Abstract

Stress-induced birefringence in cw-pumped Nd:YAG rods create stability limitations on the TEM00 polarized mode of a resonant cavity. We present and verify experimentally a thermo-optical model describing a ring cavity containing a birefringent cw-pumped Nd:YAG rod. We use the model, along with experimental evidence, to show that a fundamental TEM00 mode size and pump-power limitation exists for any cw-pumped Nd:YAG laser, implying a maximum allowable TEM00 output. We show that the largest TEM00 mode radius that can be supported in the rod is approximately 1.1 mm and is independent of the physical size of the rod.

© 1996 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. V. Magni, “Multielement stable resonators containing a variable lens,” J. Opt. Soc. Am. A 4, 1962–1969 (1987).
    [CrossRef]
  3. V. Magni, G. Valentini, S. De Silvestri, “Recent developments in laser resonator design,” Opt. Quantum Electron. 23, 1105–1134 (1991).
    [CrossRef]
  4. G. Cerullo, S. De Silvestri, V. Magni, O. Svelto, “Output limitations in CW single transverse mode Nd:YAG lasers with a rod of large cross section,” Opt. Quantum Electron. 25, 489–500 (1993).
    [CrossRef]
  5. W. Koechner, Solid State Laser Engineering, 3rd ed. (Springer-Verlag, Berlin, 1992), Chap. 7.
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    [CrossRef] [PubMed]
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  8. A. E. Seigman, Lasers (University Science Books, Mill Valley, Calif., 1986), Chap. 15.
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. N. Hodgson, H. Weber, “High power solid-state lasers with unstable resonators,” Opt. Quantum Electron. 22, S39–S55 (1990).
    [CrossRef]
  14. D. P. Devor, L. G. DeShazer, “Evidence of Nd:YAG quantum efficiency dependence on nonequivalent crystal field effects,” Opt. Commun. 46, 97–102 (1983).
    [CrossRef]
  15. D. P. Devor, L. G. DeShazer, R. C. Pastor, “Nd:YAG quantum efficiency and related radiative properties,” IEEE J. Quantum Electron. QE-25, 1863–1873 (1989).
    [CrossRef]
  16. V. Lupei, A. Lupei, S. Georgescu, C. Ionescu, “Energy transfer between Nd3+ ions in YAG,” Opt. Commun. 60, 59–63 (1986).
    [CrossRef]
  17. O. Cregut, C. N. Man, D. Shoemaker, A. Brillet, A. Menhert, P. Peuser, N. P. Schmitt, P. Zeller, K. Wallmeroth, “18 W single frequency operation of an injection-locked, CW, Nd:YAG laser,” Phys. Lett. A 140, 294–298 (1989).
    [CrossRef]
  18. S. T. Yang, R. C. Eckardt, R. L. Byer, “1.9-W cw ring-cavity KTP singly resonant optical parametric oscillator,” Opt. Lett. 19, 475–477 (1994).
    [CrossRef] [PubMed]

1994

1993

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

N. Hodgson, C. Rahlff, H. Weber, “Dependence of the refractive power of Nd:YAG rods on the intracavity intensity,” Opt. Laser Technol. 25, 179–185 (1993).
[CrossRef]

1991

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

1990

N. Hodgson, H. Weber, “High power solid-state lasers with unstable resonators,” Opt. Quantum Electron. 22, S39–S55 (1990).
[CrossRef]

1989

O. Cregut, C. N. Man, D. Shoemaker, A. Brillet, A. Menhert, P. Peuser, N. P. Schmitt, P. Zeller, K. Wallmeroth, “18 W single frequency operation of an injection-locked, CW, Nd:YAG laser,” Phys. Lett. A 140, 294–298 (1989).
[CrossRef]

D. P. Devor, L. G. DeShazer, R. C. Pastor, “Nd:YAG quantum efficiency and related radiative properties,” IEEE J. Quantum Electron. QE-25, 1863–1873 (1989).
[CrossRef]

1987

1986

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

V. Lupei, A. Lupei, S. Georgescu, C. Ionescu, “Energy transfer between Nd3+ ions in YAG,” Opt. Commun. 60, 59–63 (1986).
[CrossRef]

1983

D. P. Devor, L. G. DeShazer, “Evidence of Nd:YAG quantum efficiency dependence on nonequivalent crystal field effects,” Opt. Commun. 46, 97–102 (1983).
[CrossRef]

1975

J. P. Lortscher, J. Steffen, G. Herziger, “Dynamic stable resonators: a design procedure,” Opt. Quantum Electron. 7, 505–514 (1975).
[CrossRef]

1970

1966

Brillet, A.

