 74, number 1,2
OPTICS COMMUNICATIONS
sists of standard mirrors of Mr: r t = - 0 . 5 0 m, R l = 100% and M 2 : r 2 = 2 . 0 0 m, R2= 100%, giving a magnification M = r 2 / r ~ = - 4 and an approximate geometric loss per pass according ~ = 1 - 1 / M 2 [ 1 ] of ~ = 94% comparable with an experimental value of 91% [ 19]. The overall resonator length is L = 0 . 6 7 m, the aperture is fixed at a distance of IA=0.30 m from the mirror Mt and has a diameter of 2A =2.0 m m relaying approximately the virtual self-filtering aperture 2a=0.8 m m according the rule 2 A = 2 a [ I +lA/Lopt(1.5lM[
-
1 ) ],
Lop t is the optical length of the resonator.
The laser threshold for the P B / S F U R in free-running operation is about E t h ( U R ) = 7 . 5 J giving a small signal gain at threshold of 2go=0.32 cm -~ or Go=exp(2gol) = 17 per transit. The equivalent SR driven at optimum output coupling has a threshold for free running of about E th ( S R ) = 4 . 0 J confirming the approximate relation
Eth(UR)
1 December 1989
.~ Eth (SR) + I n M 2 / 2 K .
Fig. 3 shows the input-output energy curves of freerunning and Q-switched operation for the SR, operating in the multimode and TEMoo case, as well as the PBUR with and without self filtering. For freerunning operation our experimental findings yield in every case an UR output energy of about a half of that of a similar multimode SR output, operating nearly at optimum output coupling. Obviously this is caused by the higher losses of the UR. Introducing the self-filtering conditions to improve the near field beam quality of the PBUR results in an output energy EL of about 600 mJ in the P B / S F U R (curve 3) connected with a full angle of divergence of 0=0.2 mrad and a polarization ratio of 250: 1. Identical resuits are achieved employing a N B / S F U R (r~ =0.5 m, r~=2.0 m, L = 1.17 m). Thus apparently about 30% of stored multimode energy of the stable laser
1.o] 1500
i
i
1300
/ =d
i
@
a
i
0.5
11oo
©
9o0
0.17
1,0 soo
b
T
300
~ 1 1 1 ~ 1 -'~
10
- -
30
50
Ep[JJ
0.5. 70
Fig. 3. Laser output energy EL versus input pump energy Ep for
free-running 1-5 and Q-switch operation 6, 7. l. Multi-mode SR (rl ---oo, Rt = 35%; r2= 2.0 m, R2= 100%). 2. PBUR without selffiltering M = - 4 ( r ~ = - 0 . 5 , R l = 100%; r2=2.0 m, R2= 100%; LpB=0.67 m). 3. PBUR with self-filtering PB/SFUR. 4. Identical with curve 3, N B / S F U R ( r t - 0 . 5 , R~=100%; r2=2.0 m, R2= 100%; LNB= 1.17 m; 2a=0.8 ram). 5. TEMoo-mode o f SR according curve i. 6. Q-switched PB/SFUR. 7. Q-switched SR.
2
1
0
1
2
k,'rBI
Fig. 4. (a) Near field (40 cm from the output coupler). (b) Far field intensity distribution across the beam diameter detected by a photodiode array (relative intensity versus normalized beam radius rB= 2.4 ram).
81
Volume 74, number 1,2
OPTICS COMMUNICATIONS
resonator can be extracted in a single transversal mode using self-filtering condition in P B / S F U R or N B / S F U R and exploiting approximately 64% of the active volume of the rod by a beam dimension of 2 D ~ 1.51Ml2a. As compared to the SR TEMoo-mode, the output energy of an UR in free-running is only improved by a factor of 2-3 if smooth near field intensity distribution (fig. 4) is claimed but there is an additional improvement in divergence of course. Thus about 85% of the near field energy is contained within that small divergence angle in the far field. Fig. 5 shows the variation in the beam profile at near and far field distances in dependence on laser
1 December 1989
pump energy. There is found no considerable change especially in the far field pattern starting direct at near threshold level till several times excess pumping. The influence of the self-filtering diaphragm is clearly seen (fig. 5b, 5 and 6). For Q-switch operation in the fundamental mode the difference in output energy of SR and UR is more remarkable: E L ( U R ) = 2 5 0 mJ, i.e. about EL(UR) 4-5 EL (SR). The Q-switch operation was achieved by BDN-dye-solution or LiF2(F~-)-crystals possessing a single pass transmission of 30-40%. The pulse duration was measured by a fast fotodiode and $790 oscilloscope to be ~L=20--30 ns but still include some substructure caused by the lack of longitudinal mode selection in the present resonator configuration.
