Abstract

The in-plane scattering patterns from a complex dielectric grating were both numerically and experimentally studied in contrast to those from well-known metallic gratings. The incidence was the transverse electric or transverse magnetic wave of wavelength λ=660nm. The grating profile was complex with a period Λ=7.0μm, while the material was lightly doped crystalline silicon. Patterns of the electric field, magnetic field, and spatial intensity distribution were demonstrated at the normal (θi=0°) and oblique (θi=+30°) incidence. Electric and magnetic fields were presented in the near field as well as the far field. The measured power ratio within 90°θr+90° was plotted. Their major peaks and the numerically obtained diffraction efficiency of 21 orders (10m+10 or 15m+5) of diffracted waves occurred at the same θr. Other peaks and stair-like shoulders of major peaks also exhibited in spectra.

© 2014 Optical Society of America

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References

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2011 (1)

2010 (4)

2009 (3)

2008 (2)

Y. B. Chen and Z. M. Zhang, “Heavily doped silicon complex gratings as wavelength-selective absorbing surfaces,” J. Phys. D 41, 095406 (2008).
[CrossRef]

W. W. Feng and Q. N. Wei, “A scatterometer for measuring the polarized bidirectional reflectance distribution function of painted surfaces in the infrared,” Infrared Phys. Technol. 51, 559–563 (2008).
[CrossRef]

2007 (3)

D. C. Skigin, H. Loui, Z. Popovic, and E. F. Kuester, “Bandwidth control of forbidden transmission gaps in compound structures with subwavelength slits,” Phys. Rev. E 76, 016604 (2007).
[CrossRef]

Y. G. Ma, X. S. Rao, G. F. Zhang, and C. K. Ong, “Microwave transmission modes in compound metallic gratings,” Phys. Rev. B 76, 085413 (2007).
[CrossRef]

Y. B. Chen and Z. M. Zhang, “Design of tungsten complex gratings for thermophotovoltaic radiators,” Opt. Commun. 269, 411–417 (2007).
[CrossRef]

2006 (3)

A. P. Hibbins, I. R. Hooper, M. J. Lockyear, and J. R. Sambles, “Microwave transmission of a compound metal grating,” Phys. Rev. Lett. 96, 257402 (2006).
[CrossRef]

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
[CrossRef]

H. S. Li, S. C. Foo, K. E. Torrance, and S. H. Westin, “Automated three-axis gonioreflectometer for computer graphics applications,” Opt. Eng. 45, 043605 (2006).
[CrossRef]

2003 (2)

Y. J. Shen, Q. Z. Zhu, and Z. M. Zhang, “A scatterometer for measuring the bidirectional reflectance and transmittance of semiconductor wafers with rough surfaces,” Rev. Sci. Instrum. 74, 4885–4892 (2003).
[CrossRef]

A. Mizutani, H. Kikuta, and K. Iwata, “Wave localization of doubly periodic guided-mode resonant grating filters,” Opt. Rev. 10, 13–18 (2003).
[CrossRef]

2002 (1)

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Excitation of remarkably nondispersive surface plasmons on a nondiffracting, dual-pitch metal grating,” Appl. Phys. Lett. 80, 2410–2412 (2002).
[CrossRef]

2001 (1)

A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Resonant effects in periodic gratings comprising a finite number of grooves in each period,” Phys. Rev. E 64, 016605 (2001).
[CrossRef]

2000 (1)

W.-C. Tan, J. R. Sambles, and T. W. Preist, “Double-period zero-order metal gratings as effective selective absorbers,” Phys. Rev. B 61, 13177–13182 (2000).
[CrossRef]

1996 (1)

1995 (1)

Ayre, M.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
[CrossRef]

Baets, R.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
[CrossRef]

Baroughi, M. F.

Bayat, K.

Beruete, M.

Bienstman, P.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
[CrossRef]

Bodermann, B.

M. Wurm, F. Pilarski, and B. Bodermann, “A new flexible scatterometer for critical dimension metrology,” Rev. Sci. Instrum. 81, 023701 (2010).
[CrossRef]

Bogaerts, W.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
[CrossRef]

Chen, Y. B.

