Abstract

The performance of a wire-grid polarizer (WGP) on a curved surface was investigated with a simple numerical model. The computation model combines rigorous coupled-wave analysis with piecewise linear segmentation that approximates a curved surface for two bending configurations. A curvature-induced Rayleigh anomaly is found to be the main performance degradation mechanism that reduces transmittance and polarization contrast. A WGP on a curved surface is more likely to incur the Rayleigh anomaly with smaller surface curvature. For a given curvature, a larger WGP is more vulnerable. Effects of polar and azimuthal incidence angles were also analyzed. Suggestions were made in regard to a WGP design that minimizes the performance degradation.

© 2008 Optical Society of America

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2007

2006

J. A. Castellano, "Modifying light," Am. Sci. 94, 438-445 (2006).
[CrossRef]

2005

S.-W. Ahn, K.-D. Lee, J.-S. Kim, S. H. Kim, J.-D. Park, S.-H. Lee, and P.-W. Yoon, "Fabrication of a 50 nm half-pitch wire grid polarizer using nanoimprint lithography," Nanotechnology 16, 1874-1877 (2005).
[CrossRef]

D. Kim, "Polarization characteristics of a wire-grid polarizer in a rotating platform," Appl. Opt. 44, 1366-1371 (2005).
[CrossRef] [PubMed]

N. Bokor and N. Davidson, "Ideal collimation, concentration, and imaging with curved diffractive optical elements," Rev. Sci. Instrum. 76, 111101 (2005).
[CrossRef]

D. Kim, "Performance uniformity analysis of a wire-grid polarizer in imaging polarimetry," Appl. Opt. 44, 5398-5402 (2005).
[CrossRef] [PubMed]

2004

2003

2002

2001

N. Bokor and N. Davidson, "Aberration-free imaging with an aplanatic curved diffractive element," Appl. Opt. 40, 5825-5829 (2001).
[CrossRef]

F. A. Sadjadi and C. S. L. Chun, "Passive polarimetric IR target classification," IEEE Trans. Aerosp. Electron. Syst. 37, 740-751 (2001).
[CrossRef]

2000

1999

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, and E. A. Sornsin, "Multispectral infrared Stokes imaging polarimeter," Proc. SPIE 3754, 137-143 (1999).
[CrossRef]

1997

1996

T. Abboud and H. Ammari, "Diffraction at a curved grating: approximation by an infinite plane grating," J. Math. Anal. Appl. 202, 1076-1100 (1996).
[CrossRef]

1986

1985

1982

1907

Lord Rayleigh, "Note on the remarkable case of diffraction spectra described by Prof. Wood," Philos. Mag. 14, 60-65 (1907).

Am. Sci.

J. A. Castellano, "Modifying light," Am. Sci. 94, 438-445 (2006).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

E. Chen and S. Y. Chou, "Polarimetry of thin metal transmission gratings in the resonance region and its impact on the response of metal-semiconductor-metal photodetectors," Appl. Phys. Lett. 70, 2673-2675 (1997).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst.

F. A. Sadjadi and C. S. L. Chun, "Passive polarimetric IR target classification," IEEE Trans. Aerosp. Electron. Syst. 37, 740-751 (2001).
[CrossRef]

J. Math. Anal. Appl.

T. Abboud and H. Ammari, "Diffraction at a curved grating: approximation by an infinite plane grating," J. Math. Anal. Appl. 202, 1076-1100 (1996).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nanotechnology

S.-W. Ahn, K.-D. Lee, J.-S. Kim, S. H. Kim, J.-D. Park, S.-H. Lee, and P.-W. Yoon, "Fabrication of a 50 nm half-pitch wire grid polarizer using nanoimprint lithography," Nanotechnology 16, 1874-1877 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Philos. Mag.

Lord Rayleigh, "Note on the remarkable case of diffraction spectra described by Prof. Wood," Philos. Mag. 14, 60-65 (1907).

Proc. SPIE

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, and E. A. Sornsin, "Multispectral infrared Stokes imaging polarimeter," Proc. SPIE 3754, 137-143 (1999).
[CrossRef]

Rev. Sci. Instrum.