4. Conclusion
2
5
3
6 a 4
It
3
We have shown that the principle of self-filtering is not restricted to the NBUR but can also be realized in PBUR, revealing some technical advantages. Even with UR the demands for maximum output energy and good beam quality cannot be fullfilled simultaneously and have to be compromised [ 19]. Good near field beam structure is secured at the expense of output energy. But concerning the output energy and laser beam divergence still under this restrictions the UR clearly surpasses the SR, of course more pronounced under high-loss Q-switch operation.
References f
b
.,
6
Fig. 5. (a) Near field beam profil in dependence on pump energy ( 1, 2, 3, 4, 5, 6: El,= 12, 20, 30, 40, 60, 90 J, respectively). (b) Far field beam profil in dependence on pump energy ( l, 2, 3, 4, 5 and 6: El,= 12, 20, 40, 60, 90 J and 90 J without SF, respectively) (relative intensity versus normalized beam radius ra=2.4 mm).
82
[ 1 ] A.E. Siegman, Appl. Optics 13 (1974) 353; IEEE J. Quant. Electr. QE-12 (1976) 35. [ 2 ] A.E. Siegman and R. Arrathoon, I EEE J. Quant. Electr. QE3 (1967) 156. [ 3 ] D.B. Rensch and A.N. Chester, Appl. Optics 12 (1973) 997. [4] R. Barbini, A. Ghigo, M. Giorgi, K.N. Iyer, A. Palucci, and S. Ribezzo, Optics Comm. 60 (1986) 239. [5] V. Boffa, P. Di I.azzaro, G.P. Gallerano, G. Giordano, T. Hermsen, T. Letardi and C.E. Zheng, IEEE J. Quant. Electr. OE-23 (1987). [610.P. Varnavsky, A.N. Kirkin, A.M. Leontovich, R.G. Morzoyan, A.M. Mozharovski and I.I. Slomantin, Optics Comm. 45 (1983) 342. [7] D. Andreou, Rev. Sci. Instr. 49 (1978) 586; T.F. Ewanizky and J.M. Craig; Appl. Optics 15 (1976) 1465.
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OPTICS COMMUNICATIONS
[8] R.L. Herbst, H. Komine and R.L. Byer, Optics Comm. 24 (1977) 5. [ 9 ] D.C. Hanna, C.G. Sawyers, M.A. Yuratich, Opt. and Quant. Electr. 13 (1981) 493; P.H. Sarkies Optics Comm. 31 (1979) 189. [ 10] D.C. Hanna and LC. Laycock, Opt. and Quant. Electr. 11 (1979) 153. [ 11 ] G.C. Reali, Optics Comm. 35 (1980) 264. [ 12 ] A.H. Paxton and T.C. Salvi, Optics Comm. 26 ( 1978 ) 305. [ 13] H. Weber, Laser and Optoelectronics 2 (1988) 60. [14] W.D. Fountain and M. Bass, IEEE J. Quant Electr. QE-18 (1982) 432.
1 December 1989
[15] K. Yasui, M. Tanaka and S. Yagi, Appl. Phys. Lett. 52 (1988) 530. [ 16 ] P.G. Gobbi and G.C. Reali, Optics Comm. 52 (1984) 195. [ 17] P.G. Gobbi, S. Morosi, G.C. Reali and A.S. Zarkasi, Appl. Optics 24 ( 1985 ) 26. [ 18 ] Li Ho Min and K. Vogler, patent pending. [19]Li Ho Min and K. Vogler, patent pending, paper in preparation. [ 20 ] W. Koechner, Solid state laser engineering (Springer, New York, Heidelberg, Berlin, 1976 ) p. 86.