O. Cregut, C. N. Man, D. Shoemaker, A. Brillet, A. Menhert, P. Peuser, N. P. Schmitt, P. Zeller, K. Wallmeroth, “18 W single frequency operation of an injection-locked, CW, Nd:YAG laser,” Phys. Lett. A 140, 294–298 (1989).
[CrossRef]

Byer, R. L.

Cerullo, G.

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

Cregut, O.

O. Cregut, C. N. Man, D. Shoemaker, A. Brillet, A. Menhert, P. Peuser, N. P. Schmitt, P. Zeller, K. Wallmeroth, “18 W single frequency operation of an injection-locked, CW, Nd:YAG laser,” Phys. Lett. A 140, 294–298 (1989).
[CrossRef]

De Silvestri, S.

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

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

DeShazer, L. G.

D. P. Devor, L. G. DeShazer, R. C. Pastor, “Nd:YAG quantum efficiency and related radiative properties,” IEEE J. Quantum Electron. QE-25, 1863–1873 (1989).
[CrossRef]

D. P. Devor, L. G. DeShazer, “Evidence of Nd:YAG quantum efficiency dependence on nonequivalent crystal field effects,” Opt. Commun. 46, 97–102 (1983).
[CrossRef]

Devor, D. P.

D. P. Devor, L. G. DeShazer, R. C. Pastor, “Nd:YAG quantum efficiency and related radiative properties,” IEEE J. Quantum Electron. QE-25, 1863–1873 (1989).
[CrossRef]

D. P. Devor, L. G. DeShazer, “Evidence of Nd:YAG quantum efficiency dependence on nonequivalent crystal field effects,” Opt. Commun. 46, 97–102 (1983).
[CrossRef]

Eckardt, R. C.

Georgescu, S.

V. Lupei, A. Lupei, S. Georgescu, C. Ionescu, “Energy transfer between Nd3+ ions in YAG,” Opt. Commun. 60, 59–63 (1986).
[CrossRef]

Herziger, G.

J. P. Lortscher, J. Steffen, G. Herziger, “Dynamic stable resonators: a design procedure,” Opt. Quantum Electron. 7, 505–514 (1975).
[CrossRef]

Hodgson, N.

N. Hodgson, C. Rahlff, H. Weber, “Dependence of the refractive power of Nd:YAG rods on the intracavity intensity,” Opt. Laser Technol. 25, 179–185 (1993).
[CrossRef]

N. Hodgson, H. Weber, “High power solid-state lasers with unstable resonators,” Opt. Quantum Electron. 22, S39–S55 (1990).
[CrossRef]

Ionescu, C.

V. Lupei, A. Lupei, S. Georgescu, C. Ionescu, “Energy transfer between Nd3+ ions in YAG,” Opt. Commun. 60, 59–63 (1986).
[CrossRef]

Koechner, W.

W. Koechner, “Thermal lensing in a Nd:YAG rod,” Appl. Opt. 9, 2548–2553 (1970).
[CrossRef] [PubMed]

W. Koechner, Solid State Laser Engineering, 3rd ed. (Springer-Verlag, Berlin, 1992), Chap. 7.

Kogelnik, H.

Li, T.

Lortscher, J. P.

J. P. Lortscher, J. Steffen, G. Herziger, “Dynamic stable resonators: a design procedure,” Opt. Quantum Electron. 7, 505–514 (1975).
[CrossRef]

Lupei, A.

V. Lupei, A. Lupei, S. Georgescu, C. Ionescu, “Energy transfer between Nd3+ ions in YAG,” Opt. Commun. 60, 59–63 (1986).
[CrossRef]

Lupei, V.

V. Lupei, A. Lupei, S. Georgescu, C. Ionescu, “Energy transfer between Nd3+ ions in YAG,” Opt. Commun. 60, 59–63 (1986).
[CrossRef]

Magni, V.

