Abstract

A one-dimensional model of a laser with homogeneously broadened saturable gain and distributed loss is used to calculate the recirculating power and extraction efficiency for the case in which the mirrors are lossless. Accurate numerical results show that optimized single-ended lasers, equivalent symmetric lasers, and optimized symmetric lasers have the same extraction efficiency when the gain is small, but not when it is large. The peak efficiency of the single-ended laser is known to decrease with increasing length of the gain cell at high gain. The efficiency of the symmetric laser is found to decrease much less, so the output power nearly scales linearly with length over the range investigated. Thus past assumptions about equivalences between lasers must be reexamined. An approximate analytic solution of the laser equation is shown to be useful from threshold to closed cavity over a wide range of values of the small signal gain, the distributed loss coefficient, and the length of the gain cell.

© 1992 Optical Society of America

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References

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  1. W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
    [CrossRef]
  2. G. M. Schindler, “Optimum output efficiency of homogeneously broadened lasers with constant loss,” IEEE J. Quantum Electron. QE-16, 546–549 (1980).
    [CrossRef]
  3. D. Eimerl, “Optical extraction characteristics of homogeneously broadened cw lasers with nonsaturating lasers,” J. Appl. Phys. 51, 3008–3016 (1980).
    [CrossRef]
  4. T. R. Ferguson, “Lasers with saturable gain and distributed loss,” Appl. Opt. 26, 2522–2527 (1987).
    [CrossRef] [PubMed]
  5. W. W. Rigrod, “Homogeneously broadened cw lasers with uniform distributed loss,” IEEE J. Quantum Electron. QE-14, 377–381 (1978).
    [CrossRef]
  6. W. P. Latham, D. Statman, “Saturation characteristics of a laser amplifier,” submitted to J. Mod. Opt.
  7. W. P. Latham, Phillips Laboratory, Kirtland Air Force Base, New Mexico 87117 (personal communication).
  8. P. W. Milonni, “Saturation of anomalous dispersion in cw HF lasers,” Appl. Opt. 20, 1571–1578 (1981).
    [CrossRef] [PubMed]
  9. H. Mirels, “Inhomogeneous broadening effects in cw chemical lasers,” ALAA J. 17, 478–489 (1979).

1987 (1)

1981 (1)

1980 (2)

G. M. Schindler, “Optimum output efficiency of homogeneously broadened lasers with constant loss,” IEEE J. Quantum Electron. QE-16, 546–549 (1980).
[CrossRef]

D. Eimerl, “Optical extraction characteristics of homogeneously broadened cw lasers with nonsaturating lasers,” J. Appl. Phys. 51, 3008–3016 (1980).
[CrossRef]

1979 (1)

H. Mirels, “Inhomogeneous broadening effects in cw chemical lasers,” ALAA J. 17, 478–489 (1979).

1978 (1)

W. W. Rigrod, “Homogeneously broadened cw lasers with uniform distributed loss,” IEEE J. Quantum Electron. QE-14, 377–381 (1978).
[CrossRef]

1965 (1)

W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
[CrossRef]

Eimerl, D.

D. Eimerl, “Optical extraction characteristics of homogeneously broadened cw lasers with nonsaturating lasers,” J. Appl. Phys. 51, 3008–3016 (1980).
[CrossRef]

Ferguson, T. R.

Latham, W. P.

W. P. Latham, Phillips Laboratory, Kirtland Air Force Base, New Mexico 87117 (personal communication).

W. P. Latham, D. Statman, “Saturation characteristics of a laser amplifier,” submitted to J. Mod. Opt.

Milonni, P. W.

Mirels, H.

H. Mirels, “Inhomogeneous broadening effects in cw chemical lasers,” ALAA J. 17, 478–489 (1979).

Rigrod, W. W.

W. W. Rigrod, “Homogeneously broadened cw lasers with uniform distributed loss,” IEEE J. Quantum Electron. QE-14, 377–381 (1978).
[CrossRef]

W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
[CrossRef]

Schindler, G. M.

G. M. Schindler, “Optimum output efficiency of homogeneously broadened lasers with constant loss,” IEEE J. Quantum Electron. QE-16, 546–549 (1980).
[CrossRef]

Statman, D.

