Abstract

On the basis of theory and experiment we discuss the strong optical asymmetry in reflection exhibited by an interference wedge when it is constructed of unequal-reflectivity mirrors and show how this feature can be used to develop attractive unidirectional ring lasers. In the proposed ring cavity schemes a single interference wedge is employed simultaneously as a tuning element, as an element introducing asymmetry, and as a laser output coupler.

© 1994 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).
  2. V. Tomin, B. Bushuk, A. Rubinov, Opt. Spectrosc. (USSR) 32, 527 (1972).
  3. Y. Meyer, M. Nenchev, Opt. Lett. 6, 119 (1981); M. Nenchev, Y. Meyer, Opt. Lett. 7, 199 (1982).
    [CrossRef] [PubMed]
  4. M. Nenchev, Y. Meyer, Proc. Soc. Photo-Opt. Instrum Eng. 473, 181 (1984).
  5. H. Schroder, L. Stein, D. Frohlich, B. Fugger, H. Welling, Appl. Phys. 14, 377 (1977); C. Wagstaff, M. Dunn, J. Phys. D 12, 355 (1979).
    [CrossRef]
  6. J. Green, J. Hohimer, F. Tittel, Opt. Commun. 7, 349 (1973).
    [CrossRef]
  7. M. Nenchev, E. Stoykova, Opt. Quantum Electron. 25, 789 (1993).
    [CrossRef]
  8. Y. J. Meyer, Opt. Soc. Am. 71, 1255 (1981).
    [CrossRef]
  9. W. Demtroder, Laser Spectroscopy (Springer-Verlag, Berlin, 1982).

1993 (1)

M. Nenchev, E. Stoykova, Opt. Quantum Electron. 25, 789 (1993).
[CrossRef]

1984 (1)

M. Nenchev, Y. Meyer, Proc. Soc. Photo-Opt. Instrum Eng. 473, 181 (1984).

1981 (2)

1977 (1)

H. Schroder, L. Stein, D. Frohlich, B. Fugger, H. Welling, Appl. Phys. 14, 377 (1977); C. Wagstaff, M. Dunn, J. Phys. D 12, 355 (1979).
[CrossRef]

1973 (1)

J. Green, J. Hohimer, F. Tittel, Opt. Commun. 7, 349 (1973).
[CrossRef]

1972 (1)

V. Tomin, B. Bushuk, A. Rubinov, Opt. Spectrosc. (USSR) 32, 527 (1972).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

Bushuk, B.

V. Tomin, B. Bushuk, A. Rubinov, Opt. Spectrosc. (USSR) 32, 527 (1972).

Demtroder, W.

W. Demtroder, Laser Spectroscopy (Springer-Verlag, Berlin, 1982).

Frohlich, D.

H. Schroder, L. Stein, D. Frohlich, B. Fugger, H. Welling, Appl. Phys. 14, 377 (1977); C. Wagstaff, M. Dunn, J. Phys. D 12, 355 (1979).
[CrossRef]

Fugger, B.

H. Schroder, L. Stein, D. Frohlich, B. Fugger, H. Welling, Appl. Phys. 14, 377 (1977); C. Wagstaff, M. Dunn, J. Phys. D 12, 355 (1979).
[CrossRef]

Green, J.

J. Green, J. Hohimer, F. Tittel, Opt. Commun. 7, 349 (1973).
[CrossRef]

Hohimer, J.

J. Green, J. Hohimer, F. Tittel, Opt. Commun. 7, 349 (1973).
[CrossRef]

Meyer, Y.

Meyer, Y. J.

Y. J. Meyer, Opt. Soc. Am. 71, 1255 (1981).
[CrossRef]

Nenchev, M.

M. Nenchev, E. Stoykova, Opt. Quantum Electron. 25, 789 (1993).
[CrossRef]

M. Nenchev, Y. Meyer, Proc. Soc. Photo-Opt. Instrum Eng. 473, 181 (1984).

Y. Meyer, M. Nenchev, Opt. Lett. 6, 119 (1981); M. Nenchev, Y. Meyer, Opt. Lett. 7, 199 (1982).
[CrossRef] [PubMed]

Rubinov, A.

V. Tomin, B. Bushuk, A. Rubinov, Opt. Spectrosc. (USSR) 32, 527 (1972).

Schroder, H.

H. Schroder, L. Stein, D. Frohlich, B. Fugger, H. Welling, Appl. Phys. 14, 377 (1977); C. Wagstaff, M. Dunn, J. Phys. D 12, 355 (1979).
[CrossRef]

Stein, L.

