Abstract

A theoretical consideration is presented of the optical coupling and selection of laser array modes by the use of a developed Lummer–Gehrcke interferometer as a resonator reflector. Control of the mirror reflection of the proposed interferometer permits laser power to be redistributed through channels on the outlet resonator mirror; in particular, it makes it possible to lead power out of the resonator by a single beam. In this way it is possible to diminish the sidelobes in the far-field radiation profile of multichannel lasers and to raise the efficiency of the optical coupling of the laser array with waveguides and fibers. This method may be used for the redistribution of laser power on the outlet mirror in striped lasers as well.

© 1995 Optical Society of America

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References

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  1. V. V. Likhanskii, A. P. Napartovich, “Radiation emitted by optically coupled lasers,” Sov. Phys. Usp. 33, 228–252 (1990).
    [Crossref]
  2. M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), Chap. 7, pp. 323–329, 341–347.
  3. Yu. T. Mazurenko, Yu. A. Rubinov, “Autocollimation multibeam interferometer with spatial beam separation and its use in frequency selection of laser radiation,” Sov. J. Quantum Electron. 13, 213–216 (1983).
    [Crossref]
  4. Yu. A. Rubinov, “Fundamental properties of sequentially coupled multiple-beam interferometers with Lummer–Gehrcke type side input,” Opt. Spectrosc. 58, 693–696 (1985).
  5. M. DiDomenico, “Characteristics of a single-frequency Michelson type He–Ne gas laser,” IEEE J. Quantum Electron. QE-21, 311–322 (1966).
    [Crossref]
  6. W. W. Rigrod, “Selectivity of open-ended interferometric resonators,” IEEE J. Quantum Electron. QE-61, 9–14 (1970).
    [Crossref]
  7. S. P. Anochov, T. Ya. Marusiy, M. S. Soskin, Tunable lasers, (Radio i svjas’, Moscow, 1982), Chap. 6, pp. 219–229, in Russian.
  8. M. B. Spencer, W. E. Lamb, “Theory of two coupled lasers,” Phys. Rev. A 5, 893–898 (1972).
    [Crossref]
  9. H. Mirels, “Performance of two coupled lasers,” Appl. Opt. 25, 2130–2137 (1986).
    [Crossref] [PubMed]

1990 (1)

V. V. Likhanskii, A. P. Napartovich, “Radiation emitted by optically coupled lasers,” Sov. Phys. Usp. 33, 228–252 (1990).
[Crossref]

1986 (1)

1985 (1)

Yu. A. Rubinov, “Fundamental properties of sequentially coupled multiple-beam interferometers with Lummer–Gehrcke type side input,” Opt. Spectrosc. 58, 693–696 (1985).

1983 (1)

Yu. T. Mazurenko, Yu. A. Rubinov, “Autocollimation multibeam interferometer with spatial beam separation and its use in frequency selection of laser radiation,” Sov. J. Quantum Electron. 13, 213–216 (1983).
[Crossref]

1972 (1)

M. B. Spencer, W. E. Lamb, “Theory of two coupled lasers,” Phys. Rev. A 5, 893–898 (1972).
[Crossref]

1970 (1)

W. W. Rigrod, “Selectivity of open-ended interferometric resonators,” IEEE J. Quantum Electron. QE-61, 9–14 (1970).
[Crossref]

1966 (1)

M. DiDomenico, “Characteristics of a single-frequency Michelson type He–Ne gas laser,” IEEE J. Quantum Electron. QE-21, 311–322 (1966).
[Crossref]

Anochov, S. P.

S. P. Anochov, T. Ya. Marusiy, M. S. Soskin, Tunable lasers, (Radio i svjas’, Moscow, 1982), Chap. 6, pp. 219–229, in Russian.

Born, M.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), Chap. 7, pp. 323–329, 341–347.

DiDomenico, M.

M. DiDomenico, “Characteristics of a single-frequency Michelson type He–Ne gas laser,” IEEE J. Quantum Electron. QE-21, 311–322 (1966).
[Crossref]

Lamb, W. E.

M. B. Spencer, W. E. Lamb, “Theory of two coupled lasers,” Phys. Rev. A 5, 893–898 (1972).
[Crossref]

Likhanskii, V. V.

