Abstract

Metallic waveguide theory has been used to design subwavelength metallic grating waveguide structure which can excite the waveguide modes, especially the low frequency coupled surface plasmons mode, to achieve sub-50nm resolution lithography pattern by using the light with 436nm wavelength. The Finite Difference Time Domain method has been performed to analyze the performance of lithography pattern generated by two possible schemes. One named metal-layer scheme utilizes three different modes (two coupled surface plasmons and one non-coupled surface plasmons) on the metal layer to generate the lithography patterns with different resolution and visibility. The other named metal-cladding scheme excites the coupled mode in the metal-cladding region, which utilizes multi-layer coupled effect to generate the field with higher resolution (~34nm) and approximately same visibility compared with the metal-layer scheme. The effectively deviated range of grating period is also analyzed to keep the output pattern effective for the lithography.

© 2006 Optical Society of America

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    [CrossRef]
  4. J. G. Goodberlet, "Patterning 100 nm features using deep-ultraviolet contact photolithography," Appl. Phys. Lett. 76, 667-669 (2000).
    [CrossRef]
  5. J. G. Goodberlet and H. Kavak, "Patterning sub-50 nm features with near-field embedded-amplitude masks," Appl. Phys. Lett. 81, 1315-1317 (2002).
    [CrossRef]
  6. M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, "Sub-diffraction-limited patterning using evanescent near-field optical lithography," Appl. Phys. Lett. 75, 3560-3562 (1999).
    [CrossRef]
  7. P. G. Kik, A. L. Martin, S. A. Maier, and H. A. Atwater, "Metal nanoparticle arrays for near field optical lithography," Proc. SPIE 4810, 7-14 (2002).
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  13. Z. W. Liu, Q. H. Wei, and X. Zhang, "Surface plasmon interference nanolithography," Nano Lett. 5, 957-961 (2005).
    [CrossRef] [PubMed]
  14. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  15. N. Fang, Z. W. Liu, T. J. Yen, and X. Zhang, "Regenerating evanescent waves from a silver superlens," Opt. Express 11, 682-687 (2003).
    [CrossRef] [PubMed]
  16. D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403-4405 (2004).
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  18. R. J. Blaikie, M. M. Alkaisi, S. J. Mcnab and D. O. S. Melville, "Nanoscale optical patterning using evanescent fields and surface plasmons,"Int. J. Nanosci. 3, 405-417 (2004).
    [CrossRef]
  19. D. B. Shao, and S. C. Chen, "Surface-plasmon-assisted Nanoscale Photolithography by polarized light," Appl. Phys. Lett. 86, 253107-253110 (2005).
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  22. S. Glasberg, A. Sharon, D. Rosenblatt, and A. A. Friesem, "Long-range surface plasmon resonances in gratingwaveguide structures," Appl. Phys. Lett. 70, 1210-1212 (1997).
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2005 (3)

D. B. Shao, and S. C. Chen, "Surface-plasmon-assisted Nanoscale Photolithography by polarized light," Appl. Phys. Lett. 86, 253107-253110 (2005).
[CrossRef]

Z. W. Liu, Q. H. Wei, and X. Zhang, "Surface plasmon interference nanolithography," Nano Lett. 5, 957-961 (2005).
[CrossRef] [PubMed]

D. O. S. Melville, and R. J. Blaikie, "Super-resolution imaging through a planar silver layer," Opt. Express 13, 2127- 2134 (2005).
[CrossRef] [PubMed]

2004 (5)

X. G. Luo and T. Ishihara, "Subwavelength photolithography based on surface-plasmon polariton resonance," Opt. Express 12, 3055-3066 (2004).
[CrossRef] [PubMed]

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403-4405 (2004).
[CrossRef]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, "Plasmonic nanolithography," Nano Lett. 4, 1085-1088 (2004).
[CrossRef]

W. Srituravanich, N. Fang, S. Durant, M. Ambati, C. Sun, and X. Zhang, "Sub-100 nm lithography using ultrashort wavelength of surface plasmons," J. Vac. Sci. Technol. B 22, 3475-3478 (2004).
[CrossRef]

R. J. Blaikie, M. M. Alkaisi, S. J. Mcnab and D. O. S. Melville, "Nanoscale optical patterning using evanescent fields and surface plasmons,"Int. J. Nanosci. 3, 405-417 (2004).
[CrossRef]

2003 (1)

2002 (2)