83
OPTICS COMMUNICATIONS
1 December 1989
CONFOCAL P O S I T I V E B R A N C H - F I L T E R I N G U N S T A B L E R E S O N A T O R F O R N d : Y A G - L A S E R Li Ho M I N a n d K. V O G L E R Friedrich-Schiller-University Jena, Department of Physics, 6900 Jena, GDR Received 6 June 1989
We have developed a positive branch unstable Nd:YAG laser resonator producing a nearly gaussian beam in the far as well as in the near field. The output of the laser oscillator is characterized by an energy of 500 to 600 mJ in free-runningoperation and 200 to 300 mJ in Q-switchedoperation with a pulse duration of 20 to 30 ns. Within the full angle of divergenceof 0.2 mrad the beam contains about 85% of the output energy. This new resonator configuration fits very well the demands of various applications in research and technology.
1. Introduction Unstable resonator ( U R ) configurations have been extensively investigated [ 1-3 ] and have shown to be successfully applied to high gain gas [4,5] and solid state lasers [ 6 - 8 ], delivering a much greater output energy, better energy extraction a n d lower beam divergence than stable resonators (SR) in TEMoo-mode operation. On the other hand they are more compact and easier to handle than SR with internal telescope, a scheme which tries to overcome the drawbacks of small mode volume and unsatisfactory divergence of c o m m o n TEMoo SR [9]. U n f o r t u n a t e l y the output beam quality of most unstable configurations in the near field c o m m o n l y suffers from strong intensity modulations within the beam. Thus the near field output beam of a diffraction coupled resonator usually possesses in the centre a zero intensity a n n u l u s [ 10 ]. Even polarization coupled [ 11 ] or self-imaging resonators (SLUR) [ 12] show strong irregular Fresnel diffraction or several diffraction rings of the fundamental transversal mode in the near field. From these points there originate serious prejudice against the uncontested application of U R in small extended laboratory experiments or for material processing in industry [ 13 ], because it is very u n c o n v e n i e n t to obtain good beam quality only after several meters in the far field distance. There are some efforts to improve the near field beam pattern of U R [ 14,15 ] and great success was achieved by G o b b i et al. [ 16,17 ]
introducing a novel self-filtering U R ( S F U R ) (fig. 1 ). However suitable conditions for self-filtering are not restricted to the necessity of the use of a negative branche U R ( N B U R ) , as suggested. We have established a positive branch U R ( P B U R ) which also utilizes the self-filtering condition. With this type of much more compact resonator we also get a very smooth central Airy-function-like intensity distribution of the beam in the near field while m a i n t a i n i n g the other unique properties of an UR. We describe the function of this resonator and give an example of experimental realization.
2. Description of function Generally in the S F U R configuration (fig. 1 ) the
2o M1
Q
P
Nd:YAG
~14
M2
Fig. 1. Negative branche unstable resonator (NBUR) with selffiltering commonly labeled as SFUR (or better NB/SFUR). M~, M2 - concave mirrors both with radii of curvature r~, r2>0, (rt < rz), 2a - diameter of the diffraction aperture at the common focus location of both mirrors length, P - polarizing output coupler, A/4 - quarter-wave plate, Q - switch unit, optionally.
