Abstract

More than 50 years ago, B. Lyot and later on I. Solc introduced new types of optical filters called birefringent filters. Such filters take advantage of the phase shifts between orthogonal polarization to obtain narrow band filters. It requires birefringent wave plates for introducing phase retardation between the two orthogonal components of a linearly polarized light that correspond to the fast and slow axes of the birefringent material. In this paper we present new methods and architectures that generalize the Lyot-Ohman and Solc filters for optimally synthesizing an arbitrary all-optical filter by defining an error metric and minimizing it with simulated annealing. We also suggest the use of the electro-optic effect for controlling the retardation of individual elements that make up the tunable filter. Such a filter could be used for instance for realizing a dynamically tunable optical add/drop multiplexer in a telecommunication system.

© 2002 Optical Society of America

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References

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  1. B. Lyot, “Optical apparatus with wide field using interference of polarized light,” C.R. Acad. Sci. (Paris) 197, 1593 (1933).
  2. B. Lyot, “Filter monochromatique polarisant et ses applications en physique solaire,” Ann. Astrophys. 7, 32 (1944).
  3. Y. Ohman, “A new monochromator,” Nature 41, 157, 291 (1938).
  4. Y. Ohman, “On some new birefringent filter for solar research,” Ark. Astron. 2, 165 (1958).
  5. J. M. Beckers, L. Dickson, and R. S. Joyce, “Observing the sun with a fully tunable Lyot-Ohman filter,” Appl. Opt. 14, 2061 (1975).
    [Crossref] [PubMed]
  6. I. Solc, Ceskoslov. Casopis pro Fysiku 3, 366 (1953); Csek. Cas. Fys. 4, 607, 699 (1954); 5, 114 (1955).
  7. I. Solc, “Birefringent chain filters,” J. Opt. Soc. Am. 55, 621 (1965).
    [Crossref]
  8. P. Yeh, A. Yariv, and C. S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423 (1977).
    [Crossref]
  9. S. Kirkpatrick, C.D. Gelatt, and M.P. Vecchi, “Optimization by simulated annealing,” Science 220, 671 (1983).
    [Crossref] [PubMed]
  10. S. Kirkpatrick, “Optimization by simulated annealing: quantitive studies,” Journal of Statistical Physics,  34, 975 (1984).
    [Crossref]

1984 (1)

S. Kirkpatrick, “Optimization by simulated annealing: quantitive studies,” Journal of Statistical Physics,  34, 975 (1984).
[Crossref]

1983 (1)

S. Kirkpatrick, C.D. Gelatt, and M.P. Vecchi, “Optimization by simulated annealing,” Science 220, 671 (1983).
[Crossref] [PubMed]

1977 (1)

1975 (1)

1965 (1)

1958 (1)

Y. Ohman, “On some new birefringent filter for solar research,” Ark. Astron. 2, 165 (1958).

1944 (1)

B. Lyot, “Filter monochromatique polarisant et ses applications en physique solaire,” Ann. Astrophys. 7, 32 (1944).

1938 (1)

Y. Ohman, “A new monochromator,” Nature 41, 157, 291 (1938).

1933 (1)

B. Lyot, “Optical apparatus with wide field using interference of polarized light,” C.R. Acad. Sci. (Paris) 197, 1593 (1933).

Beckers, J. M.

Dickson, L.

Gelatt, C.D.

S. Kirkpatrick, C.D. Gelatt, and M.P. Vecchi, “Optimization by simulated annealing,” Science 220, 671 (1983).
[Crossref] [PubMed]

Hong, C. S.

Joyce, R. S.

Kirkpatrick, S.

S. Kirkpatrick, “Optimization by simulated annealing: quantitive studies,” Journal of Statistical Physics,  34, 975 (1984).
[Crossref]

S. Kirkpatrick, C.D. Gelatt, and M.P. Vecchi, “Optimization by simulated annealing,” Science 220, 671 (1983).
[Crossref] [PubMed]

Lyot, B.

