Abstract

The optical arrangement of a spectral filter without an intermediate polarizer that was developed based on optical rotatory dispersion and test measurement results are presented and described. The filter uses three dispersive polarization rotators as the key elements in combination with two additional quarter-wave retarders, and it is wavelength tunable with a spectral transmission equivalent to that of a standard Lyot two-stage filter.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. Evans, "The birefringent filter," J. Opt. Soc. Am. 39, 229-242 (1949).
    [CrossRef]
  2. A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984), Chap. 5, pp. 121-154.
  3. J. W. Evans, "Solc birefringent filter," J. Opt. Soc. Am. 48, 142-145 (1958).
    [CrossRef]
  4. I. Solc, "Birefringent chain filters," J. Opt. Soc. Am. 55, 621-625 (1965).
    [CrossRef]
  5. A. M. Title and W. J. Rosenberg, "Tunable birefringent filters," Opt. Eng. 20, 815-823 (1981).
  6. J. F. Lotspeich, R. R. Stephens, and D. M. Henderson, "Electro-optic tunable filter," Opt. Eng. 20, 830-836 (1981).
  7. W. J. Gunning, "Electro-optically tuned spectral filters: a review," Opt. Eng. 20, 837-845 (1981).
  8. G. Kopp, "Tunable birefringent filters using liquid crystal variable retarders," in Polarization Analysis and Measurement II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 2265, 193-201 (1994).
    [CrossRef]
  9. C. Ye, "Wavelength-tunable spectral filters based on the optical rotatory dispersion effect," Appl. Opt. 42, 4505-4513 (2003).
    [CrossRef] [PubMed]
  10. C. Ye, "A liquid crystal band-pass filter based on the optical rotatory dispersion effect," Appl. Opt. 43, 4007-4012 (2004).
    [CrossRef] [PubMed]
  11. P. S. Theocaria and E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer-Verlag, 1979).
  12. T. M. Lowry, Optical Rotatory Power (Dover, 1964).
  13. J. M. Beckers, L. Dickson, and R. S. Joyce, "Observing the Sun with a fully tunable Lyot-Ohman filter," Appl. Opt. 14, 2061-2066 (1975).
    [CrossRef] [PubMed]

2004 (1)

2003 (1)

1994 (1)

G. Kopp, "Tunable birefringent filters using liquid crystal variable retarders," in Polarization Analysis and Measurement II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 2265, 193-201 (1994).
[CrossRef]

1981 (3)

A. M. Title and W. J. Rosenberg, "Tunable birefringent filters," Opt. Eng. 20, 815-823 (1981).

J. F. Lotspeich, R. R. Stephens, and D. M. Henderson, "Electro-optic tunable filter," Opt. Eng. 20, 830-836 (1981).

W. J. Gunning, "Electro-optically tuned spectral filters: a review," Opt. Eng. 20, 837-845 (1981).

1975 (1)

1965 (1)

1958 (1)

1949 (1)

Beckers, J. M.

Dickson, L.

Evans, J. W.

Gdoutos, E. E.

P. S. Theocaria and E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer-Verlag, 1979).

Gunning, W. J.

W. J. Gunning, "Electro-optically tuned spectral filters: a review," Opt. Eng. 20, 837-845 (1981).

Henderson, D. M.

J. F. Lotspeich, R. R. Stephens, and D. M. Henderson, "Electro-optic tunable filter," Opt. Eng. 20, 830-836 (1981).

Joyce, R. S.

Kopp, G.

G. Kopp, "Tunable birefringent filters using liquid crystal variable retarders," in Polarization Analysis and Measurement II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 2265, 193-201 (1994).
[CrossRef]

Lotspeich, J. F.

J. F. Lotspeich, R. R. Stephens, and D. M. Henderson, "Electro-optic tunable filter," Opt. Eng. 20, 830-836 (1981).

Lowry, T. M.

T. M. Lowry, Optical Rotatory Power (Dover, 1964).

Rosenberg, W. J.

A. M. Title and W. J. Rosenberg, "Tunable birefringent filters," Opt. Eng. 20, 815-823 (1981).

Solc, I.

Stephens, R. R.

J. F. Lotspeich, R. R. Stephens, and D. M. Henderson, "Electro-optic tunable filter," Opt. Eng. 20, 830-836 (1981).

Theocaria, P. S.

P. S. Theocaria and E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer-Verlag, 1979).

Title, A. M.

A. M. Title and W. J. Rosenberg, "Tunable birefringent filters," Opt. Eng. 20, 815-823 (1981).

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984), Chap. 5, pp. 121-154.

Ye, C.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984), Chap. 5, pp. 121-154.

