Abstract

We investigate the transmission characteristics of perfectly conducting two-dimensional wire grid polarizers fabricated in finite and infinite apertures using a rigorous spectral-domain mode-matching method. Specifically, the transmission coefficient for both transverse-electric and transverse-magnetic polarizations, extinction ratio, and diffraction pattern are characterized for a wide variety of geometric and material parameters including aperture dimension, conducting wire fill factor, wire spacing, polarizer thickness, material dielectric constants, and incident wave arrival angle. The results indicate that the transmission behavior is largely insensitive to aperture dimension.

© 2001 Optical Society of America

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  1. G. R. Bird, M. Parrish, “The wire grid as a near-infrared polarizer,” J. Opt. Soc. Am. 50, 886–891 (1960).
    [CrossRef]
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    [CrossRef]
  3. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3, 1780–1787 (1986).
    [CrossRef]
  4. 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]
  5. E. Chen, S. Y. Chou, “A novel device for detecting the polarization direction of linear polarized light using integrated subwavelength gratings and photodetectors,” IEEE Photon. Technol. Lett. 9, 1259–1261 (1997).
    [CrossRef]
  6. J. Guo, D. J. Brady, “Fabrication of high-resolution micropolarizer arrays,” Opt. Eng. 36, 2268–2271 (1997).
    [CrossRef]
  7. 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]
  8. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Tarrytown, N.Y., 1975).
  9. K. Hirayama, E. N. Glytsis, T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).
    [CrossRef]
  10. 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]
  11. 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]
  12. A. Wang, A. Prata, “Lenslet analysis by rigorous vector diffraction theory,” J. Opt. Soc. Am. A 12, 1161–1169 (1995).
    [CrossRef]
  13. M. Schmitz, O. Bryngdahl, “Rigorous concept for the design of diffractive microlenses with high numerical apertures,” J. Opt. Soc. Am. A 14, 901–906 (1997).
    [CrossRef]
  14. M. A. Jensen, G. P. Nordin, “Finite-aperture wire grid polarizers,” J. Opt. Soc. Am. A 17, 2191–2198 (2000).
    [CrossRef]
  15. 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]
  16. O. M. Mendez, M. Cahilhac, R. Petit, “Diffraction of a two-dimensional electromagnetic beam wave by a thick slit pierced in a perfectly conducting screen,” J. Opt. Soc. Am. 73, 328–331 (1983).
    [CrossRef]
  17. 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]
  18. T. J. Park, S. H. Kang, H. J. Eom, “TE-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Antennas Propag. 42, 112–114 (1994).
    [CrossRef]
  19. Y.-K. Kok, “General solution to the multiple-metallic-grooves scattering problem: the fast-polarization case,” Appl. Opt. 32, 2573–2581 (1993).
    [CrossRef] [PubMed]
  20. 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, ed., Proc. SPIE2213, 288–296 (1994).
    [CrossRef]
  21. H. Lochbihler, R. Depine, “Diffraction from highly conducting wire gratings of arbitrary cross-section,” J. Mod. Opt. 40, 1273–1298 (1993).
    [CrossRef]

2000

1999

1998

1997

1995

1994

T. J. Park, S. H. Kang, H. J. Eom, “TE-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Antennas Propag. 42, 112–114 (1994).
[CrossRef]

1993

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

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]

1986

1983

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, ed., Proc. SPIE2213, 288–296 (1994).
[CrossRef]

Bird, G. R.

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Tarrytown, N.Y., 1975).

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 Photon. 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 Photon. Technol. Lett. 9, 1259–1261 (1997).
[CrossRef]

Collins, J. P.

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]

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, ed., 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]

T. J. Park, S. H. Kang, H. J. Eom, “TE-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Antennas Propag. 42, 112–114 (1994).
[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, ed., 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]

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, ed., Proc. SPIE2213, 288–296 (1994).
[CrossRef]

Hirayama, K.

Jensen, M. A.

Jones, M. W.

Kang, S. H.

T. J. Park, S. H. Kang, H. J. Eom, “TE-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Antennas Propag. 42, 112–114 (1994).
[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]

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, ed., 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.

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, ed., Proc. SPIE2213, 288–296 (1994).
[CrossRef]

Nordin, G. P.

Park, T. J.

T. J. Park, S. H. Kang, H. J. Eom, “TE-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Antennas Propag. 42, 112–114 (1994).
[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]

Parrish, M.

Peterson, E. W.

Petit, R.

Pommet, D. A.

Prata, A.

Prather, D. W.

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, ed., Proc. SPIE2213, 288–296 (1994).
[CrossRef]

Wang, A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Tarrytown, N.Y., 1975).

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.

Appl. Opt.

IEEE Photon. Technol. Lett.

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

IEEE Trans. Antennas Propag.

