Abstract

A pair of laser parameters of considerable practical interest are the small signal gain and saturation irradiance of the gain medium. These are commonly measured by observing the dependence of the output power on some adjustable cavity loss parameter and comparing the measured data with the predictions of a suitable laser model. Because of the inevitable approximations in this model the resulting estimates of gain and saturation irradiance are always affected to some extent by systematic errors. The small-gain, plane-wave, mean-field, and pure homogeneous or inhomogeneous line-broadening approximations are considered, with estimates of the magnitudes of these errors being presented for the case in which the gain, the saturation irradiance, and the cavity loss are fitted to the data. It is shown that these errors can be quite substantial, and therefore accurate absolute measurements of the three laser parameters can be quite difficult to obtain using the variable loss method. As an illustration of these errors, a comparison between the measured output power from a HCN laser and the power predicted using experimentally measured gain and saturation irradiance values is shown. The poor quality of these predictions illustrates the serious effects that the systematic errors can have, although an alternative analysis in which the cavity loss is supplied and only the gain and saturation irradiance fitted is also shown and gives good predictions despite inaccuracies in the model.

© 1999 Optical Society of America

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References

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  1. J. R. Birch, C. C. Bradley, “A variable loss determination of HCN laser gain,” Infrared Phys. 13, 99–108 (1973).
    [CrossRef]
  2. J. J. Degnan, H. E. Walker, J. H. McElroy, N. McAvoy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron. QE-9, 489–491 (1973).
    [CrossRef]
  3. B. S. Patel, “Determination of gain, saturation intensity, and internal losses of a laser using an intracavity rotatable reflector,” IEEE J. Quantum Electron. QE-9, 1150–1151 (1973).
    [CrossRef]
  4. P. Woskoboinikow, W. C. Jennings, “The measurement of far-infrared laser gain and loss using a Michelson coupler,” IEEE J. Quantum Electron. QE-12, 613–615 (1976).
    [CrossRef]
  5. C. O. Weiss, “Optically pumped FIR-laser with variable Fabry-Perot output coupler,” Appl. Phys. 13, 383–385 (1977).
    [CrossRef]
  6. L. B. Whitbourn, J. C. Macfarlane, P. A. Stimson, B. W. James, I. S. Falconer, “An experimental study of a CW optically pumped far infrared formic acid vapour laser,” Infrared Phys. 28, 7–20 (1988).
    [CrossRef]
  7. N. Takahashi, T. Sasaki, H. Gamo, “Simple method to determine the gain and saturation irradiance of a laser,” Appl. Opt. 30, 3805–3809 (1991).
    [CrossRef] [PubMed]
  8. J. Schmiedberger, J. Kodymova, O. Spalek, J. Kovar, “Experimental study of gain and output coupling characteristics of a CW chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 27, 1265–1270 (1991).
    [CrossRef]
  9. S. J. Cooper, “Output power optimization and gain and saturation irradiance measurements on a RF-pumped HCN waveguide laser,” Appl. Opt. 37, 4881–4890 (1998).
    [CrossRef]
  10. L. W. Casperson, “Laser power calculations: sources of error,” Appl. Opt. 19, 422–434 (1980).
    [CrossRef] [PubMed]
  11. S. J. Cooper, N. R. Heckenberg, “Plane-wave theory of a Michelson laser coupler with a dielectric slab beam splitter,” Appl. Opt. 35, 1395–1398 (1996).
    [CrossRef] [PubMed]
  12. S. Cooper, “A study of the indirect measurement of laser small signal gain and saturation irradiance and its application to an RF pumped HCN waveguide laser,” Ph.D. dissertation (The University of Queensland, St. Lucia, Australia, 1994).

1998 (1)

1996 (1)

1991 (2)

J. Schmiedberger, J. Kodymova, O. Spalek, J. Kovar, “Experimental study of gain and output coupling characteristics of a CW chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 27, 1265–1270 (1991).
[CrossRef]

N. Takahashi, T. Sasaki, H. Gamo, “Simple method to determine the gain and saturation irradiance of a laser,” Appl. Opt. 30, 3805–3809 (1991).
[CrossRef] [PubMed]

1988 (1)

L. B. Whitbourn, J. C. Macfarlane, P. A. Stimson, B. W. James, I. S. Falconer, “An experimental study of a CW optically pumped far infrared formic acid vapour laser,” Infrared Phys. 28, 7–20 (1988).
[CrossRef]

1980 (1)

1977 (1)

C. O. Weiss, “Optically pumped FIR-laser with variable Fabry-Perot output coupler,” Appl. Phys. 13, 383–385 (1977).
[CrossRef]

1976 (1)

P. Woskoboinikow, W. C. Jennings, “The measurement of far-infrared laser gain and loss using a Michelson coupler,” IEEE J. Quantum Electron. QE-12, 613–615 (1976).
[CrossRef]

1973 (3)

J. R. Birch, C. C. Bradley, “A variable loss determination of HCN laser gain,” Infrared Phys. 13, 99–108 (1973).
[CrossRef]

J. J. Degnan, H. E. Walker, J. H. McElroy, N. McAvoy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron. QE-9, 489–491 (1973).
[CrossRef]

B. S. Patel, “Determination of gain, saturation intensity, and internal losses of a laser using an intracavity rotatable reflector,” IEEE J. Quantum Electron. QE-9, 1150–1151 (1973).
[CrossRef]

Birch, J. R.