B. Lyot, “Filter monochromatique polarisant et ses applications en physique solaire,” Ann. Astrophys. 7, 32 (1944).

B. Lyot, “Optical apparatus with wide field using interference of polarized light,” C.R. Acad. Sci. (Paris) 197, 1593 (1933).

Ohman, Y.

Y. Ohman, “On some new birefringent filter for solar research,” Ark. Astron. 2, 165 (1958).

Y. Ohman, “A new monochromator,” Nature 41, 157, 291 (1938).

Solc, I.

I. Solc, “Birefringent chain filters,” J. Opt. Soc. Am. 55, 621 (1965).
[Crossref]

I. Solc, Ceskoslov. Casopis pro Fysiku 3, 366 (1953); Csek. Cas. Fys. 4, 607, 699 (1954); 5, 114 (1955).

Vecchi, M.P.

S. Kirkpatrick, C.D. Gelatt, and M.P. Vecchi, “Optimization by simulated annealing,” Science 220, 671 (1983).
[Crossref] [PubMed]

Yariv, A.

Yeh, P.

Ann. Astrophys. (1)

B. Lyot, “Filter monochromatique polarisant et ses applications en physique solaire,” Ann. Astrophys. 7, 32 (1944).

Appl. Opt. (1)

Ark. Astron. (1)

Y. Ohman, “On some new birefringent filter for solar research,” Ark. Astron. 2, 165 (1958).

C.R. Acad. Sci. (Paris) (1)

B. Lyot, “Optical apparatus with wide field using interference of polarized light,” C.R. Acad. Sci. (Paris) 197, 1593 (1933).

J. Opt. Soc. Am. (2)

Journal of Statistical Physics (1)

S. Kirkpatrick, “Optimization by simulated annealing: quantitive studies,” Journal of Statistical Physics,  34, 975 (1984).
[Crossref]

Nature (1)

Y. Ohman, “A new monochromator,” Nature 41, 157, 291 (1938).

Science (1)

S. Kirkpatrick, C.D. Gelatt, and M.P. Vecchi, “Optimization by simulated annealing,” Science 220, 671 (1983).
[Crossref] [PubMed]

Other (1)

I. Solc, Ceskoslov. Casopis pro Fysiku 3, 366 (1953); Csek. Cas. Fys. 4, 607, 699 (1954); 5, 114 (1955).

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Figures (9)

Fig. 1.
Fig. 1.

4-stage Lyot-Ohman filter

Fig. 2.
Fig. 2.

6-Stage Folded Solc filter

Fig. 3.
Fig. 3.

Folded Solc filter with 20 stages

Fig. 4.
Fig. 4.

Designed filter with change in the azimuth angles

Fig. 5.
Fig. 5.

20-Stage Folded Solc Filter tilt angles compared with the filter in Fig. 4

Fig. 6.
Fig. 6.

Birefringent filter in a folded architecture

Fig. 7.
Fig. 7.

Designed filter in a folded architecture

Fig. 8.
Fig. 8.

Birefringent filter in a hybrid architecture

Fig. 9.
Fig. 9.

Designed filter in hybrid architecture consisting of 3 polarizers and 12 wave-plates

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

Γ k = 2 · Γ k 1 = 2 k 1 Γ 1
T = T 0 Π k = 1 N cos 2 ( π Γ k )
φ k = ( 1 ) k · ρ
T = tan ( 2 ρ ) cos ( χ ) sin ( ) sin ( χ ) 2
cos ( χ ) = cos ( 2 ρ ) sin ( Γ / 2 )
φ k = ( 2 k + 1 ) ρ
Prob ( E ) = exp ( E / T )
p = e ΔE / T ; ΔE = E present state E possible state
Γ = 2 π λ ( n e n o ) L natural phase retardation π λ ( n e 3 r 33 n o 3 r 13 ) L d V induced phase retardation
L = 301 λ 0 2 ( n e n 0 ) = 301 λ 0 2 Δn
T = T 0 log ( 1 + i 3 )

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