Abstract

A review and analysis is performed of various resonance effects associated with subwavelength one-dimensional (1-D) metal gratings for transverse electric (TE) and transverse magnetic (TM) polarized incident radiation. It is shown that by tuning the structural geometry (especially the groove width) and material composition of the 1-D gratings, polarization independent enhanced optical transmission (EOT) can be achieved. Three different cases of EOT have been studied for 1-D metal gratings: a) EOT for TM-polarized incident radiation b) EOT for TE-polarized incident radiation, and most importantly c) EOT for un-polarized incident light. Potential uses of these results in the design and improvement of various optoelectronic devices, such as polarizers, photodetectors and wavelength filters are discussed.

© 2007 Optical Society of America

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References

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  1. F. J. Garcia-Vidal and L. Martin-Moreno, " Transmission and focusing of light in one-dimensional periodically nanostrucutred metals," Phys. Rev. B 66, 155412(1) -1554121(0) (2002)
    [CrossRef]
  2. E. Popov and L. Tsonev, "Electromagnetic field enhancement in deep metallic gratings," Opt. Commun. 69, 193-198 (1989).
    [CrossRef]
  3. R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phil. Mag. 4, 396-408 (1902).
  4. A. Hessel and A. A. Oliner, "A new theory of Wood’s anomalies on optical gratings," Appl. Opt. 4, 1275-1297 (1965).
    [CrossRef]
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    [CrossRef]
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  7. U. Schroeter, D. Heitmann " Surface plasmons enhanced transmission thorough metallic gratings," Phys. Rev. B 58, 15419-15421 (1998)
    [CrossRef]
  8. A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phy. Rev. B 66, 161403(1)- 161403(4_ (2002).
    [CrossRef]
  9. J. A. Porto, F. J. Garcia-Vidal, J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999)
    [CrossRef]
  10. Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403(1) - 057403(4) (2002).
    [CrossRef]
  11. M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105-195116 (2002)
    [CrossRef]
  12. A. G Borisov, F. J. Garcia de Abajo, S. V. Shabanov, "Role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials," Phys. Rev. B 71, 075408(1) - 075408(7) (2005).
    [CrossRef]
  13. D. Crouse and P. Keshavareddy, "Role of optical and surface plasmon modes in enhanced transmission and applications," Opt. Express 20, 7760-7771 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-20-7760
    [CrossRef]
  14. D. Crouse, "Numerical Modeling and Electromagnetic Resonant Modes in Complex Grating Structures and Optoelectronic Device Applications," IEEE Trans. Electron Devices 52, 2365-2373 (2005).
    [CrossRef]
  15. D. Crouse, M. Arend, J. Zou, and P. Keshavareddy, "Numerical modeling of electromagnetic resonance enhanced silicon metal-semiconductor-metal photodetectors," Opt. Express 14, 2047-2061 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-6-2047
    [CrossRef] [PubMed]
  16. D. Crouse and R. Solomon, "Numerical modeling of surface plasmon enhanced silicon on insulator avalanche photodiodes," Solid-State Electronics 49, 1697-1701 (2005).
    [CrossRef]
  17. D. Crouse and P. Keshavareddy, "Electromagnetic Resonance Enhanced Silicon-on-Insulator Metal-Semiconductor-Metal Photodetectors," J. Opt. A: Pure Appl. Opt. 8, 175-181 (2006).
    [CrossRef]
  18. Stephane Collin,Fabrice Pardo, and Jean-Luc Pelouard, "Resonant-cavity-enhanced subwavelength metal-semiconductor-metal photodetector," Appl. Phys. Lett. 83, 1521-1523 (2003).
    [CrossRef]
  19. Stéphane Collin,Fabrice Pardo,Roland Teissier,and Jean-Luc Pelouard, " Efficient light absorption in metal-semiconductor-metal nanostructures," Appl. Phys. Lett. 85, 194-196 (2004).
    [CrossRef]
  20. Lochbihler, H.  and R. Depine, "Highly conducting wire gratings in the resonance region," Appl. Opt. 32, 3459-3465 (1993).
    [CrossRef] [PubMed]
  21. E. Popov, L. Tsonev, "Resonant electric field enhancement in vicinity of a bare metallic grating exposed to s-polarize light," Surf. Science. Lett. 271, L378-L382 (1992).
    [CrossRef]
  22. David R. Lide, Handbook of Chemistry and Physics (CRC Press, London, 1992-1993).
  23. H. Ichikawa, "Electromagnetic analysis of diffraction gratings by the finite-difference time-domain method," J. Opt. Soc. Amer. A 15, 152-157 (1998)
    [CrossRef]
  24. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous couple-wave analysis for surface relief gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077-1086 (1995)
    [CrossRef]
  25. H. Tamada, T. Doumuki, T. Yamaguchi, and S. Matsumoto, "Al wire -grid polarizer using the s-polarization resonance effect at the 0.8μm wavelength band," Opt. Lett. 22, 419-421 (1997).
    [CrossRef] [PubMed]
  26. D. Kim, "Polarization characteristics of a wire-grid polarizer in a rotating platform," Appl. Opt. 44, 1366-1371 (2005).
    [CrossRef] [PubMed]
  27. S. S. Wang, R. Magnusson, "Theory and applications of guided-mode resonance filters," Appl. Opt. 32, 2606-2613 (1993)
    [CrossRef] [PubMed]
  28. G. Niederer, W. Nakagawa, H. P. Herzig, H. Thiele, "Design and characterization of a tunable polarization-independent resonant grating filter, " Opt. Express 13, 2196-2200 (2005).
    [CrossRef] [PubMed]
  29. G. Tayeb and R. Petit, "On the numerical study of deep conducting lamellar diffraction gratings," Optica Acta 31, 1361-1365 (1984).
    [CrossRef]