J. R. Birch, C. C. Bradley, “A variable loss determination of HCN laser gain,” Infrared Phys. 13, 99–108 (1973).
[CrossRef]

Bradley, C. C.

J. R. Birch, C. C. Bradley, “A variable loss determination of HCN laser gain,” Infrared Phys. 13, 99–108 (1973).
[CrossRef]

Casperson, L. W.

Cooper, S.

S. Cooper, “A study of the indirect measurement of laser small signal gain and saturation irradiance and its application to an RF pumped HCN waveguide laser,” Ph.D. dissertation (The University of Queensland, St. Lucia, Australia, 1994).

Cooper, S. J.

Degnan, J. J.

J. J. Degnan, H. E. Walker, J. H. McElroy, N. McAvoy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron. QE-9, 489–491 (1973).
[CrossRef]

Falconer, I. S.

L. B. Whitbourn, J. C. Macfarlane, P. A. Stimson, B. W. James, I. S. Falconer, “An experimental study of a CW optically pumped far infrared formic acid vapour laser,” Infrared Phys. 28, 7–20 (1988).
[CrossRef]

Gamo, H.

Heckenberg, N. R.

James, B. W.

L. B. Whitbourn, J. C. Macfarlane, P. A. Stimson, B. W. James, I. S. Falconer, “An experimental study of a CW optically pumped far infrared formic acid vapour laser,” Infrared Phys. 28, 7–20 (1988).
[CrossRef]

Jennings, W. C.

P. Woskoboinikow, W. C. Jennings, “The measurement of far-infrared laser gain and loss using a Michelson coupler,” IEEE J. Quantum Electron. QE-12, 613–615 (1976).
[CrossRef]

Kodymova, J.

J. Schmiedberger, J. Kodymova, O. Spalek, J. Kovar, “Experimental study of gain and output coupling characteristics of a CW chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 27, 1265–1270 (1991).
[CrossRef]

Kovar, J.

J. Schmiedberger, J. Kodymova, O. Spalek, J. Kovar, “Experimental study of gain and output coupling characteristics of a CW chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 27, 1265–1270 (1991).
[CrossRef]

Macfarlane, J. C.

L. B. Whitbourn, J. C. Macfarlane, P. A. Stimson, B. W. James, I. S. Falconer, “An experimental study of a CW optically pumped far infrared formic acid vapour laser,” Infrared Phys. 28, 7–20 (1988).
[CrossRef]

McAvoy, N.

J. J. Degnan, H. E. Walker, J. H. McElroy, N. McAvoy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron. QE-9, 489–491 (1973).
[CrossRef]

McElroy, J. H.

J. J. Degnan, H. E. Walker, J. H. McElroy, N. McAvoy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron. QE-9, 489–491 (1973).
[CrossRef]

Patel, B. S.

B. S. Patel, “Determination of gain, saturation intensity, and internal losses of a laser using an intracavity rotatable reflector,” IEEE J. Quantum Electron. QE-9, 1150–1151 (1973).
[CrossRef]

Sasaki, T.

Schmiedberger, J.

J. Schmiedberger, J. Kodymova, O. Spalek, J. Kovar, “Experimental study of gain and output coupling characteristics of a CW chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 27, 1265–1270 (1991).
[CrossRef]

Spalek, O.

J. Schmiedberger, J. Kodymova, O. Spalek, J. Kovar, “Experimental study of gain and output coupling characteristics of a CW chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 27, 1265–1270 (1991).
[CrossRef]

Stimson, P. A.

L. B. Whitbourn, J. C. Macfarlane, P. A. Stimson, B. W. James, I. S. Falconer, “An experimental study of a CW optically pumped far infrared formic acid vapour laser,” Infrared Phys. 28, 7–20 (1988).
[CrossRef]

Takahashi, N.

Walker, H. E.

J. J. Degnan, H. E. Walker, J. H. McElroy, N. McAvoy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron. QE-9, 489–491 (1973).
[CrossRef]

Weiss, C. O.

C. O. Weiss, “Optically pumped FIR-laser with variable Fabry-Perot output coupler,” Appl. Phys. 13, 383–385 (1977).
[CrossRef]

Whitbourn, L. B.