T. J. Park, S. H. Kang, H. J. Eom, “TE-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Antennas Propag. 42, 112–114 (1994).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

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. 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

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]

M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3, 1780–1787 (1986).
[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]

K. Hirayama, E. N. Glytsis, T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).
[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]

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]

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

M. Schmitz, O. Bryngdahl, “Rigorous concept for the design of diffractive microlenses with high numerical apertures,” J. Opt. Soc. Am. A 14, 901–906 (1997).
[CrossRef]

M. A. Jensen, G. P. Nordin, “Finite-aperture wire grid polarizers,” J. Opt. Soc. Am. A 17, 2191–2198 (2000).
[CrossRef]

Opt. Eng.

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

Radio Sci.

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]

Other

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Tarrytown, N.Y., 1975).

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, ed., Proc. SPIE2213, 288–296 (1994).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

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

Fig. 2
Fig. 2

(a) Transmission coefficient and (b) extinction ratio as a function of aperture size for several values of fill factor (D = 0, 5 slits/λ, M = 5).

Fig. 3
Fig. 3

Transmission coefficient as a function of aperture size for several values of polarizer thickness (fill factor is 0.4, 5 slits/λ, M = 5).

Fig. 4
Fig. 4

Transmitted diffraction pattern for a polarizer with three different aperture sizes (D = 0, 5 slits/λ, fill factor is 0.4, M = 5).

Fig. 5
Fig. 5

(a) Transmission coefficient and (b) extinction ratio as a function of slit density and fill factor (D = 0, aperture size is 2λ, M = 10).

Fig. 6
Fig. 6

(a) Transmission coefficient and (b) extinction ratio as a function of fill factor and polarizer thickness (aperture size is infinite, 5 slits/λ, M = 5).

Fig. 7
Fig. 7

Transmitted diffraction pattern for a polarizer with three different values of thickness (aperture size is 2λ, 5 slits/λ, fill factor is 0.4, M = 5).

Fig. 8
Fig. 8

(a) Transmission coefficient and (b) extinction ratio as a function of relative permittivity of region 1 for several values of relative permittivity of regions 2 and 3 (D = 0.1λ, fill factor is 0.4, aperture size is 2λ, 5 slits/λ, M = 5).

Fig. 9
Fig. 9

Transmitted diffraction pattern for a polarizer with different material permittivities (D = 0.2λ, aperture size is 2λ, 5 slits/λ, fill factor is 0.4, M = 5).

Fig. 10
Fig. 10

(a) Normalized transmission coefficient and (b) extinction ratio as a function of plane-wave incidence angle for several aperture sizes (D = 0.1λ, fill factor is 0.4, 5 slits/λ, M = 5).

Fig. 11
Fig. 11

Transmitted diffraction pattern for a polarizer with three different plane-wave incidence angles (D = 0, aperture size is 2λ, 5 slits/λ, fill factor is 0.4, M = 5).

Equations (24)

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

Eyix, z=expikxx-ikzz-d,
Eyrx, z=-expikxx+ikzz-d,
Eysx, z=12π- E˜ysξexp-iξx+ik12-ξ21/2×z-ddξ,
E˜ysξ=- Eysx, dexpiξxdx,
Eytx, z=12π- E˜ytξ×exp-iξx-ik32-ξ21/2z+ddξ,
E˜ytξ=- Eytx, -dexpiξxdx.
Eynx, z=m=1bmn cos ζmz+cmn sin ζmz× sinamx-xn+a,
G1,2m, ξ=-1m expiξa-exp±iξaξ2-am2,
E˜ys,tξ=n=1Nm=1bmn cos ζmd±cmn sin ζmdamG2m, ξexpiξxn,
Ψ1BΨ1CΨ3B-Ψ3CBC=Γ0,
ΨlB,rs=ζpa μlμ2sinζpdδrs+iamap2πcos ζmdIpmqnkl,
ΨlC,rs=-ζpa μlμ2cosζpdδrs+iamap2πsinζmdIpmqnkl,
Γr=2kzapG2p, kxexpikxxq,
Ipmqnkl=- G1p, ξG2m, ξkl2-ξ21/2×expiξxn-xqdξ.
Eys,tθs,t=k1,3i2πrs,t1/2 cos θs,tn=1Nm=1M ambmn cos ζmd±cmn sin ζmdG1m, ks,texpik1,3rs,t-ks,txn,
T=1Nk1 cos θaΔxμ1μ2n=1Nm=1MImζm*bmn cos ζmd-cmn sin ζmdbmn sin ζmd+cmn cos ζmd*.
Eys,tx, z=q=- γqs,t exp-iξqx±ik1,32-ξq21/2×zd,
γqs,t=1Δx-Δx/2Δx/2 Eys,tx, ±dexpiξqxdx,
γqs,t=1Δxm=1bm cos ζmd±cm sin ζmdamG2m, ξq,
ΨlB,pm=ζpa μlμ2sinζpdδpm+iamapΔx×cosζmdFpmkl,
ΨlC,pm=-ζpa μlμ2cosζpdδpm+iamapΔxsinζmdFpmkl,
Fpmkl=q=- G1p, ξqG2m, ξqkl2-ξq21/2.
Gtθt=10 logη3|Hytθt|2/2Pi/πrt, =10 logη3η1|Hytθt|2|Hi|2πrtNΔx cos θ,
TF=1-r1/r2-1r1/r2+12,

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