P. G. Kik, A. L. Martin, S. A. Maier, and H. A. Atwater, "Metal nanoparticle arrays for near field optical lithography," Proc. SPIE 4810, 7-14 (2002).
[CrossRef]

J. G. Goodberlet and H. Kavak, "Patterning sub-50 nm features with near-field embedded-amplitude masks," Appl. Phys. Lett. 81, 1315-1317 (2002).
[CrossRef]

2000 (2)

J. G. Goodberlet, "Patterning 100 nm features using deep-ultraviolet contact photolithography," Appl. Phys. Lett. 76, 667-669 (2000).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1999 (1)

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, "Sub-diffraction-limited patterning using evanescent near-field optical lithography," Appl. Phys. Lett. 75, 3560-3562 (1999).
[CrossRef]

1998 (2)

H. Schmid, H. Biebuyck, B. Michel, and O. J. F. Martin, "Light-coupling masks for lensless, sub-wavelength optical lithography," Appl. Phys. Lett. 72, 2379-2381 (1998).
[CrossRef]

O. J. Martin, N. B. Piller, H. Schmid, H. Biebuyck, and B. Michel, "Energy flow in light-coupling masks for lensless optical lithography," Opt. Express 3, 280-285 (1998).
[CrossRef] [PubMed]

1997 (1)

S. Glasberg, A. Sharon, D. Rosenblatt, and A. A. Friesem, "Long-range surface plasmon resonances in gratingwaveguide structures," Appl. Phys. Lett. 70, 1210-1212 (1997).
[CrossRef]

1994 (2)

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

M. D. Levenson, "Extending the lifetime of optical lithography technologies with wavefront engineering," Jpn. J. Appl. Phys. 33, 6765-6773 (1994).
[CrossRef]

1991 (1)

S. Okazaki, "Resolution limits of optical lithography," J. Vac. Sci. Technol. B 9, 2829-2833 (1991).
[CrossRef]

1986 (1)

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

1984 (1)

1981 (1)

D. Sarid, "Long-range surface-plasma waves on very thin metal-films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

1972 (1)

P. B. Johnson, and R. W. Christy, "Optical constant of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Alkaisi, M. M.

R. J. Blaikie, M. M. Alkaisi, S. J. Mcnab and D. O. S. Melville, "Nanoscale optical patterning using evanescent fields and surface plasmons,"Int. J. Nanosci. 3, 405-417 (2004).
[CrossRef]

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, "Sub-diffraction-limited patterning using evanescent near-field optical lithography," Appl. Phys. Lett. 75, 3560-3562 (1999).
[CrossRef]

Ambati, M.

W. Srituravanich, N. Fang, S. Durant, M. Ambati, C. Sun, and X. Zhang, "Sub-100 nm lithography using ultrashort wavelength of surface plasmons," J. Vac. Sci. Technol. B 22, 3475-3478 (2004).
[CrossRef]

Atwater, H. A.

P. G. Kik, A. L. Martin, S. A. Maier, and H. A. Atwater, "Metal nanoparticle arrays for near field optical lithography," Proc. SPIE 4810, 7-14 (2002).
[CrossRef]

Berenger, J. P.

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

Biebuyck, H.

O. J. Martin, N. B. Piller, H. Schmid, H. Biebuyck, and B. Michel, "Energy flow in light-coupling masks for lensless optical lithography," Opt. Express 3, 280-285 (1998).
[CrossRef] [PubMed]

H. Schmid, H. Biebuyck, B. Michel, and O. J. F. Martin, "Light-coupling masks for lensless, sub-wavelength optical lithography," Appl. Phys. Lett. 72, 2379-2381 (1998).
[CrossRef]

Blaikie, R. J.

D. O. S. Melville, and R. J. Blaikie, "Super-resolution imaging through a planar silver layer," Opt. Express 13, 2127- 2134 (2005).
[CrossRef] [PubMed]

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403-4405 (2004).
[CrossRef]

R. J. Blaikie, M. M. Alkaisi, S. J. Mcnab and D. O. S. Melville, "Nanoscale optical patterning using evanescent fields and surface plasmons,"Int. J. Nanosci. 3, 405-417 (2004).
[CrossRef]

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, "Sub-diffraction-limited patterning using evanescent near-field optical lithography," Appl. Phys. Lett. 75, 3560-3562 (1999).
[CrossRef]

Burke, J. J.

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

Chen, S. C.

D. B. Shao, and S. C. Chen, "Surface-plasmon-assisted Nanoscale Photolithography by polarized light," Appl. Phys. Lett. 86, 253107-253110 (2005).
[CrossRef]

Cheung, R.