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

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

V. Magni, “Multielement stable resonators containing a variable lens,” J. Opt. Soc. Am. A 4, 1962–1969 (1987).
[CrossRef]

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

Man, C. N.

O. Cregut, C. N. Man, D. Shoemaker, A. Brillet, A. Menhert, P. Peuser, N. P. Schmitt, P. Zeller, K. Wallmeroth, “18 W single frequency operation of an injection-locked, CW, Nd:YAG laser,” Phys. Lett. A 140, 294–298 (1989).
[CrossRef]

Menhert, A.

O. Cregut, C. N. Man, D. Shoemaker, A. Brillet, A. Menhert, P. Peuser, N. P. Schmitt, P. Zeller, K. Wallmeroth, “18 W single frequency operation of an injection-locked, CW, Nd:YAG laser,” Phys. Lett. A 140, 294–298 (1989).
[CrossRef]

Murdough, M. P.

M. P. Murdough, “Power scaling of CW injection-locked Nd: YAG lasers,” M.S. thesis (University of New Mexico, Albuquerque, New Mexico, 1995).

Pastor, R. C.

D. P. Devor, L. G. DeShazer, R. C. Pastor, “Nd:YAG quantum efficiency and related radiative properties,” IEEE J. Quantum Electron. QE-25, 1863–1873 (1989).
[CrossRef]

Peuser, P.

O. Cregut, C. N. Man, D. Shoemaker, A. Brillet, A. Menhert, P. Peuser, N. P. Schmitt, P. Zeller, K. Wallmeroth, “18 W single frequency operation of an injection-locked, CW, Nd:YAG laser,” Phys. Lett. A 140, 294–298 (1989).
[CrossRef]

Rahlff, C.

N. Hodgson, C. Rahlff, H. Weber, “Dependence of the refractive power of Nd:YAG rods on the intracavity intensity,” Opt. Laser Technol. 25, 179–185 (1993).
[CrossRef]

Schmitt, N. P.

O. Cregut, C. N. Man, D. Shoemaker, A. Brillet, A. Menhert, P. Peuser, N. P. Schmitt, P. Zeller, K. Wallmeroth, “18 W single frequency operation of an injection-locked, CW, Nd:YAG laser,” Phys. Lett. A 140, 294–298 (1989).
[CrossRef]

Seigman, A. E.

A. E. Seigman, Lasers (University Science Books, Mill Valley, Calif., 1986), Chap. 15.

Shoemaker, D.

O. Cregut, C. N. Man, D. Shoemaker, A. Brillet, A. Menhert, P. Peuser, N. P. Schmitt, P. Zeller, K. Wallmeroth, “18 W single frequency operation of an injection-locked, CW, Nd:YAG laser,” Phys. Lett. A 140, 294–298 (1989).
[CrossRef]

Steffen, J.

J. P. Lortscher, J. Steffen, G. Herziger, “Dynamic stable resonators: a design procedure,” Opt. Quantum Electron. 7, 505–514 (1975).
[CrossRef]

Svelto, O.

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

Valentini, G.

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

Wallmeroth, K.

O. Cregut, C. N. Man, D. Shoemaker, A. Brillet, A. Menhert, P. Peuser, N. P. Schmitt, P. Zeller, K. Wallmeroth, “18 W single frequency operation of an injection-locked, CW, Nd:YAG laser,” Phys. Lett. A 140, 294–298 (1989).
[CrossRef]

Weber, H.

N. Hodgson, C. Rahlff, H. Weber, “Dependence of the refractive power of Nd:YAG rods on the intracavity intensity,” Opt. Laser Technol. 25, 179–185 (1993).
[CrossRef]

N. Hodgson, H. Weber, “High power solid-state lasers with unstable resonators,” Opt. Quantum Electron. 22, S39–S55 (1990).
[CrossRef]

Yang, S. T.

Yariv, A.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989), Chaps. 6 and 7.

Zeller, P.