Y. B. Chen and M. J. Huang, “Infrared reflectance from a compound grating and its alternative componential gratings,” J. Opt. Soc. Am. B 27, 2078–2086 (2010).
[CrossRef]

Y. B. Chen, “Development of mid-infrared surface plasmon resonance-based sensors with highly-doped silicon for biomedical and chemical applications,” Opt. Express 17, 3130–3140 (2009).
[CrossRef]

Y. B. Chen and Z. M. Zhang, “Heavily doped silicon complex gratings as wavelength-selective absorbing surfaces,” J. Phys. D 41, 095406 (2008).
[CrossRef]

Y. B. Chen and Z. M. Zhang, “Design of tungsten complex gratings for thermophotovoltaic radiators,” Opt. Commun. 269, 411–417 (2007).
[CrossRef]

Fantino, A. N.

A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Resonant effects in periodic gratings comprising a finite number of grooves in each period,” Phys. Rev. E 64, 016605 (2001).
[CrossRef]

Feng, W. W.

W. W. Feng and Q. N. Wei, “A scatterometer for measuring the polarized bidirectional reflectance distribution function of painted surfaces in the infrared,” Infrared Phys. Technol. 51, 559–563 (2008).
[CrossRef]

Foo, S. C.

H. S. Li, S. C. Foo, K. E. Torrance, and S. H. Westin, “Automated three-axis gonioreflectometer for computer graphics applications,” Opt. Eng. 45, 043605 (2006).
[CrossRef]

Galipeau, D. W.

Gaylord, T. K.

Grann, E. B.

Grosz, S. I.

A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Resonant effects in periodic gratings comprising a finite number of grooves in each period,” Phys. Rev. E 64, 016605 (2001).
[CrossRef]

Guo, J. P.

Hamilton, O. K.

H. J. Rance, O. K. Hamilton, J. R. Sambles, and A. P. Hibbins, “Phase resonances on metal gratings of identical, equally spaced alternately tapered slits,” Appl. Phys. Lett. 95, 041905 (2009).
[CrossRef]

Hibbins, A. P.

H. J. Rance, O. K. Hamilton, J. R. Sambles, and A. P. Hibbins, “Phase resonances on metal gratings of identical, equally spaced alternately tapered slits,” Appl. Phys. Lett. 95, 041905 (2009).
[CrossRef]

A. P. Hibbins, I. R. Hooper, M. J. Lockyear, and J. R. Sambles, “Microwave transmission of a compound metal grating,” Phys. Rev. Lett. 96, 257402 (2006).
[CrossRef]

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Excitation of remarkably nondispersive surface plasmons on a nondiffracting, dual-pitch metal grating,” Appl. Phys. Lett. 80, 2410–2412 (2002).
[CrossRef]

Hooper, I. R.

A. P. Hibbins, I. R. Hooper, M. J. Lockyear, and J. R. Sambles, “Microwave transmission of a compound metal grating,” Phys. Rev. Lett. 96, 257402 (2006).
[CrossRef]

Howell, J. R.

R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer, 4th ed. (Taylor & Francis, 2002).

Huang, M. J.

Iwata, K.

A. Mizutani, H. Kikuta, and K. Iwata, “Wave localization of doubly periodic guided-mode resonant grating filters,” Opt. Rev. 10, 13–18 (2003).
[CrossRef]

Kikuta, H.

A. Mizutani, H. Kikuta, and K. Iwata, “Wave localization of doubly periodic guided-mode resonant grating filters,” Opt. Rev. 10, 13–18 (2003).
[CrossRef]

Kuester, E. F.

D. C. Skigin, H. Loui, Z. Popovic, and E. F. Kuester, “Bandwidth control of forbidden transmission gaps in compound structures with subwavelength slits,” Phys. Rev. E 76, 016604 (2007).
[CrossRef]

Lawrence, C. R.

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Excitation of remarkably nondispersive surface plasmons on a nondiffracting, dual-pitch metal grating,” Appl. Phys. Lett. 80, 2410–2412 (2002).
[CrossRef]

Leong, H. S.

Li, H. S.

H. S. Li, S. C. Foo, K. E. Torrance, and S. H. Westin, “Automated three-axis gonioreflectometer for computer graphics applications,” Opt. Eng. 45, 043605 (2006).
[CrossRef]

Li, L. F.

Lockyear, M. J.

A. P. Hibbins, I. R. Hooper, M. J. Lockyear, and J. R. Sambles, “Microwave transmission of a compound metal grating,” Phys. Rev. Lett. 96, 257402 (2006).
[CrossRef]

Loui, H.

