Abstract

We propose the use of an auxiliary lens or mirror to design a compact dynamically stable resonator for single-rod lasers. It was found that an intracavity divergent element (divergent lens or convex mirror) is suitable for obtaining a large TEM00-mode volume, whereas a convergent one renders the resonator insensitive to mechanical misalignment. A reliable and compact dynamically stable resonator can be designed conveniently by use of such characteristics. Both three- and four-element resonators were designed and tested with a laser-diode side-pumped Nd:YAG laser.

© 2001 Optical Society of America

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References

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  1. A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).
  2. W. Koechner, Solid-State Laser Engineering, 4th. ed. (Springer-Verlag, Berlin, 1996).
    [CrossRef]
  3. V. Magni, G. Valentini, S. De Silvestri, “Recent developments in laser resonator design,” Opt. Quantum Electron. 23, 1105–1134 (1991), and references therein.
  4. J. Steffen, J. P. Lörtscher, G. Herziger, “Fundamental mode radiation with solid-state lasers,” IEEE J. Quantum Electron. QE-8, 239–245 (1972).
    [CrossRef]
  5. V. Magni, “Resonators for solid-state lasers with large-volume fundamental mode and high alignment stability,” Appl. Opt. 25, 107–117 (1986).
    [CrossRef] [PubMed]
  6. U. J. Greiner, H. H. Klingenberg, D. R. Walker, C. J. Flood, H. M. Van Driel, “Diode-pumped Nd:YAG laser using reflective pump optics,” Appl. Phys. B 58, 393–395 (1994).
    [CrossRef]
  7. D. Golla, M. Bode, S. Knoke, W. Schöne, A. Tünnerman, “62-W cw TEM00 Nd:YAG laser side pumped by fiber-coupled diode lasers,” Opt. Lett. 21, 210–212 (1996).
  8. G. Cerullo, S. De. Silvestri, V. Magni, “High efficiency, 40 W cw Nd:YLF laser with large TEM00 mode,” Opt. Commun. 93, 77–81 (1992).
  9. R. J. Shine, A. J. Alfrey, R. L. Byer, “40 W cw, TEM00 mode, diode-laser-pumped, Nd:YAG miniature-slab laser,” Opt. Lett. 20, 459–461 (1995).
    [CrossRef] [PubMed]
  10. H. Kogelnik, “Imaging of optical modes—resonators with internal lens,” Bell Syst. Tech. J. 44, 455–494 (1965).
    [CrossRef]
  11. G. Cerullo, S. De. Silvestri, V. Magni, O. Svelto, “Output power limitations in CW single transverse mode Nd:YAG lasers with a rod-of large cross-section,” Opt. Quantum Electron. 25, 489–500 (1993).
  12. M. P. Murdough, C. A. Denman, “Mode-volume and pump-power limitations in injection-locked TEM00 Nd:YAG rod lasers,” Appl. Opt. 35, 5925–5936 (1996).
    [CrossRef] [PubMed]
  13. R. Hua, S. Wada, H. Tashiro, “Principle and limitation of a quarter-wave plate for reducing the depolarization loss from thermally induced birefringence in Nd:YAG lasers,” Opt. Commun. 175, 189–200 (2000).
    [CrossRef]
  14. R. Hua, S. Wada, H. Tashiro, “Compact TEM00 mode resonator for laser-diode side-pumped Nd:YAG laser,” in Extended Abstracts of JSAP’s 60th Autumn Meeting (Japan Society of Applied Physics, Tokyo, 1999), Vol. 3, paper 2a-L-7, p. 909.

2000 (1)

R. Hua, S. Wada, H. Tashiro, “Principle and limitation of a quarter-wave plate for reducing the depolarization loss from thermally induced birefringence in Nd:YAG lasers,” Opt. Commun. 175, 189–200 (2000).
[CrossRef]

1996 (2)

1995 (1)

1994 (2)

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

U. J. Greiner, H. H. Klingenberg, D. R. Walker, C. J. Flood, H. M. Van Driel, “Diode-pumped Nd:YAG laser using reflective pump optics,” Appl. Phys. B 58, 393–395 (1994).
[CrossRef]

1993 (1)

G. Cerullo, S. De. Silvestri, V. Magni, O. Svelto, “Output power limitations in CW single transverse mode Nd:YAG lasers with a rod-of large cross-section,” Opt. Quantum Electron. 25, 489–500 (1993).

1992 (1)

G. Cerullo, S. De. Silvestri, V. Magni, “High efficiency, 40 W cw Nd:YLF laser with large TEM00 mode,” Opt. Commun. 93, 77–81 (1992).

