Abstract

We propose a method to reduce sidelobes of multistage Lyot filters by substituting certain stages with two-plate fan Šolc stages. Parallel-aligned nematic liquid crystal (LC) cells are used as variable retarders to compose multistage Lyot LC tunable filters (LCTF). The simulation of a four-stage Lyot LCTF and a tunable filter, comprising two stages of Lyot filter and two stages of two-plate Šolc filter, are compared. With this method, the sidelobes are reduced and the full width at half-maximum intensity of transmission peak is also reduced. Experimental results and theoretical analysis are presented in detail to verify this method.

© 2010 Optical Society of America

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References

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    [CrossRef]
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2009 (3)

2007 (1)

S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6, 929-938 (2007).
[CrossRef]

2006 (1)

2005 (1)

J. Li, G. Baird, Y. H. Lin, H. W. Ren, and S. T. Wu, “Refractive-index matching between liquid crystals and photopolymers,” J. Soc. Inf. Display 13, 1017-1025 (2005).
[CrossRef]

2004 (1)

2003 (1)

H. Kursaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32, 2141-2146 (2003).
[CrossRef]

2002 (2)

2000 (1)

N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE 4056, 50-64 (2000).
[CrossRef]

1997 (1)

1996 (2)

A. Sneh and K. M. Johnson, “High-speed continuously tunable liquid crystal filter for WDM networks,” J. Lightwave Technol. 14, 1067-1080 (1996).
[CrossRef]

G. Kopp, “Tunable birefringent filters using liquid crystal variable retarders,” Proc. SPIE 2873, 324-327 (1996).
[CrossRef]

1994 (2)

G. Kopp, “Tunable birefringent filters using liquid crystal variable retarders,” Proc. SPIE 2265, 193-201 (1994).
[CrossRef]

R. S. Seymour, S. M. Rees, J. Staromlynska, J. Richards, and P. Wilson, “Design considerations for a liquid crystal tuned Lyot filter for laser bathymetry,” Opt. Eng. 33, 915-923(1994).
[CrossRef]

1993 (1)

P. Foukal, P. Miller, and C. Hoyt, “Liquid crystal tunable light filters for surveillance and remote sensing applications,” Proc. SPIE 1952, 168-177 (1993).
[CrossRef]

1990 (1)

P. J. Miller, “Tunable narrowband birefringent filters for astronomical imaging,” Proc. SPIE 1235, 466-473 (1990).
[CrossRef]

1989 (1)

1981 (1)

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

1975 (1)

H. A. Tarry, “Electrically tunable narrowband optical filter,” Electron. Lett. 11, 471-472 (1975).
[CrossRef]

1965 (1)

1958 (1)

1949 (1)

Abdulhalim, I.

Aharon, O.

Baird, G.

J. Li, G. Baird, Y. H. Lin, H. W. Ren, and S. T. Wu, “Refractive-index matching between liquid crystals and photopolymers,” J. Soc. Inf. Display 13, 1017-1025 (2005).
[CrossRef]

Blankner, J. G.

Bos, P. J.

Chen, X. X.

G. W. Yang, Z. R. Zheng, X. X. Chen, H. F. Li, and X. Liu, “Study of multiple-stage Lyot liquid crystal tunable filter,” J. Zhejiang Univ. Sci. 43, 1163-1167 (2009).

Chigrinov, V. G.

V. G. Chigrinov, E. P. Pozhidaev, D. A. Yakovlev, and H. S. Kwok, “Liquid crystal devices for optical communication systems,” presented at the Sixth Chinese Optoelectronics Symposium Hong Kong University of Science & Technology, Kowloon, China, 12-14 Sept. 2003.

Crawford, G. P.

S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6, 929-938 (2007).
[CrossRef]

Derks, M. J.

Elmore, D. F.

Evans, J. W.

Foukal, P.

P. Foukal, P. Miller, and C. Hoyt, “Liquid crystal tunable light filters for surveillance and remote sensing applications,” Proc. SPIE 1952, 168-177 (1993).
[CrossRef]

Gat, N.

N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE 4056, 50-64 (2000).
[CrossRef]

Hassler, D. M.

Hoyt, C.

P. Foukal, P. Miller, and C. Hoyt, “Liquid crystal tunable light filters for surveillance and remote sensing applications,” Proc. SPIE 1952, 168-177 (1993).
[CrossRef]

Hu, Z. F.

Huang, D. D.

Huang, H. C.

Jay, G. D.

S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6, 929-938 (2007).
[CrossRef]

Johnson, K. M.

A. Sneh and K. M. Johnson, “High-speed continuously tunable liquid crystal filter for WDM networks,” J. Lightwave Technol. 14, 1067-1080 (1996).
[CrossRef]

Kopp, G.