H. Schroder, L. Stein, D. Frohlich, B. Fugger, H. Welling, Appl. Phys. 14, 377 (1977); C. Wagstaff, M. Dunn, J. Phys. D 12, 355 (1979).
[CrossRef]

Stoykova, E.

M. Nenchev, E. Stoykova, Opt. Quantum Electron. 25, 789 (1993).
[CrossRef]

Tittel, F.

J. Green, J. Hohimer, F. Tittel, Opt. Commun. 7, 349 (1973).
[CrossRef]

Tomin, V.

V. Tomin, B. Bushuk, A. Rubinov, Opt. Spectrosc. (USSR) 32, 527 (1972).

Welling, H.

H. Schroder, L. Stein, D. Frohlich, B. Fugger, H. Welling, Appl. Phys. 14, 377 (1977); C. Wagstaff, M. Dunn, J. Phys. D 12, 355 (1979).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

Appl. Phys. (1)

H. Schroder, L. Stein, D. Frohlich, B. Fugger, H. Welling, Appl. Phys. 14, 377 (1977); C. Wagstaff, M. Dunn, J. Phys. D 12, 355 (1979).
[CrossRef]

Opt. Commun. (1)

J. Green, J. Hohimer, F. Tittel, Opt. Commun. 7, 349 (1973).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

M. Nenchev, E. Stoykova, Opt. Quantum Electron. 25, 789 (1993).
[CrossRef]

Opt. Soc. Am. (1)

Y. J. Meyer, Opt. Soc. Am. 71, 1255 (1981).
[CrossRef]

Opt. Spectrosc. (1)

V. Tomin, B. Bushuk, A. Rubinov, Opt. Spectrosc. (USSR) 32, 527 (1972).

Proc. Soc. Photo-Opt. Instrum Eng. (1)

M. Nenchev, Y. Meyer, Proc. Soc. Photo-Opt. Instrum Eng. 473, 181 (1984).

Other (2)

W. Demtroder, Laser Spectroscopy (Springer-Verlag, Berlin, 1982).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

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Figures (3)

Fig. 1
Fig. 1

Computed reflected and transmitted intensity distributions on the surface of the IW with unequal mirrors for a truncated Gaussian beam with a homogeneous phase distribution. The intensity profiles of the incident beam, the beams reflected at sides R1 and R2, and the transmitted beam (the same for both cases) are shown. The interference wedge has a thickness of 100 μm, n′ = 1, R1 = 0.94, R2 = 0.72, and a wedge angle of 0.05 mrad. The angle of incidence is 10°. The beam width at level e−1 is 200 μm, and λ = 630.18 nm. The zero point on the x axis indicates the beginning of the incident-beam impact area; x is the distance in micrometers on the wedge surface. The transmitted power through the wedge is 30% of the incident beam power.

Fig. 2
Fig. 2

Experimental points of the intensity distribution in the beams reflected at sides R1 and R2 (the wedge and beam parameters are the same as for Fig. 1). In the insets, photographs of the laser spots in a plane parallel to the wedge surface are shown. The strong asymmetry for both cases is obvious.

Fig. 3
Fig. 3

Two optical schematics of ring cavities that employ the strong reflection asymmetry of an interference wedge with unequal mirrors to produce simultaneously unidirectional operation, laser tuning, and highly efficient output coupling. AM, active medium; M’s, mirrors.

Equations (3)

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I R 1 , 2 k , k + 1 = R 1 , 2 I 0 ( x 1 ) 2 ( 1 R 1 , 2 ) 2 f ( x 1 ) G 1 k / ρ + ( 1 R 1 , 2 ) 2 ( G 1 k 2 + H 1 k 2 ) / R 1 , 2 ρ 2 ,
I R 1 , 2 kj = ( 1 R 1 , 2 ) 2 R 1 , 2 ρ 2 ( G kj 2 + H kj 2 ) ,
ρ = R 1 R 2 , f ( x ) = I 0 ( x ) , G kj = p = k + 1 j ρ p f ( x p ) cos Ω p , H kj = p = k + 1 j ρ p f ( x p ) sin Ω p , x p = β e 1 ( e e p ) e p tan α , e p = e p 1 1 + β tan α tan [ θ + 2 β ( p 1 ) α ] 1 β tan α tan [ θ + 2 β ( p 2 ) α ] = L p e p 1 , h p = L p h p 1 , Ω p = 2 π e n ( sin θ p β sin θ ) λ tan α , sin θ p = n sin [ θ + 2 β ( p 1 ) α ] n .

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