L. B. Whitbourn, J. C. Macfarlane, P. A. Stimson, B. W. James, I. S. Falconer, “An experimental study of a CW optically pumped far infrared formic acid vapour laser,” Infrared Phys. 28, 7–20 (1988).
[CrossRef]

Woskoboinikow, P.

P. Woskoboinikow, W. C. Jennings, “The measurement of far-infrared laser gain and loss using a Michelson coupler,” IEEE J. Quantum Electron. QE-12, 613–615 (1976).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. (1)

C. O. Weiss, “Optically pumped FIR-laser with variable Fabry-Perot output coupler,” Appl. Phys. 13, 383–385 (1977).
[CrossRef]

IEEE J. Quantum Electron. (4)

J. J. Degnan, H. E. Walker, J. H. McElroy, N. McAvoy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron. QE-9, 489–491 (1973).
[CrossRef]

B. S. Patel, “Determination of gain, saturation intensity, and internal losses of a laser using an intracavity rotatable reflector,” IEEE J. Quantum Electron. QE-9, 1150–1151 (1973).
[CrossRef]

P. Woskoboinikow, W. C. Jennings, “The measurement of far-infrared laser gain and loss using a Michelson coupler,” IEEE J. Quantum Electron. QE-12, 613–615 (1976).
[CrossRef]

J. Schmiedberger, J. Kodymova, O. Spalek, J. Kovar, “Experimental study of gain and output coupling characteristics of a CW chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 27, 1265–1270 (1991).
[CrossRef]

Infrared Phys. (2)

J. R. Birch, C. C. Bradley, “A variable loss determination of HCN laser gain,” Infrared Phys. 13, 99–108 (1973).
[CrossRef]

L. B. Whitbourn, J. C. Macfarlane, P. A. Stimson, B. W. James, I. S. Falconer, “An experimental study of a CW optically pumped far infrared formic acid vapour laser,” Infrared Phys. 28, 7–20 (1988).
[CrossRef]

Other (1)

S. Cooper, “A study of the indirect measurement of laser small signal gain and saturation irradiance and its application to an RF pumped HCN waveguide laser,” Ph.D. dissertation (The University of Queensland, St. Lucia, Australia, 1994).

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Figures (5)

Fig. 1
Fig. 1

Matched curves of output power P as a function of coupler transmittance T for four different laser models. The accompanying table below the figure shows the corresponding laser parameters that generated these matched curves.

Fig. 2
Fig. 2

Systematic error ratios that are due to a mixed line-broadening mechanism. The laser has a mixed broadening mechanism with a linewidth ratio Δν h ν d (model SMPM), but pure homogeneous (SHPM) or inhomogeneous (SIPM) broadening is assumed in the analysis. These groups of curves are identified with the labels SMPM/SHPM and SMPM/SIPM, respectively, and were calculated for generating model gain-to-loss ratios of 2g 01 L/ A 1 = 1.2, 2.0, 3.5, 6.0, and 10, with the extreme curves in each group being indicated by suitable labels.

Fig. 3
Fig. 3

Systematic error ratios that are due to spatial hole burning effects. The curves marked SHGM/SHPM and SIGM/SIPM show the errors that result when the laser has a Gaussian cavity mode (model SHGM or SIGM), but a plane-wave model (SHPM or SIPM) is used in the analysis. The curves marked SHPL/SHPM and SIPL/SIPM show the errors that result when the laser has longitudinal hole burning (models SHPL or SIPL), but a mean-field model (SHPM or SIPM) is used in the analysis. The homogeneous and inhomogeneous broadening cases are indicated by solid and dashed curves, respectively.

Fig. 4
Fig. 4

Systematic error ratios that are due to large-gain effects. The curves marked RHPM/SHPM and LHPM/SHPM show the errors that result when the laser has a large gain with the loss concentrated in either the output coupler (model RHPM) or the mirror opposite the coupler (model LHPM), whereas a small-gain model (SHPM) is used in the analysis. The curves marked RHPM/LHPM show the case in which the laser has a large gain with the loss concentrated at the output coupler (RHPM), whereas a large gain model with the loss concentrated at the mirror opposite the coupler (LHPM) is used in the analysis. Calculations were performed for extreme gain-to-loss ratios of 2g 01 L/ A 1 = 1.2 and 10.

Fig. 5
Fig. 5

Predicted and measured output powers as a function of gas pressure for the HCN laser discussed in the text. The solid symbols identify the measured powers, whereas the open symbols show the predicted output powers. Solid curves show the three-parameter fit results whereas the dashed curve shows the two-parameter fit. The models used to determine the gain and saturation power for the gain medium and to calculate the output powers are shown in the legend.

Tables (1)

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Table 1 Collation of Output Power Expressions for the Models used in the Papera

Equations (1)

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P=TPs2 QA+T2g0L,

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