Abstract

The dependence of the tuning behavior of a birefringent filter on the orientation of the optic axis to the surface of the plate is studied. The Jones matrix representing a tilted birefringent plate is reduced to practical form, and this leads to simplifying the theoretical operation of tuning a birefringent filter in a laser resonator. The principles of proper determination of the filter parameters are given. A design method, which takes into consideration the bandwidth, rejection and tuning range of the filter, and design examples, is provided.

© 1990 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 lumiére polarisee,” C. R. Acad. Sci. 197, 1593–1595 (1933).
  2. J. M. Yarborough, J. Hobart, Conference on Laser Engineering and Applications (Optical Society of America, Washington, DC, 1973), postdeadline paper XX.
  3. A. L. Bloom, “Modes of a Laser Resonator Containing Tilted Birefringent Plates,” J. Opt. Soc. Am. 64, 447–452 (1974).
    [Crossref]
  4. G. Holton, O. Teschke, “Design of a Birefringent Filter for High-Power Dye Lasers,” IEEE J. Quantum Electron. QE-10, 577–579 (1974).
    [Crossref]
  5. I. J. Hodgkinson, J. I. Vukusic, “Birefringent Filters for Tuning Flashlamp-Pumped Dye Lasers: Simplified Theory and Design,” Appl. Opt. 17, 1944–1948 (1978).
    [Crossref] [PubMed]
  6. R. C. Jones, “A New Calculus for the Treatment of Optical Systems,” J. Opt. Soc. Am. 31, 488–493 (1941).
    [Crossref]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  8. I. J. Hodgkinson, J. I. Vukusic, “Birefringent Tuning Filters Without Secondary Peaks,” Opt. Commun. 24, 133–134 (1978).
    [Crossref]

1978 (2)

1974 (2)

A. L. Bloom, “Modes of a Laser Resonator Containing Tilted Birefringent Plates,” J. Opt. Soc. Am. 64, 447–452 (1974).
[Crossref]

G. Holton, O. Teschke, “Design of a Birefringent Filter for High-Power Dye Lasers,” IEEE J. Quantum Electron. QE-10, 577–579 (1974).
[Crossref]

1941 (1)

1933 (1)

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

Bloom, A. L.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Hobart, J.

J. M. Yarborough, J. Hobart, Conference on Laser Engineering and Applications (Optical Society of America, Washington, DC, 1973), postdeadline paper XX.

Hodgkinson, I. J.

Holton, G.

G. Holton, O. Teschke, “Design of a Birefringent Filter for High-Power Dye Lasers,” IEEE J. Quantum Electron. QE-10, 577–579 (1974).
[Crossref]

Jones, R. C.

Lyot, B.

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

Teschke, O.

G. Holton, O. Teschke, “Design of a Birefringent Filter for High-Power Dye Lasers,” IEEE J. Quantum Electron. QE-10, 577–579 (1974).
[Crossref]

Vukusic, J. I.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Yarborough, J. M.

J. M. Yarborough, J. Hobart, Conference on Laser Engineering and Applications (Optical Society of America, Washington, DC, 1973), postdeadline paper XX.

Appl. Opt. (1)

C. R. Acad. Sci. (1)

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

IEEE J. Quantum Electron. (1)

G. Holton, 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. (2)

Opt. Commun. (1)

I. J. Hodgkinson, J. I. Vukusic, “Birefringent Tuning Filters Without Secondary Peaks,” Opt. Commun. 24, 133–134 (1978).
[Crossref]

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

J. M. Yarborough, J. Hobart, Conference on Laser Engineering and Applications (Optical Society of America, Washington, DC, 1973), postdeadline paper XX.

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Figures (5)

Fig. 1
Fig. 1

Tilted birefringent filter.

Fig. 2
Fig. 2

Ring resonator containing a single birefringent plate tilted at the Brewster angle.

Fig. 3
Fig. 3

Ring resonator containing a single birefringent plate plus the dye stream tilted at the Brewster angle.

Fig. 4
Fig. 4

Transmittance for the eigenmode of the resonator in Fig. 2 for three different filter designs.

Fig. 5
Fig. 5

Transmittance for the eigenmode of the resonator in Fig. 3 for three different filter designs.

Tables (2)

Tables Icon

Table I Birefringent Filter with e = 18°50′ and d = 660 μm

Tables Icon

Table II Birefringent Filter with e = 0° and d = 399 μm

Equations (23)

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cos η = cos ϕ cos θ cos e + sin θ sin e ,
cos α = 1 sin η sin θ ( cos ϕ cos e - cos η cos θ ) ,
tan ϕ = sin α cos α sin θ + cot η cos θ ,
sin e = cos η sin θ - sin η cos θ cos α .
cos η = cos ϕ cos θ ,
tan ϕ = tan α sin θ .
M b = { cos 2 α + sin 2 α exp ( - i 2 δ ) q sin α cos α [ 1 - exp ( - i 2 δ ) ] q sin α cos α [ 1 - exp ( - i 2 δ ) ] q 2 [ sin 2 α + cos 2 α exp ( - i 2 δ ) ] } ,
- 2 δ = 2 π ( n e - n o ) d sin 2 η λ sin θ ,
λ = ( n e - n o ) d sin 2 η m sin θ ,
M b = exp ( - i δ ) [ cos δ + i sin2 Δ α sin δ i q cos 2 Δ α sin δ i q cos 2 Δ α sin δ q 2 ( cos δ + i sin2 Δ α sin δ ] .
M b = [ cos δ + i sin2 Δ α sin δ i q cos 2 Δ α sin δ i q cos 2 Δ α sin δ q 2 ( cos δ + i sin2 Δ α sin δ ] .
M b = ( cos δ i q sin δ i q sin δ q 2 cos δ ) .
M g = ( 1 0 0 q 2 ) .
ME = t E ,
t = - ( x + i y ) ± ( x + i y ) 2 - 4 q 2 2 ,
x = - ( 1 + q 2 ) cos δ , y = ( 1 - q 2 ) sin 2 Δ α sin δ .
t = ( 1 + q 2 ) cos δ ± ( 1 + q 2 ) 2 cos 2 δ - 4 q 2 2 ,
sin δ sin δ c = 1 - q 2 1 + q 2 ,
Δ λ = λ 2 sin θ ( n e - n o ) d sin 2 η .
Δ λ = λ / m .
m = λ / Δ λ .
d λ d η = ( n e - n o ) d sin 2 η m sin θ ,
d = m λ sin θ ( n e - n o ) sin 2 η .

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