G. Kopp, “Tunable birefringent filters using liquid crystal variable retarders,” Proc. SPIE 2873, 324-327 (1996).
[CrossRef]

G. Kopp, “Tunable birefringent filters using liquid crystal variable retarders,” Proc. SPIE 2265, 193-201 (1994).
[CrossRef]

Kopp, G. A.

Koshiishi, H.

H. Kursaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32, 2141-2146 (2003).
[CrossRef]

Kursaki, H.

H. Kursaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32, 2141-2146 (2003).
[CrossRef]

Kwok, H. S.

D. D. Huang, X. J. Yu, H. C. Huang, and H. S. Kwok, “Design of polarizing color filters with double-liquid-crystal cells,” Appl. Opt. 41, 4638-4644 (2002).
[CrossRef]

V. G. Chigrinov, E. P. Pozhidaev, D. A. Yakovlev, and H. S. Kwok, “Liquid crystal devices for optical communication systems,” presented at the Sixth Chinese Optoelectronics Symposium Hong Kong University of Science & Technology, Kowloon, China, 12-14 Sept. 2003.

Li, H. F.

G. W. Yang, Z. R. Zheng, X. X. Chen, H. F. Li, and X. Liu, “Study of multiple-stage Lyot liquid crystal tunable filter,” J. Zhejiang Univ. Sci. 43, 1163-1167 (2009).

Li, J.

J. Li, G. Baird, Y. H. Lin, H. W. Ren, and S. T. Wu, “Refractive-index matching between liquid crystals and photopolymers,” J. Soc. Inf. Display 13, 1017-1025 (2005).
[CrossRef]

Lin, Y. H.

J. Li, G. Baird, Y. H. Lin, H. W. Ren, and S. T. Wu, “Refractive-index matching between liquid crystals and photopolymers,” J. Soc. Inf. Display 13, 1017-1025 (2005).
[CrossRef]

Liu, X.

G. W. Yang, Z. R. Zheng, X. X. Chen, H. F. Li, and X. Liu, “Study of multiple-stage Lyot liquid crystal tunable filter,” J. Zhejiang Univ. Sci. 43, 1163-1167 (2009).

Miller, P.

P. Foukal, P. Miller, and C. Hoyt, “Liquid crystal tunable light filters for surveillance and remote sensing applications,” Proc. SPIE 1952, 168-177 (1993).
[CrossRef]

Miller, P. J.

P. J. Miller, “Tunable narrowband birefringent filters for astronomical imaging,” Proc. SPIE 1235, 466-473 (1990).
[CrossRef]

Pozhidaev, E. P.

V. G. Chigrinov, E. P. Pozhidaev, D. A. Yakovlev, and H. S. Kwok, “Liquid crystal devices for optical communication systems,” presented at the Sixth Chinese Optoelectronics Symposium Hong Kong University of Science & Technology, Kowloon, China, 12-14 Sept. 2003.

Rees, S. M.

R. S. Seymour, S. M. Rees, J. Staromlynska, J. Richards, and P. Wilson, “Design considerations for a liquid crystal tuned Lyot filter for laser bathymetry,” Opt. Eng. 33, 915-923(1994).
[CrossRef]

Ren, H. W.

J. Li, G. Baird, Y. H. Lin, H. W. Ren, and S. T. Wu, “Refractive-index matching between liquid crystals and photopolymers,” J. Soc. Inf. Display 13, 1017-1025 (2005).
[CrossRef]

Richards, J.

R. S. Seymour, S. M. Rees, J. Staromlynska, J. Richards, and P. Wilson, “Design considerations for a liquid crystal tuned Lyot filter for laser bathymetry,” Opt. Eng. 33, 915-923(1994).
[CrossRef]

Rosenberg, W. J.

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

Saeed, S.

Seymour, R. S.

R. S. Seymour, S. M. Rees, J. Staromlynska, J. Richards, and P. Wilson, “Design considerations for a liquid crystal tuned Lyot filter for laser bathymetry,” Opt. Eng. 33, 915-923(1994).
[CrossRef]

Sneh, A.

A. Sneh and K. M. Johnson, “High-speed continuously tunable liquid crystal filter for WDM networks,” J. Lightwave Technol. 14, 1067-1080 (1996).
[CrossRef]

Šolc, I.

Staromlynska, J.

R. S. Seymour, S. M. Rees, J. Staromlynska, J. Richards, and P. Wilson, “Design considerations for a liquid crystal tuned Lyot filter for laser bathymetry,” Opt. Eng. 33, 915-923(1994).
[CrossRef]

Streete, J. L.

Suzuki, T.

H. Kursaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32, 2141-2146 (2003).
[CrossRef]

Tarry, H. A.

H. A. Tarry, “Electrically tunable narrowband optical filter,” Electron. Lett. 11, 471-472 (1975).
[CrossRef]

Title, A. M.

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

Tsuchiya, K.

H. Kursaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32, 2141-2146 (2003).
[CrossRef]

Wilson, P.

R. S. Seymour, S. M. Rees, J. Staromlynska, J. Richards, and P. Wilson, “Design considerations for a liquid crystal tuned Lyot filter for laser bathymetry,” Opt. Eng. 33, 915-923(1994).
[CrossRef]

Woltman, S. J.

S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6, 929-938 (2007).
[CrossRef]

Woods, J. C.

Wu, S. T.

J. Li, G. Baird, Y. H. Lin, H. W. Ren, and S. T. Wu, “Refractive-index matching between liquid crystals and photopolymers,” J. Soc. Inf. Display 13, 1017-1025 (2005).
[CrossRef]

S. T. Wu, “Design of a liquid crystal based tunable electrooptic filter,” Appl. Opt. 28, 48-52 (1989).
[CrossRef]

Yakovlev, D. A.

V. G. Chigrinov, E. P. Pozhidaev, D. A. Yakovlev, and H. S. Kwok, “Liquid crystal devices for optical communication systems,” presented at the Sixth Chinese Optoelectronics Symposium Hong Kong University of Science & Technology, Kowloon, China, 12-14 Sept. 2003.

Yang, G. W.

G. W. Yang, Z. R. Zheng, X. X. Chen, H. F. Li, and X. Liu, “Study of multiple-stage Lyot liquid crystal tunable filter,” J. Zhejiang Univ. Sci. 43, 1163-1167 (2009).

Yariv, A.

A. Yariv and P. Yeh, “Jones calculus and its application to birefringent optical systems,” in Handbook of Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1983), pp. 121-154.

Ye, C.

Yeh, P.

A. Yariv and P. Yeh, “Jones calculus and its application to birefringent optical systems,” in Handbook of Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1983), pp. 121-154.

Yu, X. J.

Zheng, Z. R.

G. W. Yang, Z. R. Zheng, X. X. Chen, H. F. Li, and X. Liu, “Study of multiple-stage Lyot liquid crystal tunable filter,” J. Zhejiang Univ. Sci. 43, 1163-1167 (2009).

Adv. Space Res. (1)

H. Kursaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32, 2141-2146 (2003).
[CrossRef]

Appl. Opt. (4)

Chin. Opt. Lett. (1)

Electron. Lett. (1)

H. A. Tarry, “Electrically tunable narrowband optical filter,” Electron. Lett. 11, 471-472 (1975).
[CrossRef]

J. Lightwave Technol. (1)

A. Sneh and K. M. Johnson, “High-speed continuously tunable liquid crystal filter for WDM networks,” J. Lightwave Technol. 14, 1067-1080 (1996).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

J. Soc. Inf. Display (1)

J. Li, G. Baird, Y. H. Lin, H. W. Ren, and S. T. Wu, “Refractive-index matching between liquid crystals and photopolymers,” J. Soc. Inf. Display 13, 1017-1025 (2005).
[CrossRef]

J. Zhejiang Univ. Sci. (1)

G. W. Yang, Z. R. Zheng, X. X. Chen, H. F. Li, and X. Liu, “Study of multiple-stage Lyot liquid crystal tunable filter,” J. Zhejiang Univ. Sci. 43, 1163-1167 (2009).

Nat. Mater. (1)

S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6, 929-938 (2007).
[CrossRef]

Opt. Eng. (2)

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

R. S. Seymour, S. M. Rees, J. Staromlynska, J. Richards, and P. Wilson, “Design considerations for a liquid crystal tuned Lyot filter for laser bathymetry,” Opt. Eng. 33, 915-923(1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (5)

P. J. Miller, “Tunable narrowband birefringent filters for astronomical imaging,” Proc. SPIE 1235, 466-473 (1990).
[CrossRef]

N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE 4056, 50-64 (2000).
[CrossRef]

G. Kopp, “Tunable birefringent filters using liquid crystal variable retarders,” Proc. SPIE 2265, 193-201 (1994).
[CrossRef]

G. Kopp, “Tunable birefringent filters using liquid crystal variable retarders,” Proc. SPIE 2873, 324-327 (1996).
[CrossRef]

P. Foukal, P. Miller, and C. Hoyt, “Liquid crystal tunable light filters for surveillance and remote sensing applications,” Proc. SPIE 1952, 168-177 (1993).
[CrossRef]

Other (2)

V. G. Chigrinov, E. P. Pozhidaev, D. A. Yakovlev, and H. S. Kwok, “Liquid crystal devices for optical communication systems,” presented at the Sixth Chinese Optoelectronics Symposium Hong Kong University of Science & Technology, Kowloon, China, 12-14 Sept. 2003.