0030-4018/89/$03.50 © ElsevierScience Publishers B.V. (North-Holland)
79
Volume 74, n u m b e r 1,2
OPTICS COMMUNICATIONS
diffraction from a suitable dimensioned aperture (diameter 2a) in combination with the mirror M1 generates a central Airy-disk-like laser cavity mode. In contrast to the usual cavity modes of an UR obtained in the geometric limit of small diffraction influence with N = a 2/(),f~ ) >> l, (where fl is the focal length of the mirror M, with minor radius of curvator and 2 is the wavelength), the SFUR conditions deeply involves diffraction from the aperture edge which determines the cavity field distribution, for a Fresnel number N < 1. Thus the small aperture produces a strong diffraction of the plane wave comming from the mirror ME which is counterbalanced by the focusing action of M 1 working together with the aperture as a low-pass spatial frequency filter during the mode build-up time by blocking all outer rings of the diffraction pattern as well as all higher spatial frequencies of the radiation field. In this way the cleaning up from Fresnel modulations and smoothing of the beam profile usually occuring on the way of propagation to the far field distance already takes place during multipass cavity transists. For this special operation regime the basic design condition is [ 17 ] a = r k = 1.222fl/2a,
ora=
( 0 . 6 1 2 f l ) 1/2 ,
which means to choose the aperture radius, a, so that a plane wave incident on it is focused by the mirror M~ to an Airy-disk having the same radius rA=a. As seen from this expression the aperture dimension is only determined by the radius of curvature of the mirror M ~, v~= 2f~, whereas the magnification M of the U R is appointed by the ratio M=r2/h =2D/2a ( r 2 radius of mirror M 2 ) and has to be adapted to the laser rod dimension ( ~ output beam diameter 2D), the small signal gain and the cavity losses for optimum energy extraction [ 19 ]. Up to now self-filtering condition is realized only in NBUR configurations (see also refs. [4,5] ) though we found it is also possible for PBUR installation [ 18 ]. In the case of a PBUR design there is also a well predestinated demand for the aperture diameter (2a) allowing the UR to operate in the self-filtering condition (fig. 2). This diameter is again determined by the shorter mirror focal length fz --r~/2, which is a now a convex mirror, acting together with a virtual diffraction aperture. Using a real object diaphragm 2A at a certain distance/A, which is the real counterpart of that vir80
1 December 1989
tual aperture image 2a, forces a new self-filtering laser oscillation. We have proved that both U R the N B / SFUR and the PB/SFUR, possessing an equal magnification and corresponding mirror parameters deliver almost identical output values of the laser beam. The only remarkable difference of both resonator designs is the overall optical length L, which is much shorter for the P B / S F U R configuration, L a B = r E - f l This might be of great practical importance for the construction of a small compact laser cavity. Another advantage is the relatively free decision over the position lg and the size 2A of the aperture used inside of the laser resonator. This facilitates not only the adjustment of the laser cavity but also the installation of further resonator elements.
3. Experimental findings The schematic configuration of our P B / S F U R is shown in fig. 2. The laser head used for our resonator contains a laser rod of a 6 m m × 90 m m dimension doped by a Nd-concentration of N ( N d 3+ ) = l × 1020 cm-3, and equiped with an anti-reflection coating on both front faces (Monocrystaly Turnov, CSSR). The rod is pumped by one linear xenon flashlamp which is situated together with the rod in an elliptically formed silver coated glass reflector. The Nd-YAG laser head is characterized by a pump efficiency of 2K=0.38 J-~ and a loss coefficient of a = 0 . 0 0 4 cm -1 as defined in ref. [20], whereas the overall resonator losses containing the thin film plate polarizer P and the quarterwave plate 2/4 in a SR configuration are about 25% in a full roundtrip. In the P B / S F U R configuration the resonator con-
. . . . . .
"
2a 20
M1
Q
2A
P
Nd:YAG
~/4 M 2
Fig. 2. Positive branche unstable resonator ( P B U R ) with selffiltering P B / S F U R . Mj - convex m i r r o r h < 0 , M2 - concave m i r r o r r2 > 0, ]rl I < [ r2 I, LpB = If21 -- If~ I, the other denotations as in fig. I.