2006 (2)

2005 (6)

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

G. Niederer, W. Nakagawa, H. P. Herzig, H. Thiele, "Design and characterization of a tunable polarization-independent resonant grating filter, " Opt. Express 13, 2196-2200 (2005).
[CrossRef] [PubMed]

D. Crouse and R. Solomon, "Numerical modeling of surface plasmon enhanced silicon on insulator avalanche photodiodes," Solid-State Electronics 49, 1697-1701 (2005).
[CrossRef]

A. G Borisov, F. J. Garcia de Abajo, S. V. Shabanov, "Role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials," Phys. Rev. B 71, 075408(1) - 075408(7) (2005).
[CrossRef]

D. Crouse and P. Keshavareddy, "Role of optical and surface plasmon modes in enhanced transmission and applications," Opt. Express 20, 7760-7771 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-20-7760
[CrossRef]

D. Crouse, "Numerical Modeling and Electromagnetic Resonant Modes in Complex Grating Structures and Optoelectronic Device Applications," IEEE Trans. Electron Devices 52, 2365-2373 (2005).
[CrossRef]

2004 (1)

Stéphane Collin,Fabrice Pardo,Roland Teissier,and Jean-Luc Pelouard, " Efficient light absorption in metal-semiconductor-metal nanostructures," Appl. Phys. Lett. 85, 194-196 (2004).
[CrossRef]

2003 (1)

Stephane Collin,Fabrice Pardo, and Jean-Luc Pelouard, "Resonant-cavity-enhanced subwavelength metal-semiconductor-metal photodetector," Appl. Phys. Lett. 83, 1521-1523 (2003).
[CrossRef]

2002 (4)

F. J. Garcia-Vidal and L. Martin-Moreno, " Transmission and focusing of light in one-dimensional periodically nanostrucutred metals," Phys. Rev. B 66, 155412(1) -1554121(0) (2002)
[CrossRef]

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phy. Rev. B 66, 161403(1)- 161403(4_ (2002).
[CrossRef]

Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403(1) - 057403(4) (2002).
[CrossRef]

M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105-195116 (2002)
[CrossRef]

1999 (1)

J. A. Porto, F. J. Garcia-Vidal, J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999)
[CrossRef]

1998 (2)

U. Schroeter, D. Heitmann " Surface plasmons enhanced transmission thorough metallic gratings," Phys. Rev. B 58, 15419-15421 (1998)
[CrossRef]