1991 (1)

V. Magni, G. Valentini, S. De Silvestri, “Recent developments in laser resonator design,” Opt. Quantum Electron. 23, 1105–1134 (1991), and references therein.

1986 (1)

1972 (1)

J. Steffen, J. P. Lörtscher, G. Herziger, “Fundamental mode radiation with solid-state lasers,” IEEE J. Quantum Electron. QE-8, 239–245 (1972).
[CrossRef]

1965 (1)

H. Kogelnik, “Imaging of optical modes—resonators with internal lens,” Bell Syst. Tech. J. 44, 455–494 (1965).
[CrossRef]

Alfrey, A. J.

Bode, M.

Brauch, U.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

Byer, R. L.

Cerullo, G.

G. Cerullo, S. De. Silvestri, V. Magni, O. Svelto, “Output power limitations in CW single transverse mode Nd:YAG lasers with a rod-of large cross-section,” Opt. Quantum Electron. 25, 489–500 (1993).

G. Cerullo, S. De. Silvestri, V. Magni, “High efficiency, 40 W cw Nd:YLF laser with large TEM00 mode,” Opt. Commun. 93, 77–81 (1992).

De Silvestri, S.

V. Magni, G. Valentini, S. De Silvestri, “Recent developments in laser resonator design,” Opt. Quantum Electron. 23, 1105–1134 (1991), and references therein.

Denman, C. A.

Flood, C. J.

U. J. Greiner, H. H. Klingenberg, D. R. Walker, C. J. Flood, H. M. Van Driel, “Diode-pumped Nd:YAG laser using reflective pump optics,” Appl. Phys. B 58, 393–395 (1994).
[CrossRef]

Giesen, A.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

Golla, D.

Greiner, U. J.

U. J. Greiner, H. H. Klingenberg, D. R. Walker, C. J. Flood, H. M. Van Driel, “Diode-pumped Nd:YAG laser using reflective pump optics,” Appl. Phys. B 58, 393–395 (1994).
[CrossRef]

Herziger, G.

J. Steffen, J. P. Lörtscher, G. Herziger, “Fundamental mode radiation with solid-state lasers,” IEEE J. Quantum Electron. QE-8, 239–245 (1972).
[CrossRef]

Hua, R.

R. Hua, S. Wada, H. Tashiro, “Principle and limitation of a quarter-wave plate for reducing the depolarization loss from thermally induced birefringence in Nd:YAG lasers,” Opt. Commun. 175, 189–200 (2000).
[CrossRef]

R. Hua, S. Wada, H. Tashiro, “Compact TEM00 mode resonator for laser-diode side-pumped Nd:YAG laser,” in Extended Abstracts of JSAP’s 60th Autumn Meeting (Japan Society of Applied Physics, Tokyo, 1999), Vol. 3, paper 2a-L-7, p. 909.

Hügel, H.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

Klingenberg, H. H.

U. J. Greiner, H. H. Klingenberg, D. R. Walker, C. J. Flood, H. M. Van Driel, “Diode-pumped Nd:YAG laser using reflective pump optics,” Appl. Phys. B 58, 393–395 (1994).
[CrossRef]

Knoke, S.

Koechner, W.

W. Koechner, Solid-State Laser Engineering, 4th. ed. (Springer-Verlag, Berlin, 1996).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Imaging of optical modes—resonators with internal lens,” Bell Syst. Tech. J. 44, 455–494 (1965).
[CrossRef]

Lörtscher, J. P.

J. Steffen, J. P. Lörtscher, G. Herziger, “Fundamental mode radiation with solid-state lasers,” IEEE J. Quantum Electron. QE-8, 239–245 (1972).
[CrossRef]

Magni, V.

G. Cerullo, S. De. Silvestri, V. Magni, O. Svelto, “Output power limitations in CW single transverse mode Nd:YAG lasers with a rod-of large cross-section,” Opt. Quantum Electron. 25, 489–500 (1993).

G. Cerullo, S. De. Silvestri, V. Magni, “High efficiency, 40 W cw Nd:YLF laser with large TEM00 mode,” Opt. Commun. 93, 77–81 (1992).

V. Magni, G. Valentini, S. De Silvestri, “Recent developments in laser resonator design,” Opt. Quantum Electron. 23, 1105–1134 (1991), and references therein.

V. Magni, “Resonators for solid-state lasers with large-volume fundamental mode and high alignment stability,” Appl. Opt. 25, 107–117 (1986).
[CrossRef] [PubMed]

Murdough, M. P.

Opower, H.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

Schöne, W.

Shine, R. J.

Silvestri, S. De.

G. Cerullo, S. De. Silvestri, V. Magni, O. Svelto, “Output power limitations in CW single transverse mode Nd:YAG lasers with a rod-of large cross-section,” Opt. Quantum Electron. 25, 489–500 (1993).

