Abstract

A method to determine directly the radius of the fundamental mode in a laser crystal has been developed. The radius is measured by comparison of the distribution of the spontaneous emission in the pumped region during laser operation with the fluorescence distribution without laser emission. Measuring the mode radius with various pump powers enables one to optimize the overlap between the pump and the cavity beam and to determine the dioptric power of the thermally induced lens.

© 1998 Optical Society of America

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References

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  1. C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
    [CrossRef]
  2. J. Frauchiger, P. Albers, H. P. Weber, “Modelling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd:YAG laser,” IEEE J. Quantum Electron. 28, 1046–1056 (1992).
    [CrossRef]
  3. S. Merazzi, R. Gruber, C. Pfistner, R. Weber, “Numerical simulation of mechanical and optical properties of solid-state lasers,” Tech. Rep. (Centro Svizzero di Calcolo Scientifico, Manno, Switzerland, 1993).
  4. S. C. Tidwell, J. F. Seamans, M. S. Bowers, A. K. Cousins, “Scaling cw diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
    [CrossRef]
  5. U. O. Farrukh, A. M. Buoncristiani, C. E. Byvik, “An analysis of the temperature distribution in finite solid-state laser rods,” IEEE J. Quantum Electron. 24, 2253–2263 (1988).
    [CrossRef]
  6. M. E. Innocenzi, H. T. Yura, C. L. Fincher, R. A. Fields, “Thermal modelling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
    [CrossRef]
  7. J. E. Murray, “Pulsed gain and thermal lensing of Nd:LiYF4,” IEEE J. Quantum Electron. QE-19, 488–491 (1983).
    [CrossRef]
  8. G. Cerullo, S. de Silvestri, V. Magni, “High efficient 40W Nd:YLF laser with large TEM00 mode,” Opt. Commun. 93, 77–81 (1992).
    [CrossRef]
  9. B. Neuenschwander, R. Weber, H. P. Weber, “Determination of the thermal lens in solid-state lasers with stable cavities,” IEEE J. Quantum Electron. 31, 1082–1087 (1995).
    [CrossRef]
  10. N. Hodgson, H. Weber, Optical Resonators (Springer-Verlag, Berlin, 1997), pp. 598–604.
  11. N. Hodgson, H. Weber, Optische Resonatoren (Springer-Verlag, Berlin, 1992).
    [CrossRef]
  12. S. de Silvestri, P. Laporta, V. Magni, “Pump power stability range of single-mode solid-state lasers with rod thermal lensing,” IEEE J. Quantum Electron. QE-23, 1999–2003 (1987).
    [CrossRef]
  13. Th. Graf, J. E. Balmer, R. Weber, H. P. Weber, “Variable-configuration resonator (VCR) with three diode-laser end-pumped Nd:YAG rods,” in Advanced Solid-State Lasers, Vol. 10 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 370–375.
  14. V. Magni, “Resonators for solid-state lasers with large-volume fundamental mode and high alignment stability,” Appl. Opt. 25, 107–117 (1986).
    [CrossRef] [PubMed]

1995 (1)

B. Neuenschwander, R. Weber, H. P. Weber, “Determination of the thermal lens in solid-state lasers with stable cavities,” IEEE J. Quantum Electron. 31, 1082–1087 (1995).
[CrossRef]

1994 (1)

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

1992 (3)

J. Frauchiger, P. Albers, H. P. Weber, “Modelling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd:YAG laser,” IEEE J. Quantum Electron. 28, 1046–1056 (1992).
[CrossRef]

S. C. Tidwell, J. F. Seamans, M. S. Bowers, A. K. Cousins, “Scaling cw diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[CrossRef]

G. Cerullo, S. de Silvestri, V. Magni, “High efficient 40W Nd:YLF laser with large TEM00 mode,” Opt. Commun. 93, 77–81 (1992).
[CrossRef]

1990 (1)

M. E. Innocenzi, H. T. Yura, C. L. Fincher, R. A. Fields, “Thermal modelling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

1988 (1)

U. O. Farrukh, A. M. Buoncristiani, C. E. Byvik, “An analysis of the temperature distribution in finite solid-state laser rods,” IEEE J. Quantum Electron. 24, 2253–2263 (1988).
[CrossRef]

1987 (1)

S. de Silvestri, P. Laporta, V. Magni, “Pump power stability range of single-mode solid-state lasers with rod thermal lensing,” IEEE J. Quantum Electron. QE-23, 1999–2003 (1987).
[CrossRef]

1986 (1)

1983 (1)

J. E. Murray, “Pulsed gain and thermal lensing of Nd:LiYF4,” IEEE J. Quantum Electron. QE-19, 488–491 (1983).
[CrossRef]

Albers, P.