V. V. Likhanskii, A. P. Napartovich, “Radiation emitted by optically coupled lasers,” Sov. Phys. Usp. 33, 228–252 (1990).
[Crossref]

Marusiy, T. Ya.

S. P. Anochov, T. Ya. Marusiy, M. S. Soskin, Tunable lasers, (Radio i svjas’, Moscow, 1982), Chap. 6, pp. 219–229, in Russian.

Mazurenko, Yu. T.

Yu. T. Mazurenko, Yu. A. Rubinov, “Autocollimation multibeam interferometer with spatial beam separation and its use in frequency selection of laser radiation,” Sov. J. Quantum Electron. 13, 213–216 (1983).
[Crossref]

Mirels, H.

Napartovich, A. P.

V. V. Likhanskii, A. P. Napartovich, “Radiation emitted by optically coupled lasers,” Sov. Phys. Usp. 33, 228–252 (1990).
[Crossref]

Rigrod, W. W.

W. W. Rigrod, “Selectivity of open-ended interferometric resonators,” IEEE J. Quantum Electron. QE-61, 9–14 (1970).
[Crossref]

Rubinov, Yu. A.

Yu. A. Rubinov, “Fundamental properties of sequentially coupled multiple-beam interferometers with Lummer–Gehrcke type side input,” Opt. Spectrosc. 58, 693–696 (1985).

Yu. T. Mazurenko, Yu. A. Rubinov, “Autocollimation multibeam interferometer with spatial beam separation and its use in frequency selection of laser radiation,” Sov. J. Quantum Electron. 13, 213–216 (1983).
[Crossref]

Soskin, M. S.

S. P. Anochov, T. Ya. Marusiy, M. S. Soskin, Tunable lasers, (Radio i svjas’, Moscow, 1982), Chap. 6, pp. 219–229, in Russian.

Spencer, M. B.

M. B. Spencer, W. E. Lamb, “Theory of two coupled lasers,” Phys. Rev. A 5, 893–898 (1972).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), Chap. 7, pp. 323–329, 341–347.

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

M. DiDomenico, “Characteristics of a single-frequency Michelson type He–Ne gas laser,” IEEE J. Quantum Electron. QE-21, 311–322 (1966).
[Crossref]

W. W. Rigrod, “Selectivity of open-ended interferometric resonators,” IEEE J. Quantum Electron. QE-61, 9–14 (1970).
[Crossref]

Opt. Spectrosc. (1)

Yu. A. Rubinov, “Fundamental properties of sequentially coupled multiple-beam interferometers with Lummer–Gehrcke type side input,” Opt. Spectrosc. 58, 693–696 (1985).

Phys. Rev. A (1)

M. B. Spencer, W. E. Lamb, “Theory of two coupled lasers,” Phys. Rev. A 5, 893–898 (1972).
[Crossref]

Sov. J. Quantum Electron. (1)

Yu. T. Mazurenko, Yu. A. Rubinov, “Autocollimation multibeam interferometer with spatial beam separation and its use in frequency selection of laser radiation,” Sov. J. Quantum Electron. 13, 213–216 (1983).
[Crossref]

Sov. Phys. Usp. (1)

V. V. Likhanskii, A. P. Napartovich, “Radiation emitted by optically coupled lasers,” Sov. Phys. Usp. 33, 228–252 (1990).
[Crossref]

Other (2)

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), Chap. 7, pp. 323–329, 341–347.

S. P. Anochov, T. Ya. Marusiy, M. S. Soskin, Tunable lasers, (Radio i svjas’, Moscow, 1982), Chap. 6, pp. 219–229, in Russian.

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Figures (3)

Fig. 1
Fig. 1

Optical schemes of a multibeam interferometer used as a coupler in a multichannel laser: (a) Multichannel laser, (b) two-channel laser, (c) single-beam outlet scheme, (d) output beams of equal intensities.

Fig. 2
Fig. 2

Dependences of the intensity reflection coefficients of the complex resonator mirror (top figure), and light intensities on resonator mirror RM (bottom figure) in a two-channel laser: S, selected array mode; D, discarded array mode; ch1, ch2, modes of the separated channels.

Fig. 3
Fig. 3

Dependences of the intensity reflection coefficients of the complex resonator mirror for various modes in a three-channel laser.