D. C. Skigin, H. Loui, Z. Popovic, and E. F. Kuester, “Bandwidth control of forbidden transmission gaps in compound structures with subwavelength slits,” Phys. Rev. E 76, 016604 (2007).
[CrossRef]

Ma, Y. G.

Y. G. Ma, X. S. Rao, G. F. Zhang, and C. K. Ong, “Microwave transmission modes in compound metallic gratings,” Phys. Rev. B 76, 085413 (2007).
[CrossRef]

Madou, M. J.

M. J. Madou, Fundamentals of Microfabrication: The Science of Miniaturization, 2nd ed. (CRC Press, 2002).

May, S.

Mizutani, A.

A. Mizutani, H. Kikuta, and K. Iwata, “Wave localization of doubly periodic guided-mode resonant grating filters,” Opt. Rev. 10, 13–18 (2003).
[CrossRef]

Moharam, M. G.

Navarro-Cia, M.

Ong, C. K.

Y. G. Ma, X. S. Rao, G. F. Zhang, and C. K. Ong, “Microwave transmission modes in compound metallic gratings,” Phys. Rev. B 76, 085413 (2007).
[CrossRef]

Palik, E. D.

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

Paudel, H. P.

Pilarski, F.

M. Wurm, F. Pilarski, and B. Bodermann, “A new flexible scatterometer for critical dimension metrology,” Rev. Sci. Instrum. 81, 023701 (2010).
[CrossRef]

Pommet, D. A.

Popovic, Z.

D. C. Skigin, H. Loui, Z. Popovic, and E. F. Kuester, “Bandwidth control of forbidden transmission gaps in compound structures with subwavelength slits,” Phys. Rev. E 76, 016604 (2007).
[CrossRef]

Preist, T. W.

W.-C. Tan, J. R. Sambles, and T. W. Preist, “Double-period zero-order metal gratings as effective selective absorbers,” Phys. Rev. B 61, 13177–13182 (2000).
[CrossRef]

Rance, H. J.

H. J. Rance, O. K. Hamilton, J. R. Sambles, and A. P. Hibbins, “Phase resonances on metal gratings of identical, equally spaced alternately tapered slits,” Appl. Phys. Lett. 95, 041905 (2009).
[CrossRef]

Rao, X. S.

Y. G. Ma, X. S. Rao, G. F. Zhang, and C. K. Ong, “Microwave transmission modes in compound metallic gratings,” Phys. Rev. B 76, 085413 (2007).
[CrossRef]

Sambles, J. R.

H. J. Rance, O. K. Hamilton, J. R. Sambles, and A. P. Hibbins, “Phase resonances on metal gratings of identical, equally spaced alternately tapered slits,” Appl. Phys. Lett. 95, 041905 (2009).
[CrossRef]

A. P. Hibbins, I. R. Hooper, M. J. Lockyear, and J. R. Sambles, “Microwave transmission of a compound metal grating,” Phys. Rev. Lett. 96, 257402 (2006).
[CrossRef]

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Excitation of remarkably nondispersive surface plasmons on a nondiffracting, dual-pitch metal grating,” Appl. Phys. Lett. 80, 2410–2412 (2002).
[CrossRef]

W.-C. Tan, J. R. Sambles, and T. W. Preist, “Double-period zero-order metal gratings as effective selective absorbers,” Phys. Rev. B 61, 13177–13182 (2000).
[CrossRef]

Shen, Y. J.

Y. J. Shen, Q. Z. Zhu, and Z. M. Zhang, “A scatterometer for measuring the bidirectional reflectance and transmittance of semiconductor wafers with rough surfaces,” Rev. Sci. Instrum. 74, 4885–4892 (2003).
[CrossRef]

Siegel, R.

R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer, 4th ed. (Taylor & Francis, 2002).

Skigin, D. C.

M. Beruete, M. Navarro-Cia, D. C. Skigin, and M. Sorolla, “Millimeter-wave phase resonances in compound reflection gratings with subwavelength grooves,” Opt. Express 18, 23957–23964 (2010).
[CrossRef]

D. C. Skigin, H. Loui, Z. Popovic, and E. F. Kuester, “Bandwidth control of forbidden transmission gaps in compound structures with subwavelength slits,” Phys. Rev. E 76, 016604 (2007).
[CrossRef]

A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Resonant effects in periodic gratings comprising a finite number of grooves in each period,” Phys. Rev. E 64, 016605 (2001).
[CrossRef]

Sorolla, M.

