Abstract

We present a simple, in situ technique to calculate the small-signal gain of typical solid-state continuous-wave lasers, such as Nd:YAG and Nd:YLF lasers, by measuring the frequency of the relaxation oscillation noise peak. The laser’s small-signal gain can be directly calculated from the frequency of the relaxation oscillation with knowledge of the upper-state lifetime, the cavity round-trip time, and total losses, which are typically well-known values. When the laser is pumped many times above threshold the losses do not need to be known accurately. This technique is compared with the traditional method of changing output couplers to establish its accuracy.

© 1994 Optical Society of America

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References

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  1. U. Keller, T. H. Chiu, J. F. Ferguson, Opt. Lett. 18, 217 (1993).
    [CrossRef] [PubMed]
  2. D. Findlay, R. A. Clay, Phys. Lett. 20, 277 (1966).
    [CrossRef]
  3. P. F. Moulton, J. Opt. Soc. Am. B 3, 125 (1986).
    [CrossRef]
  4. T. J. Kane, R. L. Byer, Opt. Lett. 10, 65 (1985).
    [CrossRef] [PubMed]
  5. A. Yariv, Optical Electronics (Holt, Rinehart & Winston, New York, 1976), Chap. 6, pp. 147–153.
  6. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif.1986), Chap. 25, pp. 962–964; Chap. 11, pp. 428–429.
  7. H. Shen, T. Lian, R. Zheng, Y. Zhou, G. Yu, C. Huang, H. Liao, Z. Zheng, IEEE J. Quantum Electron. 25, 144 (1989).
    [CrossRef]
  8. K. Kubodera, K. Otsuka, S. Miyazawa, Appl. Opt. 18, 884 (1979).
    [CrossRef] [PubMed]
  9. K. Otsuka, K. Kubodera, IEEE J. Quantum Electron. QE-16, 419 (1980).
    [CrossRef]
  10. A. L. Harmer, A. Linz, D. R. Gabbe, J. Phys. Chem. Solids 30, 1483 (1969).
    [CrossRef]

1993 (1)

1989 (1)

H. Shen, T. Lian, R. Zheng, Y. Zhou, G. Yu, C. Huang, H. Liao, Z. Zheng, IEEE J. Quantum Electron. 25, 144 (1989).
[CrossRef]

1986 (1)

1985 (1)

1980 (1)

K. Otsuka, K. Kubodera, IEEE J. Quantum Electron. QE-16, 419 (1980).
[CrossRef]

1979 (1)

1969 (1)

A. L. Harmer, A. Linz, D. R. Gabbe, J. Phys. Chem. Solids 30, 1483 (1969).
[CrossRef]

1966 (1)

D. Findlay, R. A. Clay, Phys. Lett. 20, 277 (1966).
[CrossRef]

Byer, R. L.

Chiu, T. H.

Clay, R. A.

D. Findlay, R. A. Clay, Phys. Lett. 20, 277 (1966).
[CrossRef]

Ferguson, J. F.

Findlay, D.

D. Findlay, R. A. Clay, Phys. Lett. 20, 277 (1966).
[CrossRef]

Gabbe, D. R.

A. L. Harmer, A. Linz, D. R. Gabbe, J. Phys. Chem. Solids 30, 1483 (1969).
[CrossRef]

Harmer, A. L.

A. L. Harmer, A. Linz, D. R. Gabbe, J. Phys. Chem. Solids 30, 1483 (1969).
[CrossRef]

Huang, C.

H. Shen, T. Lian, R. Zheng, Y. Zhou, G. Yu, C. Huang, H. Liao, Z. Zheng, IEEE J. Quantum Electron. 25, 144 (1989).
[CrossRef]

Kane, T. J.

Keller, U.

Kubodera, K.

K. Otsuka, K. Kubodera, IEEE J. Quantum Electron. QE-16, 419 (1980).
[CrossRef]

K. Kubodera, K. Otsuka, S. Miyazawa, Appl. Opt. 18, 884 (1979).
[CrossRef] [PubMed]

Lian, T.

H. Shen, T. Lian, R. Zheng, Y. Zhou, G. Yu, C. Huang, H. Liao, Z. Zheng, IEEE J. Quantum Electron. 25, 144 (1989).
[CrossRef]

Liao, H.

H. Shen, T. Lian, R. Zheng, Y. Zhou, G. Yu, C. Huang, H. Liao, Z. Zheng, IEEE J. Quantum Electron. 25, 144 (1989).
[CrossRef]

Linz, A.