H. Ichikawa, "Electromagnetic analysis of diffraction gratings by the finite-difference time-domain method," J. Opt. Soc. Amer. A 15, 152-157 (1998)
[CrossRef]

1997 (1)

1995 (1)

1993 (2)

1992 (1)

E. Popov, L. Tsonev, "Resonant electric field enhancement in vicinity of a bare metallic grating exposed to s-polarize light," Surf. Science. Lett. 271, L378-L382 (1992).
[CrossRef]

1989 (1)

E. Popov and L. Tsonev, "Electromagnetic field enhancement in deep metallic gratings," Opt. Commun. 69, 193-198 (1989).
[CrossRef]

1984 (1)

G. Tayeb and R. Petit, "On the numerical study of deep conducting lamellar diffraction gratings," Optica Acta 31, 1361-1365 (1984).
[CrossRef]

1965 (1)

1941 (1)

1902 (1)

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phil. Mag. 4, 396-408 (1902).

Arend, M.

Barbara, A.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phy. Rev. B 66, 161403(1)- 161403(4_ (2002).
[CrossRef]

Borisov, A. G

A. G Borisov, F. J. Garcia de Abajo, S. V. Shabanov, "Role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials," Phys. Rev. B 71, 075408(1) - 075408(7) (2005).
[CrossRef]

Bustarret, E.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phy. Rev. B 66, 161403(1)- 161403(4_ (2002).
[CrossRef]

Cao, Q.

Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403(1) - 057403(4) (2002).
[CrossRef]

Crouse, D.

D. Crouse and P. Keshavareddy, "Electromagnetic Resonance Enhanced Silicon-on-Insulator Metal-Semiconductor-Metal Photodetectors," J. Opt. A: Pure Appl. Opt. 8, 175-181 (2006).
[CrossRef]

D. Crouse, M. Arend, J. Zou, and P. Keshavareddy, "Numerical modeling of electromagnetic resonance enhanced silicon metal-semiconductor-metal photodetectors," Opt. Express 14, 2047-2061 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-6-2047
[CrossRef] [PubMed]

D. Crouse and R. Solomon, "Numerical modeling of surface plasmon enhanced silicon on insulator avalanche photodiodes," Solid-State Electronics 49, 1697-1701 (2005).
[CrossRef]

D. Crouse, "Numerical Modeling and Electromagnetic Resonant Modes in Complex Grating Structures and Optoelectronic Device Applications," IEEE Trans. Electron Devices 52, 2365-2373 (2005).
[CrossRef]

D. Crouse and P. Keshavareddy, "Role of optical and surface plasmon modes in enhanced transmission and applications," Opt. Express 20, 7760-7771 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-20-7760
[CrossRef]

Depine, R.

Doumuki, T.

Fano, U.

Garcia de Abajo, F. J.

A. G Borisov, F. J. Garcia de Abajo, S. V. Shabanov, "Role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials," Phys. Rev. B 71, 075408(1) - 075408(7) (2005).
[CrossRef]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal and L. Martin-Moreno, " Transmission and focusing of light in one-dimensional periodically nanostrucutred metals," Phys. Rev. B 66, 155412(1) -1554121(0) (2002)
[CrossRef]

J. A. Porto, F. J. Garcia-Vidal, J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999)
[CrossRef]

Gaylord, T. K.

Grann, E. B.

Heitmann, D.

U. Schroeter, D. Heitmann " Surface plasmons enhanced transmission thorough metallic gratings," Phys. Rev. B 58, 15419-15421 (1998)
[CrossRef]

Herzig, H. P.

Hessel, A.

Ichikawa, H.

H. Ichikawa, "Electromagnetic analysis of diffraction gratings by the finite-difference time-domain method," J. Opt. Soc. Amer. A 15, 152-157 (1998)
[CrossRef]

Keshavareddy, P.