G. Cerullo, S. De. Silvestri, V. Magni, “High efficiency, 40 W cw Nd:YLF laser with large TEM00 mode,” Opt. Commun. 93, 77–81 (1992).

Steffen, J.

J. Steffen, J. P. Lörtscher, G. Herziger, “Fundamental mode radiation with solid-state lasers,” IEEE J. Quantum Electron. QE-8, 239–245 (1972).
[CrossRef]

Svelto, O.

G. Cerullo, S. De. Silvestri, V. Magni, O. Svelto, “Output power limitations in CW single transverse mode Nd:YAG lasers with a rod-of large cross-section,” Opt. Quantum Electron. 25, 489–500 (1993).

Tashiro, H.

R. Hua, S. Wada, H. Tashiro, “Principle and limitation of a quarter-wave plate for reducing the depolarization loss from thermally induced birefringence in Nd:YAG lasers,” Opt. Commun. 175, 189–200 (2000).
[CrossRef]

R. Hua, S. Wada, H. Tashiro, “Compact TEM00 mode resonator for laser-diode side-pumped Nd:YAG laser,” in Extended Abstracts of JSAP’s 60th Autumn Meeting (Japan Society of Applied Physics, Tokyo, 1999), Vol. 3, paper 2a-L-7, p. 909.

Tünnerman, A.

Valentini, G.

V. Magni, G. Valentini, S. De Silvestri, “Recent developments in laser resonator design,” Opt. Quantum Electron. 23, 1105–1134 (1991), and references therein.

Van Driel, H. M.

U. J. Greiner, H. H. Klingenberg, D. R. Walker, C. J. Flood, H. M. Van Driel, “Diode-pumped Nd:YAG laser using reflective pump optics,” Appl. Phys. B 58, 393–395 (1994).
[CrossRef]

Voss, A.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

Wada, S.

R. Hua, S. Wada, H. Tashiro, “Principle and limitation of a quarter-wave plate for reducing the depolarization loss from thermally induced birefringence in Nd:YAG lasers,” Opt. Commun. 175, 189–200 (2000).
[CrossRef]

R. Hua, S. Wada, H. Tashiro, “Compact TEM00 mode resonator for laser-diode side-pumped Nd:YAG laser,” in Extended Abstracts of JSAP’s 60th Autumn Meeting (Japan Society of Applied Physics, Tokyo, 1999), Vol. 3, paper 2a-L-7, p. 909.

Walker, D. R.

U. J. Greiner, H. H. Klingenberg, D. R. Walker, C. J. Flood, H. M. Van Driel, “Diode-pumped Nd:YAG laser using reflective pump optics,” Appl. Phys. B 58, 393–395 (1994).
[CrossRef]

Wittig, K.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

Appl. Opt. (2)

Appl. Phys. B (2)

U. J. Greiner, H. H. Klingenberg, D. R. Walker, C. J. Flood, H. M. Van Driel, “Diode-pumped Nd:YAG laser using reflective pump optics,” Appl. Phys. B 58, 393–395 (1994).
[CrossRef]

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

Bell Syst. Tech. J. (1)

H. Kogelnik, “Imaging of optical modes—resonators with internal lens,” Bell Syst. Tech. J. 44, 455–494 (1965).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Steffen, J. P. Lörtscher, G. Herziger, “Fundamental mode radiation with solid-state lasers,” IEEE J. Quantum Electron. QE-8, 239–245 (1972).
[CrossRef]

Opt. Commun. (2)

G. Cerullo, S. De. Silvestri, V. Magni, “High efficiency, 40 W cw Nd:YLF laser with large TEM00 mode,” Opt. Commun. 93, 77–81 (1992).

R. Hua, S. Wada, H. Tashiro, “Principle and limitation of a quarter-wave plate for reducing the depolarization loss from thermally induced birefringence in Nd:YAG lasers,” Opt. Commun. 175, 189–200 (2000).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (2)

V. Magni, G. Valentini, S. De Silvestri, “Recent developments in laser resonator design,” Opt. Quantum Electron. 23, 1105–1134 (1991), and references therein.

G. Cerullo, S. De. Silvestri, V. Magni, O. Svelto, “Output power limitations in CW single transverse mode Nd:YAG lasers with a rod-of large cross-section,” Opt. Quantum Electron. 25, 489–500 (1993).

Other (2)

R. Hua, S. Wada, H. Tashiro, “Compact TEM00 mode resonator for laser-diode side-pumped Nd:YAG laser,” in Extended Abstracts of JSAP’s 60th Autumn Meeting (Japan Society of Applied Physics, Tokyo, 1999), Vol. 3, paper 2a-L-7, p. 909.

