Abstract

A comparative study of the reflection spectral resonances in weakly and strongly modulated subwavelength gratings is presented. The effects of strong modulation in resonant subwavelength gratings have been largely ignored in the literature. We show that the spectral stability of resonances as a function of angle of incidence around normal can be greatly enhanced with strongly modulated gratings while the desirable narrow linewidth associated with weakly modulated gratings is still maintained.

© 2000 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  17. S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Opt. Lett. 34, 2414–2420 (1995).
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  19. S. Tibuleac, R. Magnusson, “Diffractive narrow-band transmission filters based on guided-mode resonance effects in thin-film multilayers,” IEEE Photon. Technol. Lett. 9, 464–466 (1997).
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1998 (2)

1997 (7)

1996 (4)

1995 (5)

1994 (3)

1993 (1)

1992 (2)

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[CrossRef]

L. Li, J. Burke, “Linear propagation characteristics of periodically segmented waveguides,” Opt. Lett. 17, 1195–1197 (1992).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

H. L. Bertoni, L. S. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
[CrossRef]

1988 (3)

L. B. Mashev, E. G. Loewen, “Anomalies of all-dielectric multilayer coated reflection gratings as a function of groove profile: an experimental study,” Appl. Opt. 27, 31–32 (1988).
[CrossRef] [PubMed]

I. A. Avrutskiı̌, V. P. Duraev, E. T. N. A. M. Prokhorov, A. S. Svakhin, V. A. Sychugov, A. V. Tishchenko, “Optimization of the characteristics of a dispersive element based on a corrugated wavguide,” Sov. J. Quantum Electron. 18, 362–365 (1988).
[CrossRef]

I. A. Avrutskiı̌, V. A. Sychugov, “Interference between waveguide modes on reflection of light from the surface of a corrugated waveguide,” Sov. J. Quantum Electron. 18, 366–368 (1988).
[CrossRef]

1986 (2)

E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

E. Popov, L. Mashev, “Diffraction anomalies of coated dielectric gratings in conical diffraction mounting,” Opt. Commun. 59, 323–325 (1986).
[CrossRef]

1985 (1)

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

1984 (1)

L. Mashev, E. Popov, “Diffraction anomalies of dielectric coated gratings,” Opt. Commun. 51, 131–136 (1984).
[CrossRef]

1975 (1)

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

1974 (1)

S. T. Peng, H. L. Bertoni, T. Tamir, “Analysis of thin-film structures with rectangular profiles,” Opt. Commun. 10, 91–94 (1974).
[CrossRef]

1973 (1)

M. Nevière, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of the resonances of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

1965 (1)

Avrutskii?, I. A.

I. A. Avrutskiı̌, V. P. Duraev, E. T. N. A. M. Prokhorov, A. S. Svakhin, V. A. Sychugov, A. V. Tishchenko, “Optimization of the characteristics of a dispersive element based on a corrugated wavguide,” Sov. J. Quantum Electron. 18, 362–365 (1988).
[CrossRef]

I. A. Avrutskiı̌, V. A. Sychugov, “Interference between waveguide modes on reflection of light from the surface of a corrugated waveguide,” Sov. J. Quantum Electron. 18, 366–368 (1988).
[CrossRef]

Bagby, J. S.

Bertoni, H. L.

H. L. Bertoni, L. S. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
[CrossRef]

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

S. T. Peng, H. L. Bertoni, T. Tamir, “Analysis of thin-film structures with rectangular profiles,” Opt. Commun. 10, 91–94 (1974).
[CrossRef]

Black, T. D.

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antennas Propag. 42, 567–569 (1994).
[CrossRef]

Brundrett, D. L.

Burke, J.

Cadilhac, M.

M. Nevière, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of the resonances of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

Cheo, L. S.

H. L. Bertoni, L. S. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
[CrossRef]

Day, R. W.

R. W. Day, S. S. Wang, R. Magnusson, “Filter response lineshapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815–1824 (1996).
[CrossRef]

Duraev, V. P.

