Abstract

I explore the polarization characteristics of a wire-grid polarizer operating in a rotating platform using well-established rigorous coupled-wave analysis. The results show that the performance of a wire-grid polarizer evaluated in transmittance and extinction ratio is substantially degraded with rotation, although it is still more robust than that of a perfect polarizer. The performance may further deteriorate with inclined incidence due to an increased negative effect of a Rayleigh anomaly. Either a finer or a deeper grating reduces the adverse effect of rotation. Although implementation of such a grating is difficult, the rotation characteristics can be enhanced by means of pixelating the wire grids of various orientations and capturing the input images with a sufficiently high sampling rate.

© 2005 Optical Society of America

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2003 (1)

1999 (2)

G. P. Nordin, J. T. Meier, P. C. Deguzman, M. W. Jones, “Micropolarizer array for infrared imaging polarimetry,” J. Opt. Soc. Am. A 16, 1168–1174 (1999).
[CrossRef]

S. S. Helen, M. P. Kothiyal, R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).
[CrossRef]

1997 (4)

1996 (1)

1993 (1)

A. Straaijer, M. H. W. Verbruggen, J. M. M. de Nijs, H. H. Brongersma, “Novel fast spectroscopic rotating-polarizer ellipsometer,” Rev. Sci. Instrum. 64, 1468–1473 (1993).
[CrossRef]

1986 (1)

1982 (1)

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

1941 (1)

1907 (1)

J. W. S. Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag. 14, 60–65 (1907).
[CrossRef]

Arnold, S.

S. Arnold, E. Gardner, D. Hansen, R. Perkins, “An improved polarizing beamsplitter LCOS projection display based on wire-grid polarizers,” in SID 01 Digest (Society for Information Display, San Jose, Calif., 2001), pp. 1282–1285.
[CrossRef]

Ax, G. R.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization Measurement, Analysis, and Remote Sensing II,D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (2000).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987), Chap. 5, pp. 364–416.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987), Chap. 5, pp. 364–416.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), Sect. 10.8.

Bretenaker, F.

Brongersma, H. H.

A. Straaijer, M. H. W. Verbruggen, J. M. M. de Nijs, H. H. Brongersma, “Novel fast spectroscopic rotating-polarizer ellipsometer,” Rev. Sci. Instrum. 64, 1468–1473 (1993).
[CrossRef]

Chen, E.

E. Chen, 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]

Cheng, C.

Chou, H.

Chou, S. Y.

E. Chen, 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]

Clarke, D.

D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, Oxford, UK, 1971), pp. 22–25.

de Nijs, J. M. M.

A. Straaijer, M. H. W. Verbruggen, J. M. M. de Nijs, H. H. Brongersma, “Novel fast spectroscopic rotating-polarizer ellipsometer,” Rev. Sci. Instrum. 64, 1468–1473 (1993).
[CrossRef]

Deguzman, P. C.

Doumuki, T.

Emile, O.

Fainman, Y.

Floch, A. L.

Gardner, E.

S. Arnold, E. Gardner, D. Hansen, R. Perkins, “An improved polarizing beamsplitter LCOS projection display based on wire-grid polarizers,” in SID 01 Digest (Society for Information Display, San Jose, Calif., 2001), pp. 1282–1285.
[CrossRef]

Gaylord, T. K.

Grainger, J. F.

D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, Oxford, UK, 1971), pp. 22–25.

Hansen, D.

S. Arnold, E. Gardner, D. Hansen, R. Perkins, “An improved polarizing beamsplitter LCOS projection display based on wire-grid polarizers,” in SID 01 Digest (Society for Information Display, San Jose, Calif., 2001), pp. 1282–1285.
[CrossRef]

Helen, S. S.

S. S. Helen, M. P. Kothiyal, R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).
[CrossRef]

Howe, J. D.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization Measurement, Analysis, and Remote Sensing II,D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (2000).
[CrossRef]

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, San Diego, Calif., 1982), pp. 175–213.

Jones, M. W.

Jones, R. C.

Kim, D.

Können, G. P.

G. P. Können, Polarized Light in Nature (Cambridge U. Press, Cambridge, UK, 1985), pp. 162–163.

Kothiyal, M. P.

S. S. Helen, M. P. Kothiyal, R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).
[CrossRef]

Matsumoto, S.

Meier, J. T.

Miller, M. A.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization Measurement, Analysis, and Remote Sensing II,D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (2000).
[CrossRef]

Moharam, M. G.

Nordin, G. P.

Palik, E. D.

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

Perkins, R.

S. Arnold, E. Gardner, D. Hansen, R. Perkins, “An improved polarizing beamsplitter LCOS projection display based on wire-grid polarizers,” in SID 01 Digest (Society for Information Display, San Jose, Calif., 2001), pp. 1282–1285.
[CrossRef]

Petty, T. E.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization Measurement, Analysis, and Remote Sensing II,D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (2000).
[CrossRef]

Rayleigh, J. W. S.

J. W. S. Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag. 14, 60–65 (1907).
[CrossRef]

Rose, A. H.

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Salvekar, A.

Scherer, A.

Sirohi, R. S.