W. P. Latham, D. Statman, “Saturation characteristics of a laser amplifier,” submitted to J. Mod. Opt.

ALAA J. (1)

H. Mirels, “Inhomogeneous broadening effects in cw chemical lasers,” ALAA J. 17, 478–489 (1979).

Appl. Opt. (2)

IEEE J. Quantum Electron. (2)

G. M. Schindler, “Optimum output efficiency of homogeneously broadened lasers with constant loss,” IEEE J. Quantum Electron. QE-16, 546–549 (1980).
[CrossRef]

W. W. Rigrod, “Homogeneously broadened cw lasers with uniform distributed loss,” IEEE J. Quantum Electron. QE-14, 377–381 (1978).
[CrossRef]

J. Appl. Phys. (2)

D. Eimerl, “Optical extraction characteristics of homogeneously broadened cw lasers with nonsaturating lasers,” J. Appl. Phys. 51, 3008–3016 (1980).
[CrossRef]

W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
[CrossRef]

Other (2)

W. P. Latham, D. Statman, “Saturation characteristics of a laser amplifier,” submitted to J. Mod. Opt.

W. P. Latham, Phillips Laboratory, Kirtland Air Force Base, New Mexico 87117 (personal communication).

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Figures (4)

Fig. 1
Fig. 1

Single-ended laser and an equivalent symmetric laser with identical dependence of wave intensities on the longitudinal coordinate z.

Fig. 2
Fig. 2

Longitudinal dependence of the intensities in an optimized symmetric laser (dashed curves) and an optimized single-ended laser (solid curve) for α0L = 2 and g0L = 20.

Fig. 3
Fig. 3

Comparison of the exact results for λ and the extraction efficiency η to quadratic approximation results for λq and ηq. The exact solution for λ(r) is also shown with λ as the abscissa (rb = 1, α0L = 0.1, g0L = 2).

Fig. 4
Fig. 4

As in Fig. 2 but with rb = 1, α0L = 1, and g0L = 5.

Tables (15)

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Table I Comparison of Optimized Single-Ended Laser, Equivalent Symmetric Laser, and Optimized Symmetric Laser for α0L = 5, g0L = 10

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Table II Same as Table I but for α0L = 2, g0L = 20

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Table III Same as Table I but for α0L = 1, g0L = 2

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Table IV Peak Extraction Efficiency for Single-Ended Lasers

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Table V Reflectivity for Peak Efficiency for Single-Ended Lasers

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Table VI λ at Peak Efficiency for Single-Ended Lasers

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Table VII Peak Extraction Efficiency for Symmetric Lasers

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Table VIII Reflectivity at Peak Efficiency for Symmetric Lasers

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Table IX λ at Peak Efficiency for Symmetric Lasers

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Table X Peak Efficiency for Single-Ended Lasers in the Quadratic Approximation

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Table XI Reflectivity at Peak Efficiency for Single-Ended Lasers in the Quadratic Approximation

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Table XII λ at Peak Efficiency for Single-Ended Lasers in the Quadratic Approximation

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Table XIII Peak Extraction Efficiency for Symmetric Lasers in the Quadratic Approximation

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Table XIV Reflectivity at Peak Extraction Efficiency for Symmetric Lasers in the Quadratic Approximation

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Table XV λ at Peak Extraction Efficiency for Symmetric Lasers in the Quadratic Approximation

Equations (15)

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1 β + d β + d z = - 1 β - d β - d z = g 0 1 + β + + β - - α 0 ,
y cos ( 2 λ ) = ln [ 1 - r tan λ r - tan λ · 1 - r b tan λ r b - tan λ ] ,
y = ( 1 - α 0 / g 0 ) [ α 0 L - ln r r b ] ,
2 α 0 g 0 - α 0 β 0 = sin ( 2 λ ) .
η = β 0 g 0 L ( 1 - r r + 1 - r b r b ) ,
P out = P s β 0 ( 1 - a - r r + 1 - a b - r b r b ) .
0 = C - B λ - A λ 2 + ,
λ q = ( B 2 + 4 A C ) 1 / 2 - B 2 A ,
A = 1 2 ( 1 - r 2 r + 1 - r b 2 r b ) + 2 y ,
B = 1 - r r + 1 - r b r b ,
C = y + ln r r b ,
r th = r b - 1 exp [ - 2 ( g 0 L - α 0 L ) ]
r th = r b = exp [ - ( g 0 L - α 0 L ) ]
η p = ( 1 - α 0 / g 0 ) 2 .
r opt = exp [ - 2 g 0 L α 0 / g 0 ( 1 - α 0 / g 0 ) ] ,

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