Volume 74, number 1,2
OPTICS COMMUNICATIONS
sists of standard mirrors of Mr: r t = - 0 . 5 0 m, R l = 100% and M 2 : r 2 = 2 . 0 0 m, R2= 100%, giving a magnification M = r 2 / r ~ = - 4 and an approximate geometric loss per pass according ~ = 1 - 1 / M 2 [ 1 ] of ~ = 94% comparable with an experimental value of 91% [ 19]. The overall resonator length is L = 0 . 6 7 m, the aperture is fixed at a distance of IA=0.30 m from the mirror Mt and has a diameter of 2A =2.0 m m relaying approximately the virtual self-filtering aperture 2a=0.8 m m according the rule 2 A = 2 a [ I +lA/Lopt(1.5lM[
-
1 ) ],
Lop t is the optical length of the resonator.
The laser threshold for the P B / S F U R in free-running operation is about E t h ( U R ) = 7 . 5 J giving a small signal gain at threshold of 2go=0.32 cm -~ or Go=exp(2gol) = 17 per transit. The equivalent SR driven at optimum output coupling has a threshold for free running of about E th ( S R ) = 4 . 0 J confirming the approximate relation
Eth(UR)
1 December 1989
.~ Eth (SR) + I n M 2 / 2 K .
Fig. 3 shows the input-output energy curves of freerunning and Q-switched operation for the SR, operating in the multimode and TEMoo case, as well as the PBUR with and without self filtering. For freerunning operation our experimental findings yield in every case an UR output energy of about a half of that of a similar multimode SR output, operating nearly at optimum output coupling. Obviously this is caused by the higher losses of the UR. Introducing the self-filtering conditions to improve the near field beam quality of the PBUR results in an output energy EL of about 600 mJ in the P B / S F U R (curve 3) connected with a full angle of divergence of 0=0.2 mrad and a polarization ratio of 250: 1. Identical resuits are achieved employing a N B / S F U R (r~ =0.5 m, r~=2.0 m, L = 1.17 m). Thus apparently about 30% of stored multimode energy of the stable laser
1.o] 1500
i
i
1300
/ =d
i
@
a
i
0.5
11oo
©
9o0
0.17
1,0 soo
b
T
300
~ 1 1 1 ~ 1 -'~
10
- -
30
50
Ep[JJ
0.5. 70
Fig. 3. Laser output energy EL versus input pump energy Ep for
free-running 1-5 and Q-switch operation 6, 7. l. Multi-mode SR (rl ---oo, Rt = 35%; r2= 2.0 m, R2= 100%). 2. PBUR without selffiltering M = - 4 ( r ~ = - 0 . 5 , R l = 100%; r2=2.0 m, R2= 100%; LpB=0.67 m). 3. PBUR with self-filtering PB/SFUR. 4. Identical with curve 3, N B / S F U R ( r t - 0 . 5 , R~=100%; r2=2.0 m, R2= 100%; LNB= 1.17 m; 2a=0.8 ram). 5. TEMoo-mode o f SR according curve i. 6. Q-switched PB/SFUR. 7. Q-switched SR.
2
1
0
1
2
k,'rBI
Fig. 4. (a) Near field (40 cm from the output coupler). (b) Far field intensity distribution across the beam diameter detected by a photodiode array (relative intensity versus normalized beam radius rB= 2.4 ram).
81
Volume 74, number 1,2
OPTICS COMMUNICATIONS
resonator can be extracted in a single transversal mode using self-filtering condition in P B / S F U R or N B / S F U R and exploiting approximately 64% of the active volume of the rod by a beam dimension of 2 D ~ 1.51Ml2a. As compared to the SR TEMoo-mode, the output energy of an UR in free-running is only improved by a factor of 2-3 if smooth near field intensity distribution (fig. 4) is claimed but there is an additional improvement in divergence of course. Thus about 85% of the near field energy is contained within that small divergence angle in the far field. Fig. 5 shows the variation in the beam profile at near and far field distances in dependence on laser
1 December 1989
pump energy. There is found no considerable change especially in the far field pattern starting direct at near threshold level till several times excess pumping. The influence of the self-filtering diaphragm is clearly seen (fig. 5b, 5 and 6). For Q-switch operation in the fundamental mode the difference in output energy of SR and UR is more remarkable: E L ( U R ) = 2 5 0 mJ, i.e. about EL(UR) 4-5 EL (SR). The Q-switch operation was achieved by BDN-dye-solution or LiF2(F~-)-crystals possessing a single pass transmission of 30-40%. The pulse duration was measured by a fast fotodiode and $790 oscilloscope to be ~L=20--30 ns but still include some substructure caused by the lack of longitudinal mode selection in the present resonator configuration.