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, "Sub-diffraction-limited patterning using evanescent near-field optical lithography," Appl. Phys. Lett. 75, 3560-3562 (1999).
[CrossRef]

Chilwell, J.

Christy, R. W.

P. B. Johnson, and R. W. Christy, "Optical constant of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Cumming, D. R. S.

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, "Sub-diffraction-limited patterning using evanescent near-field optical lithography," Appl. Phys. Lett. 75, 3560-3562 (1999).
[CrossRef]

Durant, S.

W. Srituravanich, N. Fang, S. Durant, M. Ambati, C. Sun, and X. Zhang, "Sub-100 nm lithography using ultrashort wavelength of surface plasmons," J. Vac. Sci. Technol. B 22, 3475-3478 (2004).
[CrossRef]

Fang, N.

W. Srituravanich, N. Fang, S. Durant, M. Ambati, C. Sun, and X. Zhang, "Sub-100 nm lithography using ultrashort wavelength of surface plasmons," J. Vac. Sci. Technol. B 22, 3475-3478 (2004).
[CrossRef]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, "Plasmonic nanolithography," Nano Lett. 4, 1085-1088 (2004).
[CrossRef]

N. Fang, Z. W. Liu, T. J. Yen, and X. Zhang, "Regenerating evanescent waves from a silver superlens," Opt. Express 11, 682-687 (2003).
[CrossRef] [PubMed]

Friesem, A. A.

S. Glasberg, A. Sharon, D. Rosenblatt, and A. A. Friesem, "Long-range surface plasmon resonances in gratingwaveguide structures," Appl. Phys. Lett. 70, 1210-1212 (1997).
[CrossRef]

Glasberg, S.

S. Glasberg, A. Sharon, D. Rosenblatt, and A. A. Friesem, "Long-range surface plasmon resonances in gratingwaveguide structures," Appl. Phys. Lett. 70, 1210-1212 (1997).
[CrossRef]

Goodberlet, J. G.

J. G. Goodberlet and H. Kavak, "Patterning sub-50 nm features with near-field embedded-amplitude masks," Appl. Phys. Lett. 81, 1315-1317 (2002).
[CrossRef]

J. G. Goodberlet, "Patterning 100 nm features using deep-ultraviolet contact photolithography," Appl. Phys. Lett. 76, 667-669 (2000).
[CrossRef]

Hodgkinson, I.

Ishihara, T.

Johnson, P. B.

P. B. Johnson, and R. W. Christy, "Optical constant of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Kavak, H.

J. G. Goodberlet and H. Kavak, "Patterning sub-50 nm features with near-field embedded-amplitude masks," Appl. Phys. Lett. 81, 1315-1317 (2002).
[CrossRef]

Kik, P. G.

P. G. Kik, A. L. Martin, S. A. Maier, and H. A. Atwater, "Metal nanoparticle arrays for near field optical lithography," Proc. SPIE 4810, 7-14 (2002).
[CrossRef]

Levenson, M. D.

M. D. Levenson, "Extending the lifetime of optical lithography technologies with wavefront engineering," Jpn. J. Appl. Phys. 33, 6765-6773 (1994).
[CrossRef]

Liu, Z. W.

Luo, Q.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, "Plasmonic nanolithography," Nano Lett. 4, 1085-1088 (2004).
[CrossRef]

Luo, X. G.

Maier, S. A.

P. G. Kik, A. L. Martin, S. A. Maier, and H. A. Atwater, "Metal nanoparticle arrays for near field optical lithography," Proc. SPIE 4810, 7-14 (2002).
[CrossRef]

Martin, A. L.

P. G. Kik, A. L. Martin, S. A. Maier, and H. A. Atwater, "Metal nanoparticle arrays for near field optical lithography," Proc. SPIE 4810, 7-14 (2002).
[CrossRef]

Martin, O. J.

Martin, O. J. F.

H. Schmid, H. Biebuyck, B. Michel, and O. J. F. Martin, "Light-coupling masks for lensless, sub-wavelength optical lithography," Appl. Phys. Lett. 72, 2379-2381 (1998).
[CrossRef]

Mcnab, S. J.

R. J. Blaikie, M. M. Alkaisi, S. J. Mcnab and D. O. S. Melville, "Nanoscale optical patterning using evanescent fields and surface plasmons,"Int. J. Nanosci. 3, 405-417 (2004).
[CrossRef]

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, "Sub-diffraction-limited patterning using evanescent near-field optical lithography," Appl. Phys. Lett. 75, 3560-3562 (1999).
[CrossRef]

Melville, D. O. S.