I. A. Avrutskiı̌, V. P. Duraev, E. T. N. A. M. Prokhorov, A. S. Svakhin, V. A. Sychugov, A. V. Tishchenko, “Optimization of the characteristics of a dispersive element based on a corrugated wavguide,” Sov. J. Quantum Electron. 18, 362–365 (1988).
[CrossRef]

Engel, H.

Erdogan, T.

Friesem, A. A.

Gaylord, T. K.

Glasberg, S.

Glytsis, E. N.

Grann, E. B.

Hessel, A.

A. Hessel, A. A. Oliner, “A new theory of wood’s anomalies on optical gratings,” Appl. Opt. 4, 1275–1297 (1965).
[CrossRef]

A. Hessel, “General characteristics of traveling-wave antennas,” in Antenna Theory, Part 2, Vol. 7 of Inter-University Electronics Series, R. E. Collin, F. J. Zucker, eds. (McGraw-Hill, New York, 1969), Chap. 19, pp. 151–257.

Kittel, C.

C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1986).

Li, L.

Loewen, E. G.

Magnusson, R.

S. Tibuleac, R. Magnusson, “Diffractive narrow-band transmission filters based on guided-mode resonance effects in thin-film multilayers,” IEEE Photon. Technol. Lett. 9, 464–466 (1997).
[CrossRef]

S. Tibuleac, R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A 14, 1617–1626 (1997).
[CrossRef]

R. W. Day, S. S. Wang, R. Magnusson, “Filter response lineshapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815–1824 (1996).
[CrossRef]

S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Opt. Lett. 34, 2414–2420 (1995).

R. Magnusson, S. S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Opt. 34, 8106–8109 (1995).
[CrossRef] [PubMed]

S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994).
[CrossRef] [PubMed]

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antennas Propag. 42, 567–569 (1994).
[CrossRef]

S. S. Wang, R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993).
[CrossRef] [PubMed]

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[CrossRef]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990).
[CrossRef]

R. Magnusson, S. S. Wang, “Optical filter elements based on waveguide gratings,” in Holographics International ’92, Y. N. Denisyuk, F. Wyrowski, eds., Proc. SPIE1732, 7–18 (1993).
[CrossRef]

Mashev, L.

E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

E. Popov, L. Mashev, “Diffraction anomalies of coated dielectric gratings in conical diffraction mounting,” Opt. Commun. 59, 323–325 (1986).
[CrossRef]

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

L. Mashev, E. Popov, “Diffraction anomalies of dielectric coated gratings,” Opt. Commun. 51, 131–136 (1984).
[CrossRef]

Mashev, L. B.

Maystre, D.

E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

Moharam, M. G.

Morris, G. M.

Nevière, M.

M. Nevière, E. Popov, R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through the poles and zeros of the scattering operator,” J. Opt. Soc. Am. A 12, 513–523 (1995).
[CrossRef]

M. Nevière, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of the resonances of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

M. Nevière, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), Chap. 5, pp. 123–157.

Noponen, E.

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Norton, S. M.

Oliner, A. A.

Peng, S.

Peng, S. T.

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

S. T. Peng, H. L. Bertoni, T. Tamir, “Analysis of thin-film structures with rectangular profiles,” Opt. Commun. 10, 91–94 (1974).
[CrossRef]

Petit, R.

M. Nevière, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of the resonances of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

Pommet, D. A.

Popov, E.

M. Nevière, E. Popov, R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through the poles and zeros of the scattering operator,” J. Opt. Soc. Am. A 12, 513–523 (1995).
[CrossRef]

E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

E. Popov, L. Mashev, “Diffraction anomalies of coated dielectric gratings in conical diffraction mounting,” Opt. Commun. 59, 323–325 (1986).
[CrossRef]

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

L. Mashev, E. Popov, “Diffraction anomalies of dielectric coated gratings,” Opt. Commun. 51, 131–136 (1984).
[CrossRef]