Taillaert, D.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
[CrossRef]

Tan, W.-C.

W.-C. Tan, J. R. Sambles, and T. W. Preist, “Double-period zero-order metal gratings as effective selective absorbers,” Phys. Rev. B 61, 13177–13182 (2000).
[CrossRef]

Torrance, K. E.

H. S. Li, S. C. Foo, K. E. Torrance, and S. H. Westin, “Automated three-axis gonioreflectometer for computer graphics applications,” Opt. Eng. 45, 043605 (2006).
[CrossRef]

Van Laere, F.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
[CrossRef]

Van Thourhout, D.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
[CrossRef]

Wei, Q. N.

W. W. Feng and Q. N. Wei, “A scatterometer for measuring the polarized bidirectional reflectance distribution function of painted surfaces in the infrared,” Infrared Phys. Technol. 51, 559–563 (2008).
[CrossRef]

Westin, S. H.

H. S. Li, S. C. Foo, K. E. Torrance, and S. H. Westin, “Automated three-axis gonioreflectometer for computer graphics applications,” Opt. Eng. 45, 043605 (2006).
[CrossRef]

Wurm, M.

M. Wurm, F. Pilarski, and B. Bodermann, “A new flexible scatterometer for critical dimension metrology,” Rev. Sci. Instrum. 81, 023701 (2010).
[CrossRef]

Zhang, G. F.

Y. G. Ma, X. S. Rao, G. F. Zhang, and C. K. Ong, “Microwave transmission modes in compound metallic gratings,” Phys. Rev. B 76, 085413 (2007).
[CrossRef]

Zhang, Z. M.

Y. B. Chen and Z. M. Zhang, “Heavily doped silicon complex gratings as wavelength-selective absorbing surfaces,” J. Phys. D 41, 095406 (2008).
[CrossRef]

Y. B. Chen and Z. M. Zhang, “Design of tungsten complex gratings for thermophotovoltaic radiators,” Opt. Commun. 269, 411–417 (2007).
[CrossRef]

Y. J. Shen, Q. Z. Zhu, and Z. M. Zhang, “A scatterometer for measuring the bidirectional reflectance and transmittance of semiconductor wafers with rough surfaces,” Rev. Sci. Instrum. 74, 4885–4892 (2003).
[CrossRef]

Zhu, Q. Z.

Y. J. Shen, Q. Z. Zhu, and Z. M. Zhang, “A scatterometer for measuring the bidirectional reflectance and transmittance of semiconductor wafers with rough surfaces,” Rev. Sci. Instrum. 74, 4885–4892 (2003).
[CrossRef]

Appl. Phys. Lett. (2)

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Excitation of remarkably nondispersive surface plasmons on a nondiffracting, dual-pitch metal grating,” Appl. Phys. Lett. 80, 2410–2412 (2002).
[CrossRef]

H. J. Rance, O. K. Hamilton, J. R. Sambles, and A. P. Hibbins, “Phase resonances on metal gratings of identical, equally spaced alternately tapered slits,” Appl. Phys. Lett. 95, 041905 (2009).
[CrossRef]

Infrared Phys. Technol. (1)

W. W. Feng and Q. N. Wei, “A scatterometer for measuring the polarized bidirectional reflectance distribution function of painted surfaces in the infrared,” Infrared Phys. Technol. 51, 559–563 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

J. Phys. D (1)

Y. B. Chen and Z. M. Zhang, “Heavily doped silicon complex gratings as wavelength-selective absorbing surfaces,” J. Phys. D 41, 095406 (2008).
[CrossRef]

Jpn. J. Appl. Phys. (1)

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
[CrossRef]

Opt. Commun. (1)

Y. B. Chen and Z. M. Zhang, “Design of tungsten complex gratings for thermophotovoltaic radiators,” Opt. Commun. 269, 411–417 (2007).
[CrossRef]

Opt. Eng. (1)

H. S. Li, S. C. Foo, K. E. Torrance, and S. H. Westin, “Automated three-axis gonioreflectometer for computer graphics applications,” Opt. Eng. 45, 043605 (2006).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Opt. Rev. (1)

A. Mizutani, H. Kikuta, and K. Iwata, “Wave localization of doubly periodic guided-mode resonant grating filters,” Opt. Rev. 10, 13–18 (2003).
[CrossRef]