J. Frauchiger, P. Albers, H. P. Weber, “Modelling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd:YAG laser,” IEEE J. Quantum Electron. 28, 1046–1056 (1992).
[CrossRef]

Balmer, J. E.

Th. Graf, J. E. Balmer, R. Weber, H. P. Weber, “Variable-configuration resonator (VCR) with three diode-laser end-pumped Nd:YAG rods,” in Advanced Solid-State Lasers, Vol. 10 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 370–375.

Bowers, M. S.

S. C. Tidwell, J. F. Seamans, M. S. Bowers, A. K. Cousins, “Scaling cw diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[CrossRef]

Buoncristiani, A. M.

U. O. Farrukh, A. M. Buoncristiani, C. E. Byvik, “An analysis of the temperature distribution in finite solid-state laser rods,” IEEE J. Quantum Electron. 24, 2253–2263 (1988).
[CrossRef]

Byvik, C. E.

U. O. Farrukh, A. M. Buoncristiani, C. E. Byvik, “An analysis of the temperature distribution in finite solid-state laser rods,” IEEE J. Quantum Electron. 24, 2253–2263 (1988).
[CrossRef]

Cerullo, G.

G. Cerullo, S. de Silvestri, V. Magni, “High efficient 40W Nd:YLF laser with large TEM00 mode,” Opt. Commun. 93, 77–81 (1992).
[CrossRef]

Cousins, A. K.

S. C. Tidwell, J. F. Seamans, M. S. Bowers, A. K. Cousins, “Scaling cw diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[CrossRef]

de Silvestri, S.

G. Cerullo, S. de Silvestri, V. Magni, “High efficient 40W Nd:YLF laser with large TEM00 mode,” Opt. Commun. 93, 77–81 (1992).
[CrossRef]

S. de Silvestri, P. Laporta, V. Magni, “Pump power stability range of single-mode solid-state lasers with rod thermal lensing,” IEEE J. Quantum Electron. QE-23, 1999–2003 (1987).
[CrossRef]

Farrukh, U. O.

U. O. Farrukh, A. M. Buoncristiani, C. E. Byvik, “An analysis of the temperature distribution in finite solid-state laser rods,” IEEE J. Quantum Electron. 24, 2253–2263 (1988).
[CrossRef]

Fields, R. A.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, R. A. Fields, “Thermal modelling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

Fincher, C. L.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, R. A. Fields, “Thermal modelling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

Frauchiger, J.

J. Frauchiger, P. Albers, H. P. Weber, “Modelling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd:YAG laser,” IEEE J. Quantum Electron. 28, 1046–1056 (1992).
[CrossRef]

Graf, Th.

Th. Graf, J. E. Balmer, R. Weber, H. P. Weber, “Variable-configuration resonator (VCR) with three diode-laser end-pumped Nd:YAG rods,” in Advanced Solid-State Lasers, Vol. 10 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 370–375.

Gruber, R.

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

S. Merazzi, R. Gruber, C. Pfistner, R. Weber, “Numerical simulation of mechanical and optical properties of solid-state lasers,” Tech. Rep. (Centro Svizzero di Calcolo Scientifico, Manno, Switzerland, 1993).

Hodgson, N.

N. Hodgson, H. Weber, Optical Resonators (Springer-Verlag, Berlin, 1997), pp. 598–604.

N. Hodgson, H. Weber, Optische Resonatoren (Springer-Verlag, Berlin, 1992).
[CrossRef]

Innocenzi, M. E.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, R. A. Fields, “Thermal modelling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

Laporta, P.

S. de Silvestri, P. Laporta, V. Magni, “Pump power stability range of single-mode solid-state lasers with rod thermal lensing,” IEEE J. Quantum Electron. QE-23, 1999–2003 (1987).
[CrossRef]

Magni, V.