D. O. S. Melville, and R. J. Blaikie, "Super-resolution imaging through a planar silver layer," Opt. Express 13, 2127- 2134 (2005).
[CrossRef] [PubMed]

R. J. Blaikie, M. M. Alkaisi, S. J. Mcnab and D. O. S. Melville, "Nanoscale optical patterning using evanescent fields and surface plasmons,"Int. J. Nanosci. 3, 405-417 (2004).
[CrossRef]

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403-4405 (2004).
[CrossRef]

Michel, B.

H. Schmid, H. Biebuyck, B. Michel, and O. J. F. Martin, "Light-coupling masks for lensless, sub-wavelength optical lithography," Appl. Phys. Lett. 72, 2379-2381 (1998).
[CrossRef]

O. J. Martin, N. B. Piller, H. Schmid, H. Biebuyck, and B. Michel, "Energy flow in light-coupling masks for lensless optical lithography," Opt. Express 3, 280-285 (1998).
[CrossRef] [PubMed]

Okazaki, S.

S. Okazaki, "Resolution limits of optical lithography," J. Vac. Sci. Technol. B 9, 2829-2833 (1991).
[CrossRef]

Pendry, J. B.

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Piller, N. B.

Rosenblatt, D.

S. Glasberg, A. Sharon, D. Rosenblatt, and A. A. Friesem, "Long-range surface plasmon resonances in gratingwaveguide structures," Appl. Phys. Lett. 70, 1210-1212 (1997).
[CrossRef]

Sarid, D.

D. Sarid, "Long-range surface-plasma waves on very thin metal-films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

Schmid, H.

O. J. Martin, N. B. Piller, H. Schmid, H. Biebuyck, and B. Michel, "Energy flow in light-coupling masks for lensless optical lithography," Opt. Express 3, 280-285 (1998).
[CrossRef] [PubMed]

H. Schmid, H. Biebuyck, B. Michel, and O. J. F. Martin, "Light-coupling masks for lensless, sub-wavelength optical lithography," Appl. Phys. Lett. 72, 2379-2381 (1998).
[CrossRef]

Shao, D. B.

D. B. Shao, and S. C. Chen, "Surface-plasmon-assisted Nanoscale Photolithography by polarized light," Appl. Phys. Lett. 86, 253107-253110 (2005).
[CrossRef]

Sharon, A.

S. Glasberg, A. Sharon, D. Rosenblatt, and A. A. Friesem, "Long-range surface plasmon resonances in gratingwaveguide structures," Appl. Phys. Lett. 70, 1210-1212 (1997).
[CrossRef]

Srituravanich, W.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, "Plasmonic nanolithography," Nano Lett. 4, 1085-1088 (2004).
[CrossRef]

W. Srituravanich, N. Fang, S. Durant, M. Ambati, C. Sun, and X. Zhang, "Sub-100 nm lithography using ultrashort wavelength of surface plasmons," J. Vac. Sci. Technol. B 22, 3475-3478 (2004).
[CrossRef]

Stegeman, G. I.

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

Sun, C.

W. Srituravanich, N. Fang, S. Durant, M. Ambati, C. Sun, and X. Zhang, "Sub-100 nm lithography using ultrashort wavelength of surface plasmons," J. Vac. Sci. Technol. B 22, 3475-3478 (2004).
[CrossRef]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, "Plasmonic nanolithography," Nano Lett. 4, 1085-1088 (2004).
[CrossRef]

Tamir, T.

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

Wei, Q. H.

Z. W. Liu, Q. H. Wei, and X. Zhang, "Surface plasmon interference nanolithography," Nano Lett. 5, 957-961 (2005).
[CrossRef] [PubMed]

Wolf, C. R.

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403-4405 (2004).
[CrossRef]

Yen, T. J.

Zhang, X.