O. Cregut, C. N. Man, D. Shoemaker, A. Brillet, A. Menhert, P. Peuser, N. P. Schmitt, P. Zeller, K. Wallmeroth, “18 W single frequency operation of an injection-locked, CW, Nd:YAG laser,” Phys. Lett. A 140, 294–298 (1989).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

D. P. Devor, L. G. DeShazer, R. C. Pastor, “Nd:YAG quantum efficiency and related radiative properties,” IEEE J. Quantum Electron. QE-25, 1863–1873 (1989).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

V. Lupei, A. Lupei, S. Georgescu, C. Ionescu, “Energy transfer between Nd3+ ions in YAG,” Opt. Commun. 60, 59–63 (1986).
[CrossRef]

D. P. Devor, L. G. DeShazer, “Evidence of Nd:YAG quantum efficiency dependence on nonequivalent crystal field effects,” Opt. Commun. 46, 97–102 (1983).
[CrossRef]

Opt. Laser Technol.

N. Hodgson, C. Rahlff, H. Weber, “Dependence of the refractive power of Nd:YAG rods on the intracavity intensity,” Opt. Laser Technol. 25, 179–185 (1993).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

N. Hodgson, H. Weber, “High power solid-state lasers with unstable resonators,” Opt. Quantum Electron. 22, S39–S55 (1990).
[CrossRef]

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

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

J. P. Lortscher, J. Steffen, G. Herziger, “Dynamic stable resonators: a design procedure,” Opt. Quantum Electron. 7, 505–514 (1975).
[CrossRef]

Phys. Lett. A

O. Cregut, C. N. Man, D. Shoemaker, A. Brillet, A. Menhert, P. Peuser, N. P. Schmitt, P. Zeller, K. Wallmeroth, “18 W single frequency operation of an injection-locked, CW, Nd:YAG laser,” Phys. Lett. A 140, 294–298 (1989).
[CrossRef]

Other

M. P. Murdough, “Power scaling of CW injection-locked Nd: YAG lasers,” M.S. thesis (University of New Mexico, Albuquerque, New Mexico, 1995).

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989), Chaps. 6 and 7.

A. E. Seigman, Lasers (University Science Books, Mill Valley, Calif., 1986), Chap. 15.

W. Koechner, Solid State Laser Engineering, 3rd ed. (Springer-Verlag, Berlin, 1992), Chap. 7.

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Figures (17)

Fig. 1
Fig. 1

Cavity layout used in the theoretical model. The placement of intracavity lenses and rod-end curvatures is arbitrary. A ring cavity design was chosen so that the system can later be injection locked. TFP, thin-film plate.

Fig. 2
Fig. 2

Effect of increasing the TEM00 mode size on the overlap of the r- and ϕ-polarization stability zones. An intracavity telescope of variable magnification is used to change the mode size at the entrance face of the rod. An arbitrary, symmetric end curvature is placed on the laser rod to maintain a constant overlap location. At larger spot sizes, the individual stability zones grow narrower and eventually cease to overlap.

Fig. 3
Fig. 3

Curvature R of the laser rod at various pump powers Pl. The rod initially has a −80-cm curvature.

Fig. 4
Fig. 4

Stability criteria and mode size plot for the r- and ϕ-polarization modes. Note that the mode radius remains relatively constant over a range of lamp powers and increases to infinity as the stability criteria approaches 1. The laser must remain within both stability zones to generate the maximum output at a given pump power.

Fig. 5
Fig. 5

Effect of changing the rod-end curvature on the ϕ-polarization stability criteria and mode size. Radii of curvature of infinity, −100 and −50 cm are used for the three cases shown. Note that the curvature drives the stability zone to higher pump powers without changing the width of the zone or the size of the mode.

Fig. 6
Fig. 6

Laser output and cavity stability for a 50 cm × 50 cm symmetric standing-wave cavity. A flat high reflector and flat 80% reflective output coupler are used.

Fig. 7
Fig. 7

Laser output and cavity stability for a 36 cm × 78.5 cm asymmetric standing-wave cavity. A flat high reflector and a flat 80% reflective output coupler are used.

Fig. 8
Fig. 8

Laser output and cavity stability for a 70 cm × 70 cm symmetric standing-wave cavity. The laser rod has −80-cm end curvatures. A flat high reflector and a flat 80% output coupler are used. Note how the addition of end curvatures drives the stability zone to higher pump powers.

Fig. 9
Fig. 9

Theoretical and measured laser waist of a 120-cm injection-locked ring cavity.