Appl. Opt. (3)

J. Opt. Soc. Am. (3)

Opt. Eng. (3)

A. M. Title and W. J. Rosenberg, "Tunable birefringent filters," Opt. Eng. 20, 815-823 (1981).

J. F. Lotspeich, R. R. Stephens, and D. M. Henderson, "Electro-optic tunable filter," Opt. Eng. 20, 830-836 (1981).

W. J. Gunning, "Electro-optically tuned spectral filters: a review," Opt. Eng. 20, 837-845 (1981).

Proc. SPIE (1)

G. Kopp, "Tunable birefringent filters using liquid crystal variable retarders," in Polarization Analysis and Measurement II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 2265, 193-201 (1994).
[CrossRef]

Other (3)

P. S. Theocaria and E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer-Verlag, 1979).

T. M. Lowry, Optical Rotatory Power (Dover, 1964).

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984), Chap. 5, pp. 121-154.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Optical arrangement of a tunable spectral filter: pl 1 , pl 2 , polarizers (azimuths, P 1 , P 2 ); r 1 , r 2 , r 3 , polarization rotators [rotation angles, ρ ( λ ) , ρ ( λ ) , and ρ ( λ ) respectively]; q 1 , q 2 , quarter-wave retarders (azimuths, φ 1 , φ 2 ). The retarders and the exit polarizer are oriented such that (a) φ 2 = 2 φ 1 and P 2 = φ 1 and (b) φ 2 = 90 ° + 2 φ 1 and P 2 = 90 ° + φ 1 .

Fig. 2
Fig. 2

Measured spectral transmission T c ( λ ) of a spectral filter constructed according to the arrangement of Fig. 1(a) versus wavelength λ when the filter was tuned for tuning angles (a) φ 1 = 0 ° and φ 1 = 90 ° and (b) φ 1 = 45 ° and φ 1 = 135 ° .

Fig. 3
Fig. 3

Measured spectral transmission T s ( λ ) of a spectral filter constructed according to the arrangement of Fig. 1(b) versus wavelength λ when the filter was tuned for tuning angles (a) φ 1 = 30 ° and φ 1 = 120 ° and (b) φ 1 = 60 ° and φ 1 = 150 ° .

Fig. 4
Fig. 4

Measured overall transmission t low-loss ( λ ) of the constituent elements of the low-loss filter in Fig. 2 or 3 versus light of wavelength λ compared with transmissions t HN 38 S ( λ ) , t FPG 003 ( λ ) , and t 069 - 1105 ( λ ) of the elements of an equivalent two-stage filter with various polarizers used as the intermediate polarizer (see text). t low-loss ( λ ) is the tuned spectral transmission curve of the low-loss filter measured at φ 1 = 0 ° , and t HN 38 S ( λ ) , t FPG 003 ( λ ) , and t 069-1105 ( λ ) are the equivalent tuned transmission curves of the two-stage filter for t HN 38 S ( λ ) , t FPG 003 ( λ ) , and t 069 - 1105 ( λ ) , respectively.

Equations (5)

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

T ( λ ) = 1 2 { 1 cos 2 [ P 2 + ρ ( λ ) ] sin 2 [ P 2 + ρ ( λ ) ] 0 } [ 1 0 0 0 0 cos 2 2 θ 2 sin 2 θ 2 cos 2 θ 2 sin 2 θ 2 0 sin 2 θ 2 cos 2 θ 2 sin 2 2 θ 2 cos 2 θ 2 0 sin 2 θ 2 cos 2 θ 2 0 ] [ 1 0 0 0 0 cos 2 2 θ 1 sin 2 θ 1 cos 2 θ 1 sin 2 θ 1 0 sin 2 θ 1 cos 2 θ 1 sin 2 2 θ 1 cos 2 θ 1 0 sin 2 θ 1 cos 2 θ 1 0 ] [ 1 1 0 0 ] = 1 2 { 1 + cos 2 [ P 2 + ρ ( λ ) θ 2 ] cos 2 θ 1 cos 2 ( θ 2 θ 1 ) + sin 2 θ 1 sin 2 [ P 2 + ρ ( λ ) θ 2 ] } .
T c ( λ ) = ½ { 1 + cos 3 2 [ ρ ( λ ) + φ 1 ] sin 2 2 [ ρ ( λ ) + φ 1 ] } = cos 2 [ ρ ( λ ) + φ 1 ] cos 2 2 [ ρ ( λ ) + φ 1 ]
T s ( λ ) = ½ { 1 cos 3 2 [ ρ ( λ ) + φ 1 ] sin 2 2 [ ρ ( λ ) + φ 1 ] } = sin 2 [ ρ ( λ ) + φ 1 ] cos 2 2 [ ρ ( λ ) + φ 1 ] .
T r ( λ ) = { cos 2 [ 45 ° + ρ f ( λ ) ] cos 2 2 [ 45 ° + ρ f ( λ ) ] cos 2 [ 45 ° ρ f ( λ ) ] cos 2 2 [ 45 ° ρ f ( λ ) ] φ 1 = 45 ° , φ 2 = 90 ° , P 2 = 45 ° , sin 2 [ 45 ° + ρ f ( λ ) ] cos 2 2 [ 45 ° + ρ f ( λ ) ] sin 2 [ 45 ° ρ f ( λ ) ] cos 2 2 [ 45 ° ρ f ( λ ) ] φ 1 = 45 ° , φ 2 = 0 ° , P 2 = 45 ° ,
P ( λ ) = 9.5639 λ 2 0.0127493 2.3113 λ 2 - 0.000974 0.1905 ,

Metrics