Phys. Rev. B (2)

W.-C. Tan, J. R. Sambles, and T. W. Preist, “Double-period zero-order metal gratings as effective selective absorbers,” Phys. Rev. B 61, 13177–13182 (2000).
[CrossRef]

Y. G. Ma, X. S. Rao, G. F. Zhang, and C. K. Ong, “Microwave transmission modes in compound metallic gratings,” Phys. Rev. B 76, 085413 (2007).
[CrossRef]

Phys. Rev. E (2)

D. C. Skigin, H. Loui, Z. Popovic, and E. F. Kuester, “Bandwidth control of forbidden transmission gaps in compound structures with subwavelength slits,” Phys. Rev. E 76, 016604 (2007).
[CrossRef]

A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Resonant effects in periodic gratings comprising a finite number of grooves in each period,” Phys. Rev. E 64, 016605 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

A. P. Hibbins, I. R. Hooper, M. J. Lockyear, and J. R. Sambles, “Microwave transmission of a compound metal grating,” Phys. Rev. Lett. 96, 257402 (2006).
[CrossRef]

Rev. Sci. Instrum. (2)

M. Wurm, F. Pilarski, and B. Bodermann, “A new flexible scatterometer for critical dimension metrology,” Rev. Sci. Instrum. 81, 023701 (2010).
[CrossRef]

Y. J. Shen, Q. Z. Zhu, and Z. M. Zhang, “A scatterometer for measuring the bidirectional reflectance and transmittance of semiconductor wafers with rough surfaces,” Rev. Sci. Instrum. 74, 4885–4892 (2003).
[CrossRef]

Other (3)

R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer, 4th ed. (Taylor & Francis, 2002).

M. J. Madou, Fundamentals of Microfabrication: The Science of Miniaturization, 2nd ed. (CRC Press, 2002).

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

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Figures (8)

Fig. 1.
Fig. 1.

(a) Complex grating at the oblique incidence of TE waves. Ei, Hi, ki, and λ are the electric field vector, magnetic field vector, wave vector, and wavelength of the incidence, respectively. θi and θr are polar angles of the incidence and reflectance, respectively. Λ is the period of complex grating profile, while n=3.828 and κ=0.013 are optical constants of lightly doped crystalline silicon at λ=660nm. The grating profile of a period is symmetric with respect to the center of the widest ridge or the narrowest groove as marked. (b) SEM images of the complex dielectric sample and its detailed dimensions.

Fig. 2.
Fig. 2.

(a) Schematic view of TAAS; (b) magnified view of the detector and an order of diffracted wave; (c) reflectance from a plain silicon substrate measured with the TAAS and calculated from Fresnel’s equation.

Fig. 3.
Fig. 3.

Patterns of EM fields at the normal (θi=0°) incidence of TE waves. Each pattern depicts the square of magnitude normalized to that of incidence in the logarithmic scale: (a) electric fields and (b) magnetic fields in the near field; (c) electric fields and (d) magnetic fields in the far field.

Fig. 4.
Fig. 4.

Patterns of EM fields at the normal (θi=0°) incidence of TM waves: (a) magnetic fields and (b) electric fields in the near field; (c) magnetic fields and (d) electric fields in the far field.

Fig. 5.
Fig. 5.

Patterns of EM fields at the oblique (θi=+30°) incidence of TE waves: (a) electric fields and (b) magnetic fields in the near field; (c) electric fields and (d) magnetic fields in the far field.

Fig. 6.
Fig. 6.

Patterns of EM fields at the oblique (θi=+30°) incidence of TM waves: (a) magnetic fields and (b) electric fields in the near field; (c) magnetic fields and (d) electric fields in the far field.

Fig. 7.
Fig. 7.

Measured power ratios (TAAS) and the calculated diffraction efficiency (RCWA) in the logarithmic scale at the normal incidence of (a) TE waves, (b) TM waves. Every number in a parenthesis specifies the diffraction order (m).

Fig. 8.
Fig. 8.

Measured power ratios (TAAS) and the calculated diffraction efficiency (RCWA) in the logarithmic scale at the oblique incidence of (a) TE waves, (b) TM waves.

Equations (3)

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η=RR*Re(kr/kicosθi),
sinθr(m)=sinθi+mλ/Λ,
kx(m)=kx,i+2mπ/Λ,

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