A. L. Harmer, A. Linz, D. R. Gabbe, J. Phys. Chem. Solids 30, 1483 (1969).
[CrossRef]

Miyazawa, S.

Moulton, P. F.

Otsuka, K.

K. Otsuka, K. Kubodera, IEEE J. Quantum Electron. QE-16, 419 (1980).
[CrossRef]

K. Kubodera, K. Otsuka, S. Miyazawa, Appl. Opt. 18, 884 (1979).
[CrossRef] [PubMed]

Shen, H.

H. Shen, T. Lian, R. Zheng, Y. Zhou, G. Yu, C. Huang, H. Liao, Z. Zheng, IEEE J. Quantum Electron. 25, 144 (1989).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif.1986), Chap. 25, pp. 962–964; Chap. 11, pp. 428–429.

Yariv, A.

A. Yariv, Optical Electronics (Holt, Rinehart & Winston, New York, 1976), Chap. 6, pp. 147–153.

Yu, G.

H. Shen, T. Lian, R. Zheng, Y. Zhou, G. Yu, C. Huang, H. Liao, Z. Zheng, IEEE J. Quantum Electron. 25, 144 (1989).
[CrossRef]

Zheng, R.

H. Shen, T. Lian, R. Zheng, Y. Zhou, G. Yu, C. Huang, H. Liao, Z. Zheng, IEEE J. Quantum Electron. 25, 144 (1989).
[CrossRef]

Zheng, Z.

H. Shen, T. Lian, R. Zheng, Y. Zhou, G. Yu, C. Huang, H. Liao, Z. Zheng, IEEE J. Quantum Electron. 25, 144 (1989).
[CrossRef]

Zhou, Y.

H. Shen, T. Lian, R. Zheng, Y. Zhou, G. Yu, C. Huang, H. Liao, Z. Zheng, IEEE J. Quantum Electron. 25, 144 (1989).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

K. Otsuka, K. Kubodera, IEEE J. Quantum Electron. QE-16, 419 (1980).
[CrossRef]

H. Shen, T. Lian, R. Zheng, Y. Zhou, G. Yu, C. Huang, H. Liao, Z. Zheng, IEEE J. Quantum Electron. 25, 144 (1989).
[CrossRef]

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

J. Phys. Chem. Solids (1)

A. L. Harmer, A. Linz, D. R. Gabbe, J. Phys. Chem. Solids 30, 1483 (1969).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. (1)

D. Findlay, R. A. Clay, Phys. Lett. 20, 277 (1966).
[CrossRef]

Other (2)

A. Yariv, Optical Electronics (Holt, Rinehart & Winston, New York, 1976), Chap. 6, pp. 147–153.

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif.1986), Chap. 25, pp. 962–964; Chap. 11, pp. 428–429.

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Figures (4)

Fig. 1
Fig. 1

Schematic of the cavity. The pump laser at 793 nm is focused to a radius at the crystal of ≈20 μm. The laser mode radius in the crystal is calculated as 90 μm × 130 μm by the ABCD matrix method. HR, highly reflecting; HT, highly transmitting.

Fig. 2
Fig. 2

(a) Measured output power versus the pump power at the laser crystal for each output coupler, (b) thresholds and slope efficiencies versus output couplers extrapolated from the data in (a).

Fig. 3
Fig. 3

Measured relaxation oscillation frequency versus pump power. The inset is typical spectrum analyzer data showing the relaxation oscillation noise peak (resolution bandwidth 3 kHz). The total amplitude noise of the laser is less than 1%.

Fig. 4
Fig. 4

Calculated small-signal gains from the measured fro for each value of the output coupler. The small-signal gain is G = Iout/Iin = exp(δg), where δg is calculated from Eq. (4). The slope of the fit is the small-signal gain, 0.23 ± 0.01% per milliwatt of pump power.

Equations (4)

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s 1 , 2 = - r 2 τ 2 ± [ ( r 2 τ 2 ) 2 - ( r - 1 ) τ 2 τ c ] 1 / 2 ,
f ro = 1 2 π [ ( r - 1 ) τ c τ 2 - ( r 2 τ 2 ) 2 ] 1 / 2
f ro = 1 2 π [ ( δ g - δ c ) 1 T τ 2 ] 1 / 2
δ g = ( 2 π f ro ) 2 T τ 2 + δ c .

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