Abstract

A thermo-optical model describing the cavity stability and TEM00-mode volume of a repetitively pumped solid-state laser is developed and verified experimentally. The model predicts a maximum theoretical TEM00 Gaussian-mode radius in the laser rod. This maximum mode radius is caused by a bifocusing of the cavity mode and is present even in gain-polarized materials that nominally suppress the effect of birefringence on beam polarization. The mode limitation effect is not eliminated by conventional optics and is reduced only marginally by the often-described technique of placing a second identical laser head in the cavity. A maximum mode radius implies a fundamental limit on the TEM00-mode energy that can be extracted from a given laser cavity.

© 2002 Optical Society of America

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References

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  1. S. De Silvestri, “Pump power stability range of single-mode solid state lasers with rod thermal lensing,” IEEE J. Quantum Electron. QE-23, 1999–2004 (1987).
    [CrossRef]
  2. V. Magni, “Multielement stable resonators containing a variable lens,” J. Opt. Soc. Am. A 4, 1962–1969 (1987).
    [CrossRef]
  3. V. Magni, “Resonators for solid-state lasers with large-volume fundamental mode and high alignment stability,” Appl. Opt. 25, 107–117 (1986).
    [CrossRef] [PubMed]
  4. V. Magni, G. Valentini, S. De Silvestri, “Recent developments in laser resonator design,” Opt. Quantum Electron. 23, 1105–1134 (1991).
    [CrossRef]
  5. 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]
  6. J. Sherman, “Thermal compensation of a cw-pumped Nd:YAG laser,” Appl. Opt. 37, 7789–7796 (1998).
    [CrossRef]
  7. M. Murdough, C. Denman, “Mode volume and pump power limitations in injection-locked TEM00 Nd:YAG lasers,” Appl. Opt. 35, 5925–5936 (1996).
    [CrossRef] [PubMed]
  8. C. Yung-Fu, “Pump-to-mode size ratio dependence of thermal loading in diode-end-pumped solid-state lasers,” J. Opt. Soc. Am. B 17, 1835–1840 (2000).
    [CrossRef]
  9. R. Teehan, J. Bienfang, C. Denman, “Power scaling and frequency stabilization of an injection-locked Nd:YAG rod laser,” Appl. Opt. 39, 3076–3084 (2000).
    [CrossRef]
  10. R. Hua, W. Wada, H. Tashiro, “Versatile, compact, TEM00-mode resonator for side-pumped single-rod solid-state lasers,” Appl. Opt. 40, 2468–2474 (2001).
    [CrossRef]
  11. D. Udaiyan, G. Crofts, T. Omatsu, M. Damzen, “Self-consistent spatial mode analysis of self-adaptive laser oscillators,” J. Opt. Soc. Am. B 15, 1346–1352 (1998).
    [CrossRef]
  12. W. Koechner, Solid State Laser Engineering, 4th ed. (Springer-Verlag, Berlin, 1992), Chap. 7.
  13. K. Driedger, W. Krause, H. Weber, “Average refractive powers of an alexandrite laser rod,” Opt. Commun. 57, 403–406 (1986).
    [CrossRef]
  14. A. Seigman, Lasers (University Science, Sausalito, Calif., 1986), Chap. 15.
  15. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989), Chaps. 6 and 7.
  16. Ref. 12, Chap. 2.
  17. J. Verdeyen, Laser Electronics, 3rd ed. (Prentice-Hall, Upper Saddle River, N.J., 1995), Chap. 2.

2001 (1)

2000 (2)

1998 (2)

1996 (1)

1993 (1)

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]

1991 (1)

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

1987 (2)

S. De Silvestri, “Pump power stability range of single-mode solid state lasers with rod thermal lensing,” IEEE J. Quantum Electron. QE-23, 1999–2004 (1987).
[CrossRef]

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

1986 (2)

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

K. Driedger, W. Krause, H. Weber, “Average refractive powers of an alexandrite laser rod,” Opt. Commun. 57, 403–406 (1986).
[CrossRef]

Bienfang, J.

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]

Crofts, G.

Damzen, M.