4. Conclusion
2
5
3
6 a 4
It
3
We have shown that the principle of self-filtering is not restricted to the NBUR but can also be realized in PBUR, revealing some technical advantages. Even with UR the demands for maximum output energy and good beam quality cannot be fullfilled simultaneously and have to be compromised [ 19]. Good near field beam structure is secured at the expense of output energy. But concerning the output energy and laser beam divergence still under this restrictions the UR clearly surpasses the SR, of course more pronounced under high-loss Q-switch operation.
References f
b
.,
6
Fig. 5. (a) Near field beam profil in dependence on pump energy ( 1, 2, 3, 4, 5, 6: El,= 12, 20, 30, 40, 60, 90 J, respectively). (b) Far field beam profil in dependence on pump energy ( l, 2, 3, 4, 5 and 6: El,= 12, 20, 40, 60, 90 J and 90 J without SF, respectively) (relative intensity versus normalized beam radius ra=2.4 mm).
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[ 1 ] A.E. Siegman, Appl. Optics 13 (1974) 353; IEEE J. Quant. Electr. QE-12 (1976) 35. [ 2 ] A.E. Siegman and R. Arrathoon, I EEE J. Quant. Electr. QE3 (1967) 156. [ 3 ] D.B. Rensch and A.N. Chester, Appl. Optics 12 (1973) 997. [4] R. Barbini, A. Ghigo, M. Giorgi, K.N. Iyer, A. Palucci, and S. Ribezzo, Optics Comm. 60 (1986) 239. [5] V. Boffa, P. Di I.azzaro, G.P. Gallerano, G. Giordano, T. Hermsen, T. Letardi and C.E. Zheng, IEEE J. Quant. Electr. OE-23 (1987). [610.P. Varnavsky, A.N. Kirkin, A.M. Leontovich, R.G. Morzoyan, A.M. Mozharovski and I.I. Slomantin, Optics Comm. 45 (1983) 342. [7] D. Andreou, Rev. Sci. Instr. 49 (1978) 586; T.F. Ewanizky and J.M. Craig; Appl. Optics 15 (1976) 1465.
Volume 74, number 1,2
OPTICS COMMUNICATIONS
[8] R.L. Herbst, H. Komine and R.L. Byer, Optics Comm. 24 (1977) 5. [ 9 ] D.C. Hanna, C.G. Sawyers, M.A. Yuratich, Opt. and Quant. Electr. 13 (1981) 493; P.H. Sarkies Optics Comm. 31 (1979) 189. [ 10] D.C. Hanna and LC. Laycock, Opt. and Quant. Electr. 11 (1979) 153. [ 11 ] G.C. Reali, Optics Comm. 35 (1980) 264. [ 12 ] A.H. Paxton and T.C. Salvi, Optics Comm. 26 ( 1978 ) 305. [ 13] H. Weber, Laser and Optoelectronics 2 (1988) 60. [14] W.D. Fountain and M. Bass, IEEE J. Quant Electr. QE-18 (1982) 432.
1 December 1989
[15] K. Yasui, M. Tanaka and S. Yagi, Appl. Phys. Lett. 52 (1988) 530. [ 16 ] P.G. Gobbi and G.C. Reali, Optics Comm. 52 (1984) 195. [ 17] P.G. Gobbi, S. Morosi, G.C. Reali and A.S. Zarkasi, Appl. Optics 24 ( 1985 ) 26. [ 18 ] Li Ho Min and K. Vogler, patent pending. [19]Li Ho Min and K. Vogler, patent pending, paper in preparation. [ 20 ] W. Koechner, Solid state laser engineering (Springer, New York, Heidelberg, Berlin, 1976 ) p. 86.
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