Equations (31)

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h = 2 d sin α ,
a 1 exp ( i ϕ 1 ) ,             a 2 exp ( i ϕ 2 ) ,
I ch 1 = R m [ I 1 T 2 2 + I 1 R 1 2 R 2 2 + I 2 R 1 T 1 R 2 + 2 I 1 R 1 R 2 T 2 cos 2 δ + 2 T 2 ( I 1 I 2 R 1 T 1 R 2 ) 1 / 2 cos ( δ + Δ ϕ ) + 2 R 1 R 2 ( I 1 I 2 R 1 T 1 R 2 ) 1 / 2 cos ( δ - Δ ϕ ) ] ,
I ch 2 = R m T 1 [ I 2 T 1 + I 1 R 1 R 2 + 2 ( I 1 I 2 R 1 T 1 R 2 ) 1 / 2 cos ( δ - Δ ϕ ) ] ,
I ( 1 ) = I 1 T 1 R 2 + I 2 R 1 - 2 ( I 1 I 2 R 1 T 1 R 2 ) 1 / 2 cos ( δ - Δ ϕ ) ,
I ( 2 ) = R m T 2 [ I 1 R 2 + I 1 R 1 2 R 2 + I 2 R 1 T 1 - 2 I 1 R 1 R 2 cos 2 δ + 2 ( I 1 I 2 R 1 3 T 1 R 2 ) 1 / 2 cos ( δ - Δ ϕ ) - 2 ( I 1 I 2 R 1 T 1 R 2 ) 1 / 2 cos ( δ + Δ ϕ ) ] .
δ = 2 k π ,
δ = ( 2 k + 1 ) π .
I ch 1 = R m [ I 1 ( T 2 + R 1 R 2 ) + ( I 2 R 1 T 1 R 2 ) 1 / 2 ] 2 ,
I ch 2 = R m T 1 [ ( I 1 R 1 R 2 ) 1 / 2 + ( I 2 T 1 ) 1 / 2 ] 2 ,
I ( 1 ) = [ ( I 1 T 1 R 2 ) 1 / 2 - ( I 2 R 1 ) 1 / 2 ] 2 ,
I ( 2 ) = R m T 2 { ( I 1 R 2 ) 1 / 2 - R 1 [ ( I 1 R 1 R 2 ) 1 / 2 + ( I 2 T 1 ) 1 / 2 ] } 2 .
I ch 1 * = R m [ I 1 ( T 2 + R 1 R 2 ) - ( I 2 R 1 T 1 R 2 ) 1 / 2 ] 2 ,
I ch 2 * = R m T 1 [ ( I 1 R 1 R 2 ) 1 / 2 - ( I 2 T 1 ) 1 / 2 ] 2 .
( I 2 R 1 ) 1 / 2 = ( I 1 T 1 R 2 ) 1 / 2 .
R ch 1 = I ch 1 / I 2 = R m ,
R ch 2 = I ch 1 / I 2 = R m ,
R ch 1 * = R m [ T 2 + R 2 ( R 2 - T 1 ) ] 2 ,
R ch 2 * = R m ( R 1 - T 1 ) 2 .
I 1 ( m ) = I 1 T 2 = I 1 ( 1 - I 2 R 1 / I 1 T 1 ) ,
I 2 ( m ) = I 2 / T 1 .
T 1 , 1 = 1 ,
I i - 1 R 2 , i - 1 = I i T 1 , i - 1 R 1 , i / T 1 , i ,             i > 1.
R 1 , i = R 1 ,
R 1 , i = { R 1 / T 1 , i = 1 R 1 , i > 1.
R 2 , i = R 2 ,
T 1 , i = 1 / m = 0 i - 1 R 2 m .
T 1 , i = 1 / i .
M ch 1 = τ ch 2 , ch 1 / r ch 1 , ch 1 = ( T 1 R 1 R 2 T 2 2 + R 1 2 R 2 2 + 2 R 1 T 2 R 2 cos 2 δ ) 1 / 2 × exp [ i ( δ - ψ ) ] ,
M ch 2 = τ ch 1 , ch 2 / r ch 2 , ch 2 = ( R 1 R 2 T 1 ) 1 / 2 exp ( i δ ) ,
ψ = arctan [ sin 2 δ cos 2 δ + ( T 2 / R 1 R 2 ) ] .

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