N. Bokor and N. Davidson, "Ideal collimation, concentration, and imaging with curved diffractive optical elements," Rev. Sci. Instrum. 76, 111101 (2005).
[CrossRef]

Other

X.-D. Mi, D. Kessler, L. W. Tutt, and L. Weller-Brophy, "Low-fill-factor wire-grid polarizers for LCD backlighting," in 2005 SID International Symposium, Seminar, and Exhibition Digest (Society for Information Display, 2005), pp. 1004-1007.
[CrossRef]

S. J. Lee, M. J. Kim, H. J. Min, H. S. Kim, S. C. Kang, S. E. Lee, K. H. Park, J. H. Oh, S. H. Kim, D. H. Kang, J. S. Choi, S. M. Hong, J. H. Hur, and J. Jang, "A wire grid stereoscopic display," in 2006 SID International Symposium, Seminar, and Exhibition Digest (Society for Information Display, 2006), pp. 89-92.
[CrossRef]

K.-H. Liu, C.-C. Liao, Y.-C. Hung, and C.-H. Chan, "A high contrast micro-cell liquid crystal display film," in 2004 SID International Symposium, Seminar, and Exhibition Digest (Society for Information Display, 2004), pp. 610-613.
[CrossRef]

Y. Fujisaki, H. Sato, Y. Inoue, H. Fujikake, and T. Kurita, "Fast-response flexible LCD panel driven by a low-voltage organic TFT," in 2006 SID International Symposium, Seminar, and Exhibition Digest (Society for Information Display, 2006), pp. 119-122.
[CrossRef]

H.-L. Kuo, C.-H. Chiu, and P.-C. Chen, "A novel wire grid polarizer," in 2004 SID International Symposium, Seminar, and Exhibition Digest (Society for Information Display, 2004), pp. 732-735.
[CrossRef]

S. Arnold, E. Gardner, D. Hansen, and R. Perkins, "An improved polarizing beamsplitter LCOS projection display based on wire-grid polarizers," in 2001 SID International Symposium, Seminar, and Exhibition Digest (Society for Information Display, 2001), pp. 1282-1285.
[CrossRef]

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic of a WGP on a curved surface. S WGP represents the size of a WGP. R is the radius of curvature of the bent substrate. (b) Piecewise segmented flat WGP. The number of segments N = 4 in this schematic. L is the size of a segment. θ s is the angle between contiguous segments. Λ is the wire-grid period.

Fig. 2
Fig. 2

Bending configurations: (a) grating vector in the plane of incidence, parallel bending, and (b) grating vector orthogonal to the plane of incidence, perpendicular bending.

Fig. 3
Fig. 3

Effect of curvature on (a) ER and (b) transmittance for parallel bending and (c) ER and (d) transmittance for perpendicular bending. S WGP = 10 mm , Λ = 200 nm , and L = 200 μ m at λ = 400 nm .

Fig. 4
Fig. 4

Minimum radius of curvature as a function of the WGP size, above which the Rayleigh anomaly does not occur.

Fig. 5
Fig. 5

Effect of wire-grid period on (a) ER and (b) transmittance of a WGP for Λ = 200 nm 300 nm . The parallel bending configuration is assumed.

Fig. 6
Fig. 6

ER and transmittance of an overall WGP as a function of radius of curvature. Solid lines represent those of a straight surface ( R ) . PP, perfect polarizer.

Fig. 7
Fig. 7

Sign conventions for θ in and Eq. (11). ϕ = 0 ° is assumed.

Fig. 8
Fig. 8

(a) ER and (b) transmittance of a WGP with radius of curvature, as the azimuthal angle ϕ is varied from to 0° to 90° for θ in = 0 ° and Λ = 200 nm .

Equations (13)

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

I = i I i ( θ i ) cos θ i i cos θ i ,
cos θ s = 1 ( L 2 R ) 2 1 + ( L 2 R ) 2 ,
sin θ cos ϕ + ( n s 2 sin 2 θ sin 2 ϕ ) 1 2 = m λ Λ .
sin θ = ( m λ Λ ) cos ϕ ± [ n s 2 ( m λ Λ ) 2 sin 2 ϕ ] 1 2 .
sin θ = n s 1 ( m λ n s Λ ) ,
i RA = R L sin 1 n s m λ Λ ,
sin θ = n s 2 ( λ Λ ) 2 .
R > R min = S WGP 2 sin 1 n s ( λ Λ ) .
I s = θ 2 θ 1 4 cos θ n s 2 sin 2 θ ( cos θ + n s 2 sin 2 θ ) 2 2 cos θ d θ θ 2 θ 1 cos θ d θ ,
I p = θ 2 θ 1 4 cos θ n s 2 sin 2 θ ( n s cos θ + 1 sin 2 θ n s 2 ) 2 2 cos θ d θ θ 2 θ 1 cos θ d θ .
i R L ( sin 1 n s λ Λ ± θ in )
i R L ( sin 1 n s 2 ( λ Λ ) 2 ± θ in ) ,
R > R min = S WGP 2 sin 1 λ Λ cos ϕ [ n s 2 ( λ Λ ) 2 sin 2 ϕ ] ,

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