G. Cerullo, S. de Silvestri, V. Magni, “High efficient 40W Nd:YLF laser with large TEM00 mode,” Opt. Commun. 93, 77–81 (1992).
[CrossRef]

S. de Silvestri, P. Laporta, V. Magni, “Pump power stability range of single-mode solid-state lasers with rod thermal lensing,” IEEE J. Quantum Electron. QE-23, 1999–2003 (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]

Merazzi, S.

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

S. Merazzi, R. Gruber, C. Pfistner, R. Weber, “Numerical simulation of mechanical and optical properties of solid-state lasers,” Tech. Rep. (Centro Svizzero di Calcolo Scientifico, Manno, Switzerland, 1993).

Murray, J. E.

J. E. Murray, “Pulsed gain and thermal lensing of Nd:LiYF4,” IEEE J. Quantum Electron. QE-19, 488–491 (1983).
[CrossRef]

Neuenschwander, B.

B. Neuenschwander, R. Weber, H. P. Weber, “Determination of the thermal lens in solid-state lasers with stable cavities,” IEEE J. Quantum Electron. 31, 1082–1087 (1995).
[CrossRef]

Pfistner, C.

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

S. Merazzi, R. Gruber, C. Pfistner, R. Weber, “Numerical simulation of mechanical and optical properties of solid-state lasers,” Tech. Rep. (Centro Svizzero di Calcolo Scientifico, Manno, Switzerland, 1993).

Seamans, J. F.

S. C. Tidwell, J. F. Seamans, M. S. Bowers, A. K. Cousins, “Scaling cw diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[CrossRef]

Tidwell, S. C.

S. C. Tidwell, J. F. Seamans, M. S. Bowers, A. K. Cousins, “Scaling cw diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[CrossRef]

Weber, H.

N. Hodgson, H. Weber, Optical Resonators (Springer-Verlag, Berlin, 1997), pp. 598–604.

N. Hodgson, H. Weber, Optische Resonatoren (Springer-Verlag, Berlin, 1992).
[CrossRef]

Weber, H. P.

B. Neuenschwander, R. Weber, H. P. Weber, “Determination of the thermal lens in solid-state lasers with stable cavities,” IEEE J. Quantum Electron. 31, 1082–1087 (1995).
[CrossRef]

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

J. Frauchiger, P. Albers, H. P. Weber, “Modelling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd:YAG laser,” IEEE J. Quantum Electron. 28, 1046–1056 (1992).
[CrossRef]

Th. Graf, J. E. Balmer, R. Weber, H. P. Weber, “Variable-configuration resonator (VCR) with three diode-laser end-pumped Nd:YAG rods,” in Advanced Solid-State Lasers, Vol. 10 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 370–375.

Weber, R.

B. Neuenschwander, R. Weber, H. P. Weber, “Determination of the thermal lens in solid-state lasers with stable cavities,” IEEE J. Quantum Electron. 31, 1082–1087 (1995).
[CrossRef]

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

Th. Graf, J. E. Balmer, R. Weber, H. P. Weber, “Variable-configuration resonator (VCR) with three diode-laser end-pumped Nd:YAG rods,” in Advanced Solid-State Lasers, Vol. 10 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 370–375.

S. Merazzi, R. Gruber, C. Pfistner, R. Weber, “Numerical simulation of mechanical and optical properties of solid-state lasers,” Tech. Rep. (Centro Svizzero di Calcolo Scientifico, Manno, Switzerland, 1993).

Yura, H. T.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, R. A. Fields, “Thermal modelling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. E. Innocenzi, H. T. Yura, C. L. Fincher, R. A. Fields, “Thermal modelling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

IEEE J. Quantum Electron. (7)

J. E. Murray, “Pulsed gain and thermal lensing of Nd:LiYF4,” IEEE J. Quantum Electron. QE-19, 488–491 (1983).
[CrossRef]

B. Neuenschwander, R. Weber, H. P. Weber, “Determination of the thermal lens in solid-state lasers with stable cavities,” IEEE J. Quantum Electron. 31, 1082–1087 (1995).
[CrossRef]

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

J. Frauchiger, P. Albers, H. P. Weber, “Modelling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd:YAG laser,” IEEE J. Quantum Electron. 28, 1046–1056 (1992).
[CrossRef]

S. C. Tidwell, J. F. Seamans, M. S. Bowers, A. K. Cousins, “Scaling cw diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[CrossRef]

