Abstract

Transmission formulas and transmission curves of birefringent filters when the optic axis is not in the plane of the filter plates are given and discussed in detail. The optimum parameters of birefringent filters, such as the most suitable ratio of thicknesses, tuning angles, and plate thicknesses, are obtained. As far as we know this is the first design of birefringent filters used in a tunable laser pumped by a quasi-cw source.

© 1992 Optical Society of America

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References

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  1. B. Lyot, “Un monochromateur à grand champ utilisant les interférences en lumière polarisee,” C. R. Acad. Sci. 197, 1593–1595 (1933).
  2. B. H. Billings, “A tunable narrow-band optical filter,” J. Opt. Soc. Am. 37, 738–746 (1947).
    [CrossRef] [PubMed]
  3. J. W. Evans, “The birefringent filter,” J. Opt. Soc. Am. 39, 229–242 (1949).
    [CrossRef]
  4. J. M. Yarborough, J. Hobart, in Proceedings of the Conference on Laser Engineering and Applications (Optical Soc. of America, Washington, D.C., 1973), postdeadline paper.
  5. G. Holtom, O. Teschke, “Design of a birefringent filter for high-power dye lasers,” IEEE J. Quantum Electron. QE-10, 577–579 (1974).
    [CrossRef]
  6. J. M. Yarborough, J. L. Hobart, “Tuning apparatus for an optical oscillator,” U. S. patent3,934,310 (20January1976).
  7. A. L. Bloom, “Modes of a resonator containing tilted plates,” J. Opt. Soc. Am. 64, 447–452 (1974).
    [CrossRef]
  8. D. R. Preuss, J. L. Gole, “Three-stage birefringent filter tuning smoothly over the visible region: theoretical treatment and experimental design,” Appl. Opt. 19, 702–710 (1980).
    [CrossRef] [PubMed]
  9. M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970).
  10. Qu Jinjie, Physical Optics (The National Defence Industrial Press, Beijing, China, 1979).

1980 (1)

1974 (2)

G. Holtom, O. Teschke, “Design of a birefringent filter for high-power dye lasers,” IEEE J. Quantum Electron. QE-10, 577–579 (1974).
[CrossRef]

A. L. Bloom, “Modes of a resonator containing tilted plates,” J. Opt. Soc. Am. 64, 447–452 (1974).
[CrossRef]

1949 (1)

1947 (1)

1933 (1)

B. Lyot, “Un monochromateur à grand champ utilisant les interférences en lumière polarisee,” C. R. Acad. Sci. 197, 1593–1595 (1933).

Billings, B. H.

Bloom, A. L.

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970).

Evans, J. W.

Gole, J. L.

Hobart, J.

J. M. Yarborough, J. Hobart, in Proceedings of the Conference on Laser Engineering and Applications (Optical Soc. of America, Washington, D.C., 1973), postdeadline paper.

Hobart, J. L.

J. M. Yarborough, J. L. Hobart, “Tuning apparatus for an optical oscillator,” U. S. patent3,934,310 (20January1976).

Holtom, G.

G. Holtom, O. Teschke, “Design of a birefringent filter for high-power dye lasers,” IEEE J. Quantum Electron. QE-10, 577–579 (1974).
[CrossRef]

Jinjie, Qu

Qu Jinjie, Physical Optics (The National Defence Industrial Press, Beijing, China, 1979).

Lyot, B.

B. Lyot, “Un monochromateur à grand champ utilisant les interférences en lumière polarisee,” C. R. Acad. Sci. 197, 1593–1595 (1933).

Preuss, D. R.

Teschke, O.

G. Holtom, O. Teschke, “Design of a birefringent filter for high-power dye lasers,” IEEE J. Quantum Electron. QE-10, 577–579 (1974).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970).

Yarborough, J. M.

