Abstract

Numerical calculations using the Prony method have shown that the feedback coefficient in unstable laser resonators can be increased by factors of as much as 5 over the geometrical value using a mirror with a phase step at its center. A phase shift of close to π over an area of an equivalent Fresnel number of 0.5 leads to minimum output losses. Experiments with a TEA CO2 laser confirm the prediction. The results can be attributed to a cancellation of the output wave by destructive interference, which confines the laser beam around the resonator axis.

© 1991 Optical Society of America

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References

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  1. A. E. Siegman, Proc. IEEE 53, 277 (1965).
    [Crossref]
  2. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  3. N. McCarthy, P. Lavigne, Opt. Lett. 10, 553 (1985).
    [Crossref] [PubMed]
  4. K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, Opt. Commun. 65, 377 (1988).
    [Crossref]
  5. S. de Silvestri, P. Laporta, V. Magni, O. Svelto, IEEE J. Quantum Electron. 24, 1172 (1988).
    [Crossref]
  6. A. E. Siegman, H. Y. Miller, Appl. Opt. 9, 2729 (1970).
    [Crossref] [PubMed]
  7. J. L. Soret, Arch. Sci. Phys. Nat. 52, 320 (1875).

1988 (2)

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, Opt. Commun. 65, 377 (1988).
[Crossref]

S. de Silvestri, P. Laporta, V. Magni, O. Svelto, IEEE J. Quantum Electron. 24, 1172 (1988).
[Crossref]

1985 (1)

1970 (1)

1965 (1)

A. E. Siegman, Proc. IEEE 53, 277 (1965).
[Crossref]

1875 (1)

J. L. Soret, Arch. Sci. Phys. Nat. 52, 320 (1875).

de Silvestri, S.

S. de Silvestri, P. Laporta, V. Magni, O. Svelto, IEEE J. Quantum Electron. 24, 1172 (1988).
[Crossref]

Laporta, P.

S. de Silvestri, P. Laporta, V. Magni, O. Svelto, IEEE J. Quantum Electron. 24, 1172 (1988).
[Crossref]

Lavigne, P.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, Opt. Commun. 65, 377 (1988).
[Crossref]

N. McCarthy, P. Lavigne, Opt. Lett. 10, 553 (1985).
[Crossref] [PubMed]

Magni, V.

S. de Silvestri, P. Laporta, V. Magni, O. Svelto, IEEE J. Quantum Electron. 24, 1172 (1988).
[Crossref]

McCarthy, N.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, Opt. Commun. 65, 377 (1988).
[Crossref]

N. McCarthy, P. Lavigne, Opt. Lett. 10, 553 (1985).
[Crossref] [PubMed]

Miller, H. Y.

Piché, M.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, Opt. Commun. 65, 377 (1988).
[Crossref]

Siegman, A. E.

A. E. Siegman, H. Y. Miller, Appl. Opt. 9, 2729 (1970).
[Crossref] [PubMed]

A. E. Siegman, Proc. IEEE 53, 277 (1965).
[Crossref]

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Snell, K. J.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, Opt. Commun. 65, 377 (1988).
[Crossref]

Soret, J. L.

J. L. Soret, Arch. Sci. Phys. Nat. 52, 320 (1875).

Svelto, O.

S. de Silvestri, P. Laporta, V. Magni, O. Svelto, IEEE J. Quantum Electron. 24, 1172 (1988).
[Crossref]

Appl. Opt. (1)

Arch. Sci. Phys. Nat. (1)

J. L. Soret, Arch. Sci. Phys. Nat. 52, 320 (1875).

IEEE J. Quantum Electron. (1)

S. de Silvestri, P. Laporta, V. Magni, O. Svelto, IEEE J. Quantum Electron. 24, 1172 (1988).
[Crossref]

Opt. Commun. (1)

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, Opt. Commun. 65, 377 (1988).
[Crossref]

Opt. Lett. (1)

Proc. IEEE (1)

A. E. Siegman, Proc. IEEE 53, 277 (1965).
[Crossref]

Other (1)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

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Figures (5)

Fig. 1
Fig. 1

Unstable laser resonator with a uniform phase step on one mirror.

Fig. 2
Fig. 2

Curves of the feedback coefficient of the dominant resonator mode as a function of the value of the phase shift introduced by the phase step for different sizes of the phase step. The resonator parameters are M = 2 and Neq = 10.5.

Fig. 3
Fig. 3

Curves of the feedback coefficient of the dominant mode with a phase step of π (curve A) or without it (curve B) as a function of resonator magnification. The resonator parameters are Neq = 10.5 and Nϕ = 0.5.

Fig. 4
Fig. 4

Curves of the feedback coefficient of the dominant mode as a function of the equivalent Fresnel number of the unstable resonator, for M = 2 (curve A) and M = 5 (curve B), assuming a phase step of π with Nϕ = 0.5.

Fig. 5
Fig. 5

Experimental values of the output energy as a function of the resonator magnification with a phase step (+) or without it (□).

Equations (6)

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γ E ( r ) = j l + 1 2 π N exp [ j Φ ( r ) / 2 ] × 0 1 exp [ j π N A ( r 2 + r 1 2 ) ] × exp [ j Φ ( r 1 ) / 2 ] J l ( 2 π N r r 1 ) E ( r 1 ) r 1 d r 1 ,
A = 2 g 1 g 2 1 ,
N = a 1 2 λ L g 2 .
M = A ± A 2 1 ,
N eq = ( M 2 1 ) N 2 M ,
N Φ = ( M 2 1 ) a ϕ 2 4 M λ L g 2 .

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