S. S. Helen, M. P. Kothiyal, R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).
[CrossRef]

Smith, M. H.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization Measurement, Analysis, and Remote Sensing II,D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (2000).
[CrossRef]

Sornsin, E. A.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization Measurement, Analysis, and Remote Sensing II,D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (2000).
[CrossRef]

Straaijer, A.

A. Straaijer, M. H. W. Verbruggen, J. M. M. de Nijs, H. H. Brongersma, “Novel fast spectroscopic rotating-polarizer ellipsometer,” Rev. Sci. Instrum. 64, 1468–1473 (1993).
[CrossRef]

Sun, P. C.

Tamada, H.

Tyan, R.

Vaccaro, K.

Verbruggen, M. H. W.

A. Straaijer, M. H. W. Verbruggen, J. M. M. de Nijs, H. H. Brongersma, “Novel fast spectroscopic rotating-polarizer ellipsometer,” Rev. Sci. Instrum. 64, 1468–1473 (1993).
[CrossRef]

Wang, C. M.

Warde, C.

Williams, P. A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), Sect. 10.8.

Woodruff, J. B.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization Measurement, Analysis, and Remote Sensing II,D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (2000).
[CrossRef]

Woods, C.

Xu, F.

Yamaguchi, T.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

E. Chen, 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]

J. Mod. Opt. (1)

S. S. Helen, M. P. Kothiyal, R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

Opt. Lett. (2)

Philos. Mag. (1)

J. W. S. Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag. 14, 60–65 (1907).
[CrossRef]

Rev. Sci. Instrum. (1)

A. Straaijer, M. H. W. Verbruggen, J. M. M. de Nijs, H. H. Brongersma, “Novel fast spectroscopic rotating-polarizer ellipsometer,” Rev. Sci. Instrum. 64, 1468–1473 (1993).
[CrossRef]

Sov. Phys. JETP (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Other (8)

M. C. Hutley, Diffraction Gratings (Academic, San Diego, Calif., 1982), pp. 175–213.

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

D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, Oxford, UK, 1971), pp. 22–25.

G. P. Können, Polarized Light in Nature (Cambridge U. Press, Cambridge, UK, 1985), pp. 162–163.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), Sect. 10.8.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987), Chap. 5, pp. 364–416.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization Measurement, Analysis, and Remote Sensing II,D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (2000).
[CrossRef]

S. Arnold, E. Gardner, D. Hansen, R. Perkins, “An improved polarizing beamsplitter LCOS projection display based on wire-grid polarizers,” in SID 01 Digest (Society for Information Display, San Jose, Calif., 2001), pp. 1282–1285.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Rotation angle ϕ is defined as the azimuthal angle of the incident wave vector ki projected onto the grating plane with respect to the grating vector kg. θin and θt are the angles of incidence and transmittance, respectively. Orientations of TM and TE polarization are also shown.

Fig. 2
Fig. 2

Cross section of a WGP explored in this paper. The grating on top of a silicon substrate is assumed to be made of gold with a grating depth d and a period Λ. Polar incidence angle θin is defined with respect to the normal to the grating surface.

Fig. 3
Fig. 3

(a) Transmittance and (b) extinction ratio of the WGP (d = 250 nm and Λ = 1.0 μm) of Fig. 2 at normal incidence (θin = 0°) as it is rotated azimuthally by an angle ϕ = 0°, 60°, and 90°.

Fig. 4
Fig. 4

(a) Transmittance and (b) extinction ratio of the WGP (d = 250 nm and Λ = 1.0 μm) of Fig. 2 at an incidence angle of θin = 14° corresponding to an f-number of 2 as it is rotated azimuthally by an angle ϕ = 0°, 30°, 60°, and 90°.

Fig. 5
Fig. 5

ER as a function of rotation angle ϕ for a perfect polarizer in a Jones calculus notation shown by the thin solid curve and ER for WGPs (d = 250 nm and Λ = 0.5, 1.0, or 1.5 μm) by the thick solid curves. For WGPs, both normal (θin = 0°) and inclined (θin = 14°) incidence are shown, although the differences are not readily distinguishable.

Tables (1)

Tables Icon

Table 1 Range of Rotation Angles with an ER > 10 for a Perfect Polarizer and a WGPa

Equations (9)

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k i 2 sin 2 θ t - 2 m k g k i sin θ t cos ϕ + m 2 k g 2 = k 0 2 sin 2 θ out , m ,
m = n s Λ λ ,
λ RA = n s Λ m [ sin θ t cos ϕ ± ( 1 - sin 2 θ t sin 2 ϕ ) 1 / 2 ] ,
d λ RA d ϕ = - n s Λ m sin θ t sin ψ [ 1 ± sin θ t cos ϕ ( 1 - sin 2 θ t sin 2 ϕ ) 1 / 2 ] .
λ a = n s Λ m cos θ t .
[ k 1 0 0 k 2 ] k 1 = 1 , k 2 = 0 .
ER = cos 2 ϕ + cos ϕ sin ϕ cos ϕ sin ϕ + sin 2 ϕ ,
Λ < 3 n s ( 1 + sin θ t ) ,
5 n s ( 1 - sin θ t ) < Λ < 6 n s ( 1 + sin θ t ) ,

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