J. M. Yarborough, J. L. Hobart, “Tuning apparatus for an optical oscillator,” U. S. patent3,934,310 (20January1976).

J. M. Yarborough, J. Hobart, in Proceedings of the Conference on Laser Engineering and Applications (Optical Soc. of America, Washington, D.C., 1973), postdeadline paper.

Appl. Opt. (1)

C. R. Acad. Sci. (1)

B. Lyot, “Un monochromateur à grand champ utilisant les interférences en lumière polarisee,” C. R. Acad. Sci. 197, 1593–1595 (1933).

IEEE J. Quantum Electron. (1)

G. Holtom, O. Teschke, “Design of a birefringent filter for high-power dye lasers,” IEEE J. Quantum Electron. QE-10, 577–579 (1974).
[CrossRef]

J. Opt. Soc. Am. (3)

Other (4)

J. M. Yarborough, J. Hobart, in Proceedings of the Conference on Laser Engineering and Applications (Optical Soc. of America, Washington, D.C., 1973), postdeadline paper.

J. M. Yarborough, J. L. Hobart, “Tuning apparatus for an optical oscillator,” U. S. patent3,934,310 (20January1976).

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970).

Qu Jinjie, Physical Optics (The National Defence Industrial Press, Beijing, China, 1979).

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Figures (6)

Fig. 1
Fig. 1

Light beam incident upon a BF: θ, incident angle (Brewster angle); θ′, refractive angle; c, BF optic axis; α, angle between the optic axis and the BF surface; A, tuning angle; k, direction of the internal ray; N, BF normal direction; γ, angle between the internal ray and the optic axis.

Fig. 2
Fig. 2

BF refractive ellipsoid: x, y, and z form a rectangular axis; z(c), optic axis; D′ and D″, electric displacement vectors. The plane decided by D′ and D″ is normal to k.

Fig. 3
Fig. 3

Relationship between tuning angle A and angle γ: x, y, and z form a rectangular axis; θ, incident angle; θ′ refractive angle; k, refractive light direction; angle SCO = 90°; angle BCO = 90°.

Fig. 4
Fig. 4

Single-plate BF transmission curves: (a) d = 1.0 mm, α = 0°, A = 39.1°; (b) d = 0.5 mm, α = 0°, A = 39.1°; (c) d = 0.5 mm, α = 30°, A = 39.1°; (d) d = 0.5 mm, α = 30°, A = 52.4°.

Fig. 5
Fig. 5

Multiple-plate BF transmission curves of d = 0.5 mm, α = 30°, A = 52.4°: (a) r = 1:2, (b) r = 1:2:9, (c) r = 1:4:16, (d) r = 1:2:3:4.

Fig. 6
Fig. 6

Four-plate BF transmission curves of d = 0.5 mm, α = 30°, r = 1:2:5:9. The main transmission peaks tune smoothly over a broad region when angle A is tuned: (a) A = 42°, (b) A = 48°, (c) A = 54°, (d) A = 60°.

Equations (12)

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δ = 2 π d ( n o - n e ) sin 2 γ λ sin θ ,
T = I / I 0 = 1 - sin 2 2 ϕ sin 2 ( δ / 2 ) ,
sin ϕ = cot γ sin θ / cos α tan α cos γ [ 1 - ( sin θ / cos α - tan α cos γ ) 2 ] 1 / 2 ,
sin ϕ = cot γ tan θ .
T = 1 - 4 cot 2 γ tan 2 θ ( 1 - cot 2 γ tan 2 θ ) sin 2 ( δ / 2 ) .
sin 2 ϕ sin ( δ / 2 ) = 0.
λ = d ( n o - n e ) sin 2 γ k sin θ .
λ max = - d ( n o - n e ) sin 2 γ sin θ .
cos A = cos γ - sin θ sin α cos θ cos α .
n o ( λ ) = A o + B o / λ 2 + C o / λ 2 ,
n e ( λ = A e + B e / λ 2 + C e / λ 4 ,
θ ( λ ) = arctan n o ( λ ) + n e ( λ ) 2 ,

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