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]

S. De Silvestri, “Pump power stability range of single-mode solid state lasers with rod thermal lensing,” IEEE J. Quantum Electron. QE-23, 1999–2004 (1987).
[CrossRef]

Denman, C.

Driedger, K.

K. Driedger, W. Krause, H. Weber, “Average refractive powers of an alexandrite laser rod,” Opt. Commun. 57, 403–406 (1986).
[CrossRef]

Hua, R.

Koechner, W.

W. Koechner, Solid State Laser Engineering, 4th ed. (Springer-Verlag, Berlin, 1992), Chap. 7.

Krause, W.

K. Driedger, W. Krause, H. Weber, “Average refractive powers of an alexandrite laser rod,” Opt. Commun. 57, 403–406 (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]

Murdough, M.

Omatsu, T.

Seigman, A.

A. Seigman, Lasers (University Science, Sausalito, Calif., 1986), Chap. 15.

Sherman, J.

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]

Tashiro, H.

Teehan, R.

Udaiyan, D.

Valentini, G.

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

Verdeyen, J.

J. Verdeyen, Laser Electronics, 3rd ed. (Prentice-Hall, Upper Saddle River, N.J., 1995), Chap. 2.

Wada, W.

Weber, H.

K. Driedger, W. Krause, H. Weber, “Average refractive powers of an alexandrite laser rod,” Opt. Commun. 57, 403–406 (1986).
[CrossRef]

Yariv, A.

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

Yung-Fu, C.

Appl. Opt. (5)

IEEE J. Quantum Electron. (1)

S. De Silvestri, “Pump power stability range of single-mode solid state lasers with rod thermal lensing,” IEEE J. Quantum Electron. QE-23, 1999–2004 (1987).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

K. Driedger, W. Krause, H. Weber, “Average refractive powers of an alexandrite laser rod,” Opt. Commun. 57, 403–406 (1986).
[CrossRef]

Opt. Quantum Electron. (2)

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]

Other (5)

W. Koechner, Solid State Laser Engineering, 4th ed. (Springer-Verlag, Berlin, 1992), Chap. 7.

A. Seigman, Lasers (University Science, Sausalito, Calif., 1986), Chap. 15.

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

Ref. 12, Chap. 2.

J. Verdeyen, Laser Electronics, 3rd ed. (Prentice-Hall, Upper Saddle River, N.J., 1995), Chap. 2.

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Figures (14)

Fig. 1
Fig. 1

Resolution of the electric field E of a linearly polarized laser beam into radial and azimuthal components. The field polarized parallel to the low-gain axis in a gain-polarized material will be suppressed. The field polarized along the high-gain axis can still be resolved into r and ϕ components and will thus exhibit bifocusing even though birefringence is suppressed.

Fig. 2
Fig. 2

Ring cavity model showing the laser rod, intracavity lens, and translation distances used for ABCD matrix analysis.

Fig. 3
Fig. 3

Stability criteria and TEM00-mode radius plot for a 1.7-m ring cavity with no intracavity optics. Cavity is stable where the stability criteria (light lines) are between 0 and 1. The bifocusing effect splits the cavity stability into r- and ϕ-polarization zones. The laser operates only in the stability zone between 0 and 21 Hz where both polarizations are simultaneously stable. Mode radii (dark lines) are relatively constant at the center of the stability zone but increase rapidly to infinity at both edges.

Fig. 4
Fig. 4

Average laser output power as a function of pump repetition rate at 150-J total lamp energy. A 50-cm positive lens is placed 70 cm from the pump head in a 194-cm ring cavity. The β r and βϕ constants are selected to match the maximum r and ϕ cavity stability points to the peak output power and shutoff repetition rates of the laser, respectively.

Fig. 5
Fig. 5

Average laser output power as a function of pump repetition rate at 189-J total lamp energy. A 50-cm positive lens is placed 70 cm from the pump head in a 194-cm-long ring cavity. The β r and βϕ coefficients are the same as those fit to form an identical cavity at 150 J, as shown in Fig. 4.

Fig. 6
Fig. 6

Average laser output power as a function of pump repetition rate at 112-J total lamp energy. A 50-cm positive lens is placed 70 cm from the pump head in a 194-cm ring cavity. The β r and βϕ coefficients are the same as those fit to form an identical cavity at 150 J, as shown in Fig. 4.