A. Yariv and P. Yeh, “Jones calculus and its application to birefringent optical systems,” in Handbook of Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1983), pp. 121-154.

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Figures (12)

Fig. 1
Fig. 1

Single stage of a Lyot LCTF consists of an integrated retarder, which includes an LC cell and a quartz wave plate oriented at 45 ° between two aligned polarizers.

Fig. 2
Fig. 2

Two-plate fan Šolc filter consists of two identical retarders at the prescribed azimuth angle between two parallel polarizers.

Fig. 3
Fig. 3

Calculated transmission profiles of a single-stage Lyot filter and a two-plate fan Šolc filter, whose integrated retarders are the same.

Fig. 4
Fig. 4

(a) Calculated transmission spectra of a four-stage Lyot filter and the third and fourth stages in the filter. (b) Third and fourth stages in the four-stage Lyot filter are modified into two corresponding two-plate fan Šolc stages; the sidelobes are reduced. (c) Transmission spectra of a four-stage Lyot filter and the first and second stages in the filter. (d) First and second stages in a four-stage Lyot filter are modified into two corresponding two-plate fan Šolc stages; the secondary maxima are not reduced.

Fig. 5
Fig. 5

(a) Schematic diagram of a four-stage Lyot LCTF. (b) Four-stage Lyot LCTF. (c) Schematic diagram of the modified LCTF with the third and fourth two-plate fan Šolc stages. The angles 1, 2, 3, and 4 are 22.5 ° , 22.5 ° , 22.5 ° , and 22.5 ° , respectively. (d) Modified LCTF.

Fig. 6
Fig. 6

Calculated transmission curves of a four-stage Lyot filter (solid curve) and the modified filter (dashed curve) with transmission peaks at 500 nm , 540 nm , 580 nm , 620 nm , and 700 nm .

Fig. 7
Fig. 7

Normalized measured transmission spectra of the fourth Lyot stage used in the four-stage Lyot LCTF and the corresponding two-plate fan Šolc stage.

Fig. 8
Fig. 8

(a) Measured transmission curves are presented on a linear vertical scale of T * 100 % . (b) Measured transmission curves are presented on a logarithmic vertical scale of log 10 ( T * 100 ) . All sidelobes are reduced in the modified LCTF.

Fig. 9
Fig. 9

Six examples of actually measured transmission spectra of the modified LCTF. Main transmission peaks are tuned at 500 nm , 525 nm , 540 nm , 580 nm , 620 nm , and 700 nm , and the transmission relative to unpolarized light averages 10%.

Fig. 10
Fig. 10

Measured transmission spectrum of a single-stage Lyot filter using only a 10 μ m LC cell as a retarder; the marked peak is at 589.3 nm .

Fig. 11
Fig. 11

Transmission curves are calculated without considering birefringent dispersion and measured and calculated with considering birefringent dispersion, respectively. In this case, a 4     μ m LC cell was used as a retarder for the single-stage Lyot filter, which proves the measurement and correction are effective.

Fig. 12
Fig. 12

Proposed method is applied to a different four-stage Lyot filter and a six-stage Lyot filter. Calculated results of the original Lyot filters (solid curves) and the modified filters (dashed curves) are shown in (a) and (b).

Tables (3)

Tables Icon

Table 1 Details of Four-Stage Lyot LCTF and Modified LCTF

Tables Icon

Table 2 Birefringence of E44 at the Wavelength Peaks

Tables Icon

Table 3 Birefringence of E44 at the Wavelength Valleys

Equations (8)

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

Γ = ( n e n o ) d 2 π λ = Δ n d 2 π λ ,
T = cos 2 1 2 Γ lyot = cos 2 1 2 ( Γ lc + Γ qz ) ,
T = | tan ( 2 ρ ) cos χ sin ( N χ ) sin χ | 2 ,
cos χ = cos ( 2 ρ ) cos ( 1 2 Γ solc ) ,
T = cos 4 1 2 Γ solc = [ cos 2 1 2 ( Γ lc + Γ qz ) ] 2 .
T = cos 2 ( 1 2 Γ ) cos 2 ( 2 · 1 2 Γ ) cos 2 ( 4 · 1 2 Γ ) ... cos 2 ( 2 N 1 · 1 2 Γ ) .
cos 2 1 2 Γ lyot = 1 2 ,
cos 4 1 2 Γ solc = 1 2 ,

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