D. Crouse, M. Arend, J. Zou, and P. Keshavareddy, "Numerical modeling of electromagnetic resonance enhanced silicon metal-semiconductor-metal photodetectors," Opt. Express 14, 2047-2061 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-6-2047
[CrossRef] [PubMed]

D. Crouse and P. Keshavareddy, "Electromagnetic Resonance Enhanced Silicon-on-Insulator Metal-Semiconductor-Metal Photodetectors," J. Opt. A: Pure Appl. Opt. 8, 175-181 (2006).
[CrossRef]

D. Crouse and P. Keshavareddy, "Role of optical and surface plasmon modes in enhanced transmission and applications," Opt. Express 20, 7760-7771 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-20-7760
[CrossRef]

Kim, D.

Lalanne, P.

Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403(1) - 057403(4) (2002).
[CrossRef]

Lochbihler,

Lopez-Rios, T.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phy. Rev. B 66, 161403(1)- 161403(4_ (2002).
[CrossRef]

Magnusson, R.

Martin-Moreno, L.

F. J. Garcia-Vidal and L. Martin-Moreno, " Transmission and focusing of light in one-dimensional periodically nanostrucutred metals," Phys. Rev. B 66, 155412(1) -1554121(0) (2002)
[CrossRef]

Matsumoto, S.

Moharam, M. G.

Nakagawa, W.

Niederer, G.

Oliner, A. A.

Pendry, J. B.

J. A. Porto, F. J. Garcia-Vidal, J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999)
[CrossRef]

Petit, R.

G. Tayeb and R. Petit, "On the numerical study of deep conducting lamellar diffraction gratings," Optica Acta 31, 1361-1365 (1984).
[CrossRef]

Pommet, D. A.

Popov, E.

E. Popov, L. Tsonev, "Resonant electric field enhancement in vicinity of a bare metallic grating exposed to s-polarize light," Surf. Science. Lett. 271, L378-L382 (1992).
[CrossRef]

E. Popov and L. Tsonev, "Electromagnetic field enhancement in deep metallic gratings," Opt. Commun. 69, 193-198 (1989).
[CrossRef]

Porto, J. A.

J. A. Porto, F. J. Garcia-Vidal, J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999)
[CrossRef]

Quemerais, P.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phy. Rev. B 66, 161403(1)- 161403(4_ (2002).
[CrossRef]

Schroeter, U.

U. Schroeter, D. Heitmann " Surface plasmons enhanced transmission thorough metallic gratings," Phys. Rev. B 58, 15419-15421 (1998)
[CrossRef]

Shabanov, S. V.

A. G Borisov, F. J. Garcia de Abajo, S. V. Shabanov, "Role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials," Phys. Rev. B 71, 075408(1) - 075408(7) (2005).
[CrossRef]

Solomon, R.

D. Crouse and R. Solomon, "Numerical modeling of surface plasmon enhanced silicon on insulator avalanche photodiodes," Solid-State Electronics 49, 1697-1701 (2005).
[CrossRef]

Tamada, H.

Tayeb, G.

G. Tayeb and R. Petit, "On the numerical study of deep conducting lamellar diffraction gratings," Optica Acta 31, 1361-1365 (1984).
[CrossRef]

Thiele, H.

Treacy,

M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105-195116 (2002)
[CrossRef]

Tsonev, L.

E. Popov, L. Tsonev, "Resonant electric field enhancement in vicinity of a bare metallic grating exposed to s-polarize light," Surf. Science. Lett. 271, L378-L382 (1992).
[CrossRef]

E. Popov and L. Tsonev, "Electromagnetic field enhancement in deep metallic gratings," Opt. Commun. 69, 193-198 (1989).
[CrossRef]

Wang, S. S.

Wood, R. W.

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phil. Mag. 4, 396-408 (1902).

Yamaguchi, T.

Zou, J.