W. Koechner, Solid-State Laser Engineering, 4th. ed. (Springer-Verlag, Berlin, 1996).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

(a) Traditional two-mirror dynamically stable resonator whose length is typically longer than 1 m. (b) Model resonator designed by our new method. The spacings of the optical components are measured from the principal planes of the laser rod, which acts as a thermal lens. By varying d 1 of Arm1, one is able to vary the curvature and the location of the image mirror M1′, and an appropriate beam size in the laser rod is achieved. Similarly, the location of M2′ can be adjusted to either the left- or the right-hand side of the laser rod by means of varying d 2 of Arm2, and therefore M1′ can always be imaged to M2′ by the thermal lens of the laser rod to keep the resonator insensitive to mechanical misalignment.

Fig. 2
Fig. 2

Dependence of the effective parameters of the image mirrors M1′ and M2′ on d 1 or d 2 for the resonator as shown in Fig. 1(b). Both M1 and M2 are plane mirrors. Lens1 is a plano–concave lens (f 1 = -5 cm), and Lens2 is a plano–convex lens (f 2 = 7.5 cm). The Nd: YAG rod is 5.5 cm long, and its principal planes are 1.51 cm away from each end surface of the rod. The other parameters are Δ1 = 7.5 cm and Δ2 = 4 cm. Arm1 controls the MGBR through |u 1′| (L1′ remains nearly constant). Arm2 controls the location L2′ of M2′ without interfering the MGBR (|u 2′| remains small and nearly constant).

Fig. 3
Fig. 3

Dependence of the beam radii at the end mirrors on (a) d 1 (d 2 = 12.5 cm) and on (b) d 2 (d 1 = 3 cm). f thm is assumed to be 40 cm, and the other parameters of the resonator are the same as those in Fig. 2.

Fig. 4
Fig. 4

Dependence of the beam radii at the end mirrors and in the laser rod on diopter of the thermal lens. Here d 1 = 3 cm, d 2 = 12.5 cm, and the other parameters of the resonator are the same as those in Fig. 2.

Fig. 5
Fig. 5

Dependence of the beam radius in the laser rod on the thermal-lens focal length of the laser rod (a) at different d 2 and (b) on d 2 at different focal lengths of the thermal lens. The resonator is the four-element resonator shown in Fig. 1(b). d 1 = 3 cm, and the other parameters of the resonator are noted in the caption of Fig. 2. It is apparent that the optimized d 2 decreases as f thm decreases with increasing pump power.

Fig. 6
Fig. 6

(a) Dependence of the laser output powers and the beam quality on LD current for d 2 = 11.63 cm (higher-power operation, M 2 = 1.9) and d 2 = 11.22 cm (lower-power operation, M 2 = 1.5), respectively. (b) Measured and calculated misalignment half-angles of the end mirrors at different LD currents. The resonator is the four-element resonator as shown in Fig. 1(b), and the other parameters of the resonator are the same as those in Fig. 4.

Fig. 7
Fig. 7

Dependence of the output power and beam quality on (a) d 1 (d 2 = 11.22 cm) and (b) d 2 (d 1 = 3 cm) at a LD current of 35 A. The resonator is the four-element resonator shown in Fig. 1(b), and the other parameters of the resonator are noted in the caption of Fig. 2.

Fig. 8
Fig. 8

Dependence on the LD current of (a) the laser output power and the beam quality and (b) the misalignment half-angles of the end mirrors. The resonator is a three-mirror resonator with d 2 = 10.25 cm. M1 is a convex mirror (R = -20 cm) placed 19 cm from the left principal plane of the laser rod. Lens2 of Fig. 1(b) is replaced with a folding concave mirror (R F = 20 cm) at 16 cm from the right principal plane of the laser rod.

Fig. 9
Fig. 9

Dependence of the laser output power and the beam quality on (a) L 1 and (b) d 2 at a LD current of 33 A. The resonator is a three-mirror resonator, and its parameters are the same as those in Fig. 8.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

ω02=2λ/πmax|u1|, |u2|,
ui=Li1-LiRi,  i=1, 2,
Li=Δi+fidifi-di,  i=1, 2,
Ri=fi2fi-diRiRi+fi-di,  i=1, 2.
ω102=λ/πd1+Δ1|f1|/Δ1+|f1|,
ω202=λ/πf22/2|u1|,
Si=miω0Liui11R1-L1+1R2-L2+1fth,  i =1, 2,
mi=1-di/fi,  i=1, 2.
ω102=λ/πL12/|u1|,
ω202=m22λ/πL2/u22|u1|-u12-u221/2.
1fth0=1L1-12u1+1L2.

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