Abstract

The transmission characteristics of wire grid polarizers fabricated in finite apertures are investigated by using a three-dimensional finite-difference time-domain formulation. Specifically, the optical transmissivity and extinction ratio are characterized for a wide variety of geometrical parameters including aperture size in both dimensions, conducting wire fill factor, and polarizer thickness. A dispersive material model is used to investigate the performance of polarizers fabricated by using realistic metals at infrared wavelengths. The results indicate that the aperture dimension significantly impacts the polarizer transmission behavior and that the extinction of the unwanted polarization is often limited by depolarizing scattering that is due to the finite aperture size.

© 2000 Optical Society of America

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    [CrossRef]
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    [CrossRef]

1999

1998

1997

1996

Z. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, R. M. Joseph, A. Taflove, C. W. Tu, S. T. Ho, “Nanofabrication of 1-D photonic bandgap structures along a photonic wire,” IEEE Photonics Technol. Lett. 8, 491–493 (1996).
[CrossRef]

H. Y. D. Yang, “Finite difference analysis of 2-D photonic crystal,” IEEE Trans. Microwave Theory Tech. 44, 2688–2695 (1996).
[CrossRef]

K. Hirayama, E. N. Glytsis, T. K. Gaylord, D. W. Wilson, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).
[CrossRef]

1995

1994

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guid. Wave Lett. 4, 268–270 (1994).
[CrossRef]

M. A. Jensen, Y. Rahmat-Samii, “Performance analysis of antennas for hand-held transceivers using FDTD,” IEEE Trans. Antennas Propag. 42, 1106–1113 (1994).
[CrossRef]

1993

H. Lochbihler, R. Depine, “Diffraction from highly conducting wire gratings of arbitrary cross-section,” J. Mod. Opt. 40, 1273–1298 (1993).
[CrossRef]

S. H. Kang, H. J. Eom, T. J. Park, “TM-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Microwave Theory Tech. 41, 895–899 (1993).
[CrossRef]

Y.-K. Kok, “General solution to the multiple-metallic-grooves scattering problem: the fast-polarization case,” Appl. Opt. 32, 2573–2581 (1993).
[CrossRef] [PubMed]

1986

1983

1966

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

1965

1960

Abraham, M.

B. Stenkamp, M. Abraham, W. Ehrfeld, E. Knapek, M. Hintermaier, M. T. Gale, R. Morf, “Grid polarizer for the visible spectral region,” in Nanofabrication Technologies and Device Integration, W. Karthe, Proc. SPIE2213, 288–296 (1994).
[CrossRef]

Barbour, B.

G. P. Nordin, J. T. Meier, P. Deguzman, B. Barbour, M. W. Jones, “Arrays of infrared micropolarizers,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 133–135.

Berenger, J.-P.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Bi, W. G.

Z. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, R. M. Joseph, A. Taflove, C. W. Tu, S. T. Ho, “Nanofabrication of 1-D photonic bandgap structures along a photonic wire,” IEEE Photonics Technol. Lett. 8, 491–493 (1996).
[CrossRef]

Bird, G. R.

Bjarklev, A.

Brady, D. J.

J. Guo, D. J. Brady, “Fabrication of high-resolution micropolarizer arrays,” Opt. Eng. 36, 2268–2271 (1997).
[CrossRef]

Bryngdahl, O.

Cahilhac, M.

Chen, E.

E. Chen, S. Y. Chou, “A novel device for detecting the polarization direction of linear polarized light using integrated subwavelength gratings and photodetectors,” IEEE Photonics Technol. Lett. 9, 1259–1261 (1997).
[CrossRef]

Chou, S. Y.

E. Chen, S. Y. Chou, “A novel device for detecting the polarization direction of linear polarized light using integrated subwavelength gratings and photodetectors,” IEEE Photonics Technol. Lett. 9, 1259–1261 (1997).
[CrossRef]

Chu, D. Y.

Z. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, R. M. Joseph, A. Taflove, C. W. Tu, S. T. Ho, “Nanofabrication of 1-D photonic bandgap structures along a photonic wire,” IEEE Photonics Technol. Lett. 8, 491–493 (1996).
[CrossRef]

Collins, J. P.

Deguzman, P.

G. P. Nordin, J. T. Meier, P. Deguzman, B. Barbour, M. W. Jones, “Arrays of infrared micropolarizers,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 133–135.

Deguzman, P. C.

Depine, R.

H. Lochbihler, R. Depine, “Diffraction from highly conducting wire gratings of arbitrary cross-section,” J. Mod. Opt. 40, 1273–1298 (1993).
[CrossRef]

Dridi, K. M.

Ehrfeld, W.