Fig. 7
Fig. 7

Theoretical and experimental TEM00-mode diameters 3.02 m from the output coupler as a function of pump repetition rate at 182-J lamp energy with no intracavity lens. β r and βϕ constants determined from the plot in Fig. 4 were used to calculate the theoretical cavity mode diameters.

Fig. 8
Fig. 8

Theoretical and experimental TEM00-mode diameters 3.02 m from the output coupler as a function of pump repetition rate at 189-J lamp energy and with a +2.0-m intracavity lens. β r and βϕ coefficients determined from the plot in Fig. 4 were used to calculate the theoretical cavity mode diameters.

Fig. 9
Fig. 9

Stability criteria and TEM00-mode radius plot for a 1.7-m ring cavity with a -20-cm lens placed 80 cm from the laser rod. The cavity is stable where the stability criteria (light lines) are between 0 and 1. The laser operates only in the stability zone between 37 and 42 Hz where both polarizations are simultaneously stable. Mode radii (dark lines) for each polarization are significantly different except at the exact center of the stability zone.

Fig. 10
Fig. 10

Upper plot: stability zone width as a function of intracavity lens focal power. The cavity is stable in the shaded region where the r- and ϕ-polarization stability zones overlap. Lower plot: the intersection of the r maximum and ϕ minimum stable pump repetition rates defines the location of the largest TEM00-mode radius.

Fig. 11
Fig. 11

Experimental stability data as a function of intracavity lens focal power. Theoretical maximum and ϕ minimum stable pump repetition rates for M 2 = 1.0 and M 2 = 1.25 are shown representing the potential uncertainty in the stability region for a given data set. Points at which lasing was observed are marked with an x, nonlasing points are shown by an o.

Fig. 12
Fig. 12

Upper plot: stability zone width as a function of intracavity lens focal power for an arbitrarily long 20-m ring cavity with no rod end curvature. The cavity is stable in the shaded regions where the r- and ϕ-polarization stability zones overlap. Lower plot: the intersection of the r maximum and ϕ minimum stable pump repetition rates defines the location of the largest TEM00-mode radius. Note that the cavity is stable with large mode radii but only at low repetition rates.

Fig. 13
Fig. 13

Upper plot: stability zone width as a function of intracavity lens focal power for an arbitrarily long 20-m ring cavity with concave rod end curvatures of 1.0 m. The cavity is stable at higher repetition rates than the similarly sized cavity analyzed in Fig. 12. Lower plot: The higher repetition rates come at the expense of much smaller mode radii, comparable to those that can be seen in the 1.7-m cavity analyzed in Fig. 10.

Fig. 14
Fig. 14

Stability criteria and TEM00-mode radius plot for a 1.7-m ring cavity with two identical pump heads and a 90° polarization rotator. The upper plot shows a cavity with no intracavity lens that operates at small mode radii. The r- and ϕ-polarization zones overlap each other, eliminating the bifocusing effect. The TEM00-mode radius (dark lines) are identical for both polarizations. The lower plot shows the same cavity with a -3.0-cm intracavity lens. The lens allows the cavity to operate with much bigger TEM00-mode radii, but in a much narrower stability zone. Perfect bifocusing compensation is also lost.

Tables (1)

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Table 1 Model Parameters Used in Theoretical Plots

Equations (13)

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Tr=Tr0+Q4Kr02-r2,
Q=ηTE0νπr02z,
nr=n01-Q2K12n0dndT+n02αCr,ϕr2,
nr=n0-12 nr,ϕr2.
nr,ϕ=βr,ϕE0ν,
βr,ϕ=ηTπr02zK12dndT+n03αCr,ϕ.
Zr,ϕ=cosγr,ϕz1γr,ϕsinγr,ϕz-γr,ϕ sinγr,ϕzcosγr,ϕz,
γr,ϕ=nr,ϕn01/2=βr,ϕE0νn01/2.
Qr,ϕ=RexitZr,ϕRentrance,
r2=1r1+dM2r1,
M2r2=0r1+M2r1,
r2r2=Tr1r1,
T=1dM201.

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