Appl. Opt. (4)

Appl. Phys. Lett. (2)

Stephane Collin,Fabrice Pardo, and Jean-Luc Pelouard, "Resonant-cavity-enhanced subwavelength metal-semiconductor-metal photodetector," Appl. Phys. Lett. 83, 1521-1523 (2003).
[CrossRef]

Stéphane Collin,Fabrice Pardo,Roland Teissier,and Jean-Luc Pelouard, " Efficient light absorption in metal-semiconductor-metal nanostructures," Appl. Phys. Lett. 85, 194-196 (2004).
[CrossRef]

IEEE Trans. Electron Devices (1)

D. Crouse, "Numerical Modeling and Electromagnetic Resonant Modes in Complex Grating Structures and Optoelectronic Device Applications," IEEE Trans. Electron Devices 52, 2365-2373 (2005).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

D. Crouse and P. Keshavareddy, "Electromagnetic Resonance Enhanced Silicon-on-Insulator Metal-Semiconductor-Metal Photodetectors," J. Opt. A: Pure Appl. Opt. 8, 175-181 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

H. Ichikawa, "Electromagnetic analysis of diffraction gratings by the finite-difference time-domain method," J. Opt. Soc. Amer. A 15, 152-157 (1998)
[CrossRef]

Opt. Commun. (1)

E. Popov and L. Tsonev, "Electromagnetic field enhancement in deep metallic gratings," Opt. Commun. 69, 193-198 (1989).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Optica Acta (1)

G. Tayeb and R. Petit, "On the numerical study of deep conducting lamellar diffraction gratings," Optica Acta 31, 1361-1365 (1984).
[CrossRef]

Phil. Mag. (1)

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phil. Mag. 4, 396-408 (1902).

Phy. Rev. B (1)

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phy. Rev. B 66, 161403(1)- 161403(4_ (2002).
[CrossRef]

Phys. Rev. B (4)

U. Schroeter, D. Heitmann " Surface plasmons enhanced transmission thorough metallic gratings," Phys. Rev. B 58, 15419-15421 (1998)
[CrossRef]

F. J. Garcia-Vidal and L. Martin-Moreno, " Transmission and focusing of light in one-dimensional periodically nanostrucutred metals," Phys. Rev. B 66, 155412(1) -1554121(0) (2002)
[CrossRef]

M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105-195116 (2002)
[CrossRef]

A. G Borisov, F. J. Garcia de Abajo, S. V. Shabanov, "Role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials," Phys. Rev. B 71, 075408(1) - 075408(7) (2005).
[CrossRef]

Phys. Rev. Lett. (2)

J. A. Porto, F. J. Garcia-Vidal, J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999)
[CrossRef]

Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403(1) - 057403(4) (2002).
[CrossRef]

Solid-State Electronics (1)

D. Crouse and R. Solomon, "Numerical modeling of surface plasmon enhanced silicon on insulator avalanche photodiodes," Solid-State Electronics 49, 1697-1701 (2005).
[CrossRef]

Surf. Science. Lett. (1)

E. Popov, L. Tsonev, "Resonant electric field enhancement in vicinity of a bare metallic grating exposed to s-polarize light," Surf. Science. Lett. 271, L378-L382 (1992).
[CrossRef]

Other (2)

David R. Lide, Handbook of Chemistry and Physics (CRC Press, London, 1992-1993).

D. Maystre, "General study of grating anomalies from electromagnetic surface modes," in Electromagnetic Surface Modes, A. D. Boardman, ed. (John Wiley and Sons, Belfast, 1982), pp. 661-724.

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Figures (8)

Fig. 1.
Fig. 1.

(a) The effective electromagnetic energy density for the 1.11eV horizontally oriented surface plasmons (HSPs). This energy profile illustrates typical HSP characteristics. The magnetic field intensities for (b) 1.16eV WR and (c) 0.73eV CM. For the WR and CM modes, the structure has a Si substrate and Au contacts with d = 0.3μm, c = 0.15μm and h = 0.4μm and grooves filled with air. For the CM mode, the structure is altered to increase the aspect ratio of the groove by having c = 0.075μm and h = 0.57μm; all other dimensions remain the same. In all cases, a TM-polarized beam is incident on the structure from above (i.e., the air layer).

Fig. 2.
Fig. 2.

The three different cases of EOT in 1-D metal gratings that are described in this paper.

Fig. 3.
Fig. 3.

The dependence of the peaks in transmission for the first three order modes for TE-polarized and TM-polarized light. It is seen that the CMs for TE-polarized light have a strong dependence on groove width that can be exploited to align these modes with TM-polarization CMs.