B. Stenkamp, M. Abraham, W. Ehrfeld, E. Knapek, M. Hintermaier, M. T. Gale, R. Morf, “Grid polarizer for the visible spectral region,” in Nanofabrication Technologies and Device Integration, W. Karthe, Proc. SPIE2213, 288–296 (1994).
[CrossRef]

Eom, H. J.

Y. S. Kim, H. J. Eom, J. W. Lee, K. Yoshitomi, “Scattering from multiple slits in a thick conducting plane,” Radio Sci. 30, 1341–1347 (1995).
[CrossRef]

S. H. Kang, H. J. Eom, T. J. Park, “TM-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Microwave Theory Tech. 41, 895–899 (1993).
[CrossRef]

Gale, M. T.

B. Stenkamp, M. Abraham, W. Ehrfeld, E. Knapek, M. Hintermaier, M. T. Gale, R. Morf, “Grid polarizer for the visible spectral region,” in Nanofabrication Technologies and Device Integration, W. Karthe, Proc. SPIE2213, 288–296 (1994).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Graham, H. A.

Grann, E. B.

Guo, J.

J. Guo, D. J. Brady, “Fabrication of high-resolution micropolarizer arrays,” Opt. Eng. 36, 2268–2271 (1997).
[CrossRef]

Harrigtan, M. E.

Hintermaier, M.

B. Stenkamp, M. Abraham, W. Ehrfeld, E. Knapek, M. Hintermaier, M. T. Gale, R. Morf, “Grid polarizer for the visible spectral region,” in Nanofabrication Technologies and Device Integration, W. Karthe, Proc. SPIE2213, 288–296 (1994).
[CrossRef]

Hirayama, K.

Ho, S. T.

Z. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, R. M. Joseph, A. Taflove, C. W. Tu, S. T. Ho, “Nanofabrication of 1-D photonic bandgap structures along a photonic wire,” IEEE Photonics Technol. Lett. 8, 491–493 (1996).
[CrossRef]

Jensen, M. A.

M. A. Jensen, Y. Rahmat-Samii, “Performance analysis of antennas for hand-held transceivers using FDTD,” IEEE Trans. Antennas Propag. 42, 1106–1113 (1994).
[CrossRef]

M. A. Jensen, G. P. Nordin, “Finite-aperture wire grid polarizers,” (Brigham Young University Microwave Earth Remote Sensing Laboratory, Provo, Utah, 1999) ( http://www.ee.byu.edu/ee/mers/MERS_reports.html ).

Jones, M. W.

G. P. Nordin, J. T. Meier, P. C. Deguzman, M. W. Jones, “Micropolarizer array for infrared imaging polarimetry,” J. Opt. Soc. Am. A 16, 1184–1193 (1999).
[CrossRef]

G. P. Nordin, J. T. Meier, P. Deguzman, B. Barbour, M. W. Jones, “Arrays of infrared micropolarizers,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 133–135.

Joseph, R. M.

Z. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, R. M. Joseph, A. Taflove, C. W. Tu, S. T. Ho, “Nanofabrication of 1-D photonic bandgap structures along a photonic wire,” IEEE Photonics Technol. Lett. 8, 491–493 (1996).
[CrossRef]

Judkins, J. B.

Kang, S. H.

S. H. Kang, H. J. Eom, T. J. Park, “TM-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Microwave Theory Tech. 41, 895–899 (1993).
[CrossRef]

Katz, D. S.

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guid. Wave Lett. 4, 268–270 (1994).
[CrossRef]

Kim, Y. S.

Y. S. Kim, H. J. Eom, J. W. Lee, K. Yoshitomi, “Scattering from multiple slits in a thick conducting plane,” Radio Sci. 30, 1341–1347 (1995).
[CrossRef]

Knapek, E.

B. Stenkamp, M. Abraham, W. Ehrfeld, E. Knapek, M. Hintermaier, M. T. Gale, R. Morf, “Grid polarizer for the visible spectral region,” in Nanofabrication Technologies and Device Integration, W. Karthe, Proc. SPIE2213, 288–296 (1994).
[CrossRef]

Kok, Y.-K.

Lee, J. W.

Y. S. Kim, H. J. Eom, J. W. Lee, K. Yoshitomi, “Scattering from multiple slits in a thick conducting plane,” Radio Sci. 30, 1341–1347 (1995).
[CrossRef]

Lochbihler, H.

H. Lochbihler, R. Depine, “Diffraction from highly conducting wire gratings of arbitrary cross-section,” J. Mod. Opt. 40, 1273–1298 (1993).
[CrossRef]

Mait, J. N.

Meier, J. T.

G. P. Nordin, J. T. Meier, P. C. Deguzman, M. W. Jones, “Micropolarizer array for infrared imaging polarimetry,” J. Opt. Soc. Am. A 16, 1184–1193 (1999).
[CrossRef]

G. P. Nordin, J. T. Meier, P. Deguzman, B. Barbour, M. W. Jones, “Arrays of infrared micropolarizers,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 133–135.