Z. W. Liu, Q. H. Wei, and X. Zhang, "Surface plasmon interference nanolithography," Nano Lett. 5, 957-961 (2005).
[CrossRef] [PubMed]

W. Srituravanich, N. Fang, S. Durant, M. Ambati, C. Sun, and X. Zhang, "Sub-100 nm lithography using ultrashort wavelength of surface plasmons," J. Vac. Sci. Technol. B 22, 3475-3478 (2004).
[CrossRef]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, "Plasmonic nanolithography," Nano Lett. 4, 1085-1088 (2004).
[CrossRef]

N. Fang, Z. W. Liu, T. J. Yen, and X. Zhang, "Regenerating evanescent waves from a silver superlens," Opt. Express 11, 682-687 (2003).
[CrossRef] [PubMed]

Appl. Phys. Lett. (7)

H. Schmid, H. Biebuyck, B. Michel, and O. J. F. Martin, "Light-coupling masks for lensless, sub-wavelength optical lithography," Appl. Phys. Lett. 72, 2379-2381 (1998).
[CrossRef]

J. G. Goodberlet, "Patterning 100 nm features using deep-ultraviolet contact photolithography," Appl. Phys. Lett. 76, 667-669 (2000).
[CrossRef]

J. G. Goodberlet and H. Kavak, "Patterning sub-50 nm features with near-field embedded-amplitude masks," Appl. Phys. Lett. 81, 1315-1317 (2002).
[CrossRef]

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, "Sub-diffraction-limited patterning using evanescent near-field optical lithography," Appl. Phys. Lett. 75, 3560-3562 (1999).
[CrossRef]

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403-4405 (2004).
[CrossRef]

D. B. Shao, and S. C. Chen, "Surface-plasmon-assisted Nanoscale Photolithography by polarized light," Appl. Phys. Lett. 86, 253107-253110 (2005).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Schematic diagram illustrating the MGWS and illumination conditions used for the simulations.

Fig. 2.
Fig. 2.

Near field intensity profiles of electric field of (a) HFSPs (symmetric mode, p 1=236nm) and (b) LFSPs (antisymmetric mode, p 2=174nm) in single silver grating illuminated at 436nm. The other parameters are t=40nm and w=30nm. The lateral scale is two periods for (a) and three periods for (b) for convenience of compare.

Fig. 3.
Fig. 3.

Near field intensity profiles of electric field for the MGWS of metal-layer scheme supporting (a) the HFSPs mode (p 1=236nm) and (b) the LFSPs mode (p 2=174nm) illuminated at 436nm. The other parameters are t 1=t 2=40nm, w=30nm and s=60nm. The lateral scale is two periods for (a) and three periods for (b) for convenience of compare.

Fig. 4.
Fig. 4.

Near field intensity profile of electric field for the MGWS of metal-layer scheme supporting SPs mode on the output surface. The parameters are p=208nm, t=40nm and w=30nm. The lateral scale is two periods.

Fig. 5.
Fig. 5.

The average intensity profiles of electric field along the lateral direction y at different distance x beneath the output surface of (A) typical SPAN structure and (B) MGWS of metal-layer scheme supporting HFSPs. The lateral scale is two periods.

Fig. 6.
Fig. 6.

Image visibility V as a function of distance x beneath the output surface of MGWS of metal-layer scheme supporting different modes (HFSPs p=236nm, SPs p=208nm and LFSPs p=174nm) and typical SPAN.

Fig. 7.
Fig. 7.

Image visibility V as a function of distance x beneath the output surface of MGWS of metal-layer scheme in non-resonant condition. (p=240nm, p=222nm, p=190nm and p=170nm))

Fig. 8.
Fig. 8.

Near field intensity profile of electric field for the MGWS of metal-cladding scheme illuminated at 436nm. The parameters are t 1=t 2=40nm, p=154nm, w=30nm and s=60nm. The lateral scale is three periods.

Fig. 9.
Fig. 9.

(a) Image visibility V as a function of distance x beneath the bottom surface of silver grating in the MGWS of metal-cladding scheme with different periods (p=154nm, p=152nm and p=156nm). The region of silver film is bounded by the dash-lines. (b) The average intensity profiles of electric field along the lateral direction y at the distance x=23nm beneath the bottom surface of silver grating in resonant condition (p=154nm). The lateral scale is three periods.

Equations (5)

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tanh ( α 2 t 2 ) = ( ε 2 α 1 ε 1 α 2 + ε 2 α 3 ε 3 α 2 ) ( 1 + ε 2 α 1 ε 1 α 2 . ε 2 α 3 ε 3 α 2 )
α j 2 = k 2 k 0 2 ε j , j = 1 , 2 , 3
tanh ( α 2 s 2 ) = ( p ε 2 ) ( α 2 ε 1 )
α j 2 = k 2 k 0 2 ε j , j = 1 , 2 , 3
p = α 1 tanh [ atanh ( α 3 ε 1 α 1 ε 3 ) + α 1 t 1 ]

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