Fig. 4.
Fig. 4.

(a)Left: Reflectance (black) and Zero-order transmission (red) coefficients for the structure with d = 1.75μ, c = 0.45μm, h = 1μm, εgroove=11.9, showing optical characteristics consistent with Case 1 at 0.333eV and Case 2 at 0.415eV. Right (b): Reflectance (black) and Zero-order transmission (red) coefficients for the structure with d = 1.75μm, c = 0.615μm, h = 1 μm, εgroove=11.9, exhibiting aligned TE and TM polarization EOT (Case 3). In both the left-hand and right-hand plots, solid lines correspond to TM polarization and dotted lines correspond to TE polarization results.

Fig. 5.
Fig. 5.

Left: The magnitude of the z-component of the magnetic field produced by TM polarized 0.5eV normal incident light. Right: The magnitude of the z-component of the electric field produced by TE polarized 0.5eV normal incident light.

Fig. 6.
Fig. 6.

Left: The Poynting vector for TM polarized 0.5eV normal incident light. Right: The Poynting vector for TE polarized 0.5eV normal incident light.

Fig. 7.
Fig. 7.

Reflectance (black) and Zero-Order transmittance (red) for a un-polarized (50%TM, 50%TE) light incident on 1-D grating with d = 690nm, c = 287.5nm, h = 1193.7nm, with silicon inside the groove and SiO2 (ε = 2) as the substrate. This is an example of a polarization-independent wavelength filter that can be achieved using the tuning techniques mentioned in this paper at 1550nm with a peak transmission for un-polarized light at 86% and FWHM of transmission equal to 41nm.

Fig. 8.
Fig. 8.

The figure defines the coordinate system used in the calculation. Only one period of the grating is shown. In the calculations, the top layer is assumed to be air (ε = 1).

Equations (22)

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

E = Z n ̂ × H
f air ( x , y ) = exp ( i ( α o x β o ( y h 2 ) ) ) + n = R n exp ( i ( α n x + β n ( y h 2 ) ) )
f groove ( x , y ) = n = 0 Φ n ( x , y )
f substrate ( x , y ) = n = T n exp ( i ( α n x β ˜ n ( y + h 2 ) ) )
Φ n ( x , y ) = X n ( x ) Y n ( y )
X n ( x ) = d n sin ( μ n x ) + cos ( μ n x )
Y n ( y ) = a n exp ( i υ n y ) + b n exp ( i υ n y )
μ n 2 + υ n 2 = ε groove k o 2
d n = η groove μ n
tan ( c μ n ) = 2 η groove μ n μ n 2 η 2 2
n = ( I n + R n ) e i α n x = m X m ( x ) ( φ m a m + φ m 1 b m ) 0 x c
i n = β n ( I n + R n ) e i α n x = { i γ air γ groove m X ( x ) υ m ( φ m a m φ m 1 b m ) 0 x c η air n = ( I n + R n ) e i α n x c x d
n = T qn e i α n x = m X ( x ) ( φ m 1 a m + φ m b m ) 0 x c
i n = β ˜ n T n e i α n x = { i γ substrate γ groove m X m ( x ) υ m ( φ m 1 a m φ m b m ) 0 x c η substrate n = T n e i α n x c x d
M Ψ = Ω
M = ( G N φ 1 0 η air J i γ air γ groove Kυφ i γ air γ groove φ 1 0 0 N φ 1 G 0 i γ substrate γ groove φ 1 i γ substrate γ groove Kυφ i β ˜ + η substrate J )
Ψ = R a b T and Ω = GI ( + η air J ) I 0 0
G mn = 0 c X m ( x ) exp ( i α n x ) dx
K nm = 1 d 0 c X m ( x ) exp ( i α n x ) dx
J qn = 1 d c d exp ( i ( α n α q ) x ) dx
N mn = 0 c X m ( x ) X n ( x ) dx = δ mn [ ( ( η groove μ m ) 2 + 1 ) c 2 + η groove μ m 2 ]
S y , n S y , incident = ε i γ i cos θ outward , n cos θ incident Ψ outward , n 2

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