U. O. Farrukh, A. M. Buoncristiani, C. E. Byvik, “An analysis of the temperature distribution in finite solid-state laser rods,” IEEE J. Quantum Electron. 24, 2253–2263 (1988).
[CrossRef]

S. de Silvestri, P. Laporta, V. Magni, “Pump power stability range of single-mode solid-state lasers with rod thermal lensing,” IEEE J. Quantum Electron. QE-23, 1999–2003 (1987).
[CrossRef]

Opt. Commun. (1)

G. Cerullo, S. de Silvestri, V. Magni, “High efficient 40W Nd:YLF laser with large TEM00 mode,” Opt. Commun. 93, 77–81 (1992).
[CrossRef]

Other (4)

N. Hodgson, H. Weber, Optical Resonators (Springer-Verlag, Berlin, 1997), pp. 598–604.

N. Hodgson, H. Weber, Optische Resonatoren (Springer-Verlag, Berlin, 1992).
[CrossRef]

S. Merazzi, R. Gruber, C. Pfistner, R. Weber, “Numerical simulation of mechanical and optical properties of solid-state lasers,” Tech. Rep. (Centro Svizzero di Calcolo Scientifico, Manno, Switzerland, 1993).

Th. Graf, J. E. Balmer, R. Weber, H. P. Weber, “Variable-configuration resonator (VCR) with three diode-laser end-pumped Nd:YAG rods,” in Advanced Solid-State Lasers, Vol. 10 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 370–375.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup. The laser crystal is pumped from the right-hand side with a fiber-coupled diode laser. The spontaneously emitted light is recorded with a CCD camera through the plane facet perpendicular to the resonator axis. The laser is forced to operate in fundamental mode by an aperture in the resonator. The resonator parameters are l = 12 mm, d = 10 mm, L 2 = 90 mm, ρ2 = -1000 mm, and R 2 = 95%.

Fig. 2
Fig. 2

Coordinate system for the numerical reconstruction of the distribution of spontaneous emission. The circular area is subdivided into stripes parallel to the y axis (the direction of integration) and concentric circles (with constant values of f).

Fig. 3
Fig. 3

Effects of errors in measurement such as (a) constant background (constant shift), (b) linearly increasing background (linearly increasing shift), and (c) low-frequency image distortion (low-frequency spatial modulation) on the calculated mode radius w(P). The ordinates show the maximum relative error of the calculated mode radius as a function of the maximum relative error in the measured data (abscissas).

Fig. 4
Fig. 4

Integrated (measured) and reconstructed intensity distributions. The solid curves correspond to the fluorescence without laser emission; the dashed curves were recorded during laser operation. The pump power was 10 W.

Fig. 5
Fig. 5

Measured dependence of mode radius on pump power in the laser crystal (points) and best fit for f* (solid curve). Dashed curves, lower and upper limits of the mode radii w(P) calculated with an f* that is 15% smaller and 15% larger than the f* found as the best fit.

Equations (14)

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f = f x ,   y ,   z = f r ,   z ,     r = x 2 + y 2 .
F x ,   z = - R R   f x ,   y ,   z d y ,
f r ,   z - g r ,   z     g r ,   z Φ r ,   z
Φ r ,   z     f r ,   z - g r ,   z g r ,   z ,     g r ,   z 0 .
Φ x ,   y ,   z 0 = α   exp - β 2 x 2 + y 2 .
F x ,   z 0 - G x ,   z 0     - R R   g x ,   y ,   z 0 Φ x ,   y ,   z 0 d y
R mode = 2 / β   half-width at   1 / e 2 of   Φ r ,   z 0 .
w = 1 λ π Im 1 q 1 / 2 .
P i = 2   j = 1 N - i + 1   f i , j A i , j ,     f i , j = 0 ,     j > N - i + 1 ,
f N , 1 = P N / A N , 1 .
f i - 1 , j + 1 = f i , j .
f i , 1 = 1 A i , 1 P i 2 - n = 2 N - i + 1   A i , n f i + n - 1 , 1 .
f N , 1 = P N - δ N 2 A N , 1 ,
f i , 1 = 1 A i , 1 P i - δ i 2 - n = 2 N - i + 1   A i , n f i + n - 1 , 1 .

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