Fig. 10
Fig. 10

Effect of rod-end curvature R on the overlap of the r- and ϕ-polarization zones for a given cavity configuration. If the rod-end curvatures are too short, the two polarizations lack sufficient overlap to allow lasing.

Fig. 11
Fig. 11

Stability criteria, mode size, and laser output power for cavity configuration #1. An intracavity lens was not used.

Fig. 12
Fig. 12

Stability criteria, mode size, and laser output power for cavity configuration 2. A −20-cm intracavity lens was used to increase the mode size in the rod.

Fig. 13
Fig. 13

Stability criteria, mode size, and laser output power for cavity configuration 3. A −15-cm intracavity lens was used to increase the mode size in the rod.

Fig. 14
Fig. 14

Stability criteria, mode size, and laser output power for cavity configuration 4. A −10-cm intracavity lens was used to increase the mode size. No lasing was observed from this cavity.

Fig. 15
Fig. 15

Extrapolation of cavity case 2 to higher pump powers. A −100-cm curvature is assumed on the ends of the laser rod to generate the stability and mode radius curves.

Fig. 16
Fig. 16

Extrapolation of power data from an injection-locked laser with a 105-cm cavity as depicted in Fig. 1 and laser head 1 from Table 1. For these data, a 10 cm × 4 mm rod (0.8 at. % Nd) with flat ends and a −25-cm intracavity lens were used. A maximum of 27.5 W of cw, single-frequency polarized TEM00 (M2 = 1.07) laser power at 1.064 μm was obtained with the same configuration as above except for the change to a rod with −80-cm-radius end curvature.

Fig. 17
Fig. 17

Stability and mode radii for the r- and ϕ-polarizations with single-pump head and two-pump head laser cavities. The x axis is the total lamp power of each pump head, not both heads combined. The presence of the second head forces the laser to operate in a narrower stability zone with a lower maximum pump power and a near-exact overlap of the r- and ϕ-polarization modes.

Tables (2)

Tables Icon

Table 1 Typical Results of Four Different Laser Heads Analyzed by Our Theoretical Model

Tables Icon

Table 2 Cavity Configurations to Determine the Maximum TEM00 Mode Volume Allowable for Stable Operation of an Nd:YAG Rod Laser

Equations (17)

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T ( r ) = T ( r 0 ) + Q 4 K ( r 0 2 - r 2 ) ,
n ( r ) = n 0 [ 1 + Q 2 K ( 1 2 n 0 d n d T + n 0 2 α C r , ϕ ) r 2 ] ,
n ( r ) = n 0 - 1 2 n r , ϕ r 2 ,
n r , ϕ = β r , ϕ P l .
β r , ϕ = η T π r 0 2 z K [ 1 2 d n d T + n 0 3 α C r , ϕ ] = { 3.40 × 10 - 5 η T π r 0 2 z 1 W cm 2             r polarization 2.72 × 10 - 5 η T π r 0 2 z 1 W cm 2             ϕ polarization ,
Q = η T P l π r 0 2 z .
Z r , ϕ = [ cos ( γ r , ϕ z ) 1 γ r , ϕ sin ( γ r , ϕ z ) - γ r , ϕ sin ( γ r , ϕ z ) cos ( γ r , ϕ z ) ] .
γ r , ϕ = n r , ϕ n 0 .
P r , ϕ = n 0 γ r , ϕ tan ( γ z ) .
T ( r ) = T F + η T P l 2 π r 0 z h + ( η T P l 4 π r 0 2 z K ) ( r 0 2 - r 2 ) ,
Δ l ( r ) = α z Δ T ( r ) 2 ,
Δ z curv ( r ) = R curv { 1 - cos [ tan - 1 ( r R curv ) ] } .
Δ z curv ( r ) 1 2 r 2 R curv .
Δ z eff ( r ) Δ l ( r ) - Δ z curv ( r ) .
R eff r 0 2 2 [ Δ z eff ( 0 ) - Δ z eff ( r 0 ) ] .
Q r , ϕ = C ex T ex Z r , ϕ T ent C ent .
M r , ϕ = T 1 T 4 F 2 T 3 F 1 T 2 Q r , ϕ = ( A r , ϕ B r , ϕ C r , ϕ D r , ϕ ) ,

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