Mendez, O. M.

Mirotznik, M. S.

Moharam, M. G.

Morf, R.

B. Stenkamp, M. Abraham, W. Ehrfeld, E. Knapek, M. Hintermaier, M. T. Gale, R. Morf, “Grid polarizer for the visible spectral region,” in Nanofabrication Technologies and Device Integration, W. Karthe, Proc. SPIE2213, 288–296 (1994).
[CrossRef]

Nordin, G. P.

G. P. Nordin, J. T. Meier, P. C. Deguzman, M. W. Jones, “Micropolarizer array for infrared imaging polarimetry,” J. Opt. Soc. Am. A 16, 1184–1193 (1999).
[CrossRef]

G. P. Nordin, J. T. Meier, P. Deguzman, B. Barbour, M. W. Jones, “Arrays of infrared micropolarizers,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 133–135.

M. A. Jensen, G. P. Nordin, “Finite-aperture wire grid polarizers,” (Brigham Young University Microwave Earth Remote Sensing Laboratory, Provo, Utah, 1999) ( http://www.ee.byu.edu/ee/mers/MERS_reports.html ).

Park, T. J.

S. H. Kang, H. J. Eom, T. J. Park, “TM-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Microwave Theory Tech. 41, 895–899 (1993).
[CrossRef]

Parrish, M.

Peterson, E. W.

Petit, R.

Pommet, D. A.

Prata, A.

Prather, D. W.

Rahmat-Samii, Y.

M. A. Jensen, Y. Rahmat-Samii, “Performance analysis of antennas for hand-held transceivers using FDTD,” IEEE Trans. Antennas Propag. 42, 1106–1113 (1994).
[CrossRef]

Schmitz, M.

Stenkamp, B.

B. Stenkamp, M. Abraham, W. Ehrfeld, E. Knapek, M. Hintermaier, M. T. Gale, R. Morf, “Grid polarizer for the visible spectral region,” in Nanofabrication Technologies and Device Integration, W. Karthe, Proc. SPIE2213, 288–296 (1994).
[CrossRef]

Taflove, A.

Z. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, R. M. Joseph, A. Taflove, C. W. Tu, S. T. Ho, “Nanofabrication of 1-D photonic bandgap structures along a photonic wire,” IEEE Photonics Technol. Lett. 8, 491–493 (1996).
[CrossRef]

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guid. Wave Lett. 4, 268–270 (1994).
[CrossRef]

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 1995).

Thiele, E. T.

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guid. Wave Lett. 4, 268–270 (1994).
[CrossRef]

Tiberio, R. C.

Z. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, R. M. Joseph, A. Taflove, C. W. Tu, S. T. Ho, “Nanofabrication of 1-D photonic bandgap structures along a photonic wire,” IEEE Photonics Technol. Lett. 8, 491–493 (1996).
[CrossRef]

Tu, C. W.

Z. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, R. M. Joseph, A. Taflove, C. W. Tu, S. T. Ho, “Nanofabrication of 1-D photonic bandgap structures along a photonic wire,” IEEE Photonics Technol. Lett. 8, 491–493 (1996).
[CrossRef]

Wang, A.

Wilson, D. W.

Wu, S. L.

Z. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, R. M. Joseph, A. Taflove, C. W. Tu, S. T. Ho, “Nanofabrication of 1-D photonic bandgap structures along a photonic wire,” IEEE Photonics Technol. Lett. 8, 491–493 (1996).
[CrossRef]

Yang, H. Y. D.

H. Y. D. Yang, “Finite difference analysis of 2-D photonic crystal,” IEEE Trans. Microwave Theory Tech. 44, 2688–2695 (1996).
[CrossRef]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

Yoshitomi, K.

Y. S. Kim, H. J. Eom, J. W. Lee, K. Yoshitomi, “Scattering from multiple slits in a thick conducting plane,” Radio Sci. 30, 1341–1347 (1995).
[CrossRef]

Young, J. B.

Zhang, Z. P.

Z. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, R. M. Joseph, A. Taflove, C. W. Tu, S. T. Ho, “Nanofabrication of 1-D photonic bandgap structures along a photonic wire,” IEEE Photonics Technol. Lett. 8, 491–493 (1996).
[CrossRef]

Ziolkowski, R. W.

Appl. Opt.

IEEE Microwave Guid. Wave Lett.

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guid. Wave Lett. 4, 268–270 (1994).
[CrossRef]

IEEE Photonics Technol. Lett.

Z. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, R. M. Joseph, A. Taflove, C. W. Tu, S. T. Ho, “Nanofabrication of 1-D photonic bandgap structures along a photonic wire,” IEEE Photonics Technol. Lett. 8, 491–493 (1996).
[CrossRef]

E. Chen, S. Y. Chou, “A novel device for detecting the polarization direction of linear polarized light using integrated subwavelength gratings and photodetectors,” IEEE Photonics Technol. Lett. 9, 1259–1261 (1997).
[CrossRef]

IEEE Trans. Antennas Propag.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

M. A. Jensen, Y. Rahmat-Samii, “Performance analysis of antennas for hand-held transceivers using FDTD,” IEEE Trans. Antennas Propag. 42, 1106–1113 (1994).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

H. Y. D. Yang, “Finite difference analysis of 2-D photonic crystal,” IEEE Trans. Microwave Theory Tech. 44, 2688–2695 (1996).
[CrossRef]

S. H. Kang, H. J. Eom, T. J. Park, “TM-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Microwave Theory Tech. 41, 895–899 (1993).
[CrossRef]

J. Comput. Phys.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

J. Mod. Opt.

H. Lochbihler, R. Depine, “Diffraction from highly conducting wire gratings of arbitrary cross-section,” J. Mod. Opt. 40, 1273–1298 (1993).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

K. Hirayama, E. N. Glytsis, T. K. Gaylord, D. W. Wilson, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).
[CrossRef]

M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
[CrossRef]

A. Wang, A. Prata, “Lenslet analysis by rigorous vector diffraction theory,” J. Opt. Soc. Am. A 12, 1161–1169 (1995).
[CrossRef]

J. B. Judkins, R. W. Ziolkowski, “Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings,” J. Opt. Soc. Am. A 12, 1974–1983 (1995).
[CrossRef]

G. P. Nordin, J. T. Meier, P. C. Deguzman, M. W. Jones, “Micropolarizer array for infrared imaging polarimetry,” J. Opt. Soc. Am. A 16, 1184–1193 (1999).
[CrossRef]

D. W. Prather, J. N. Mait, M. S. Mirotznik, J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A 15, 1599–1607 (1998).
[CrossRef]

D. W. Prather, M. S. Mirotznik, J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34–43 (1997).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Geometry for a plane wave incident on the finite-aperture wire grid polarizer.

Fig. 2
Fig. 2

Computational geometry for FDTD simulation of the finite-aperture wire grid polarizer.

Fig. 3
Fig. 3

(a) Transmissivity and (b) extinction ratio as a function of aperture side length for a square aperture for several values of fill factor (D=0.05λ, Lx=Ly).

Fig. 4
Fig. 4

Spatial map of the x-polarized transmitted field for a y-polarized incident plane wave on the square aperture of dimensions Lx=Ly=1.45λ and with 75% fill factor.

Fig. 5
Fig. 5

(a) Transmissivity and (b) extinction ratio as a function of aperture side length Ly for a rectangular aperture for several values of fill factor (D=0.05λ).

Fig. 6
Fig. 6

(a) Transmissivity and (b) extinction ratio as a function of aperture side length Lx for a rectangular aperture for several values of fill factor (D=0.05λ).

Fig. 7
Fig. 7

x-polarized transmitted field strength for y-polarized illumination with 75% fill factor and Ly=3.85λ (D=0.05λ): (a) Lx=1.05λ, (b) Lx=3.85λ.

Fig. 8
Fig. 8

(a) Transmissivity and (b) extinction ratio as a function of aperture side length Lx for an infinitely long aperture (Ly) for several values of fill factor (D=0.05λ). These results are obtained by using the mode-matching solution technique.

Fig. 9
Fig. 9

(a) Transmissivity and (b) extinction ratio as a function of aperture side length for a square aperture for several values of thickness (50% fill factor).

Fig. 10
Fig. 10

Extinction ratio as a function of aperture side length for several values of thickness: (a) square aperture with 25% fill factor and (b) 2-D aperture (Ly) with 50% fill factor.

Fig. 11
Fig. 11

(a) Transmissivity and (b) extinction ratio as a function of aperture side length for a square aperture for several values of fill factor (D=0.05λ) when the metal parameters are those of molybdenum.

Fig. 12
Fig. 12

(a) Transmissivity and (b) extinction ratio as a function of aperture side length for a square aperture for several values of thickness (50% fill factor) when the metal parameters are those of molybdenum.

Fig. 13
Fig. 13

(a) Transmissivity and (b) extinction ratio as a function of aperture side length for a square aperture for several different types of metal (50% fill factor, D=0.05λ).

Tables (1)

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Table 1 Refractive-Index and Relative Permittivity Values for Different Metalsat λ=4 µm

Equations (4)

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PT=12ReAE×H*·zˆdxdy,
T=2η0APT|Ei|2,
fillfactor=w/Δx,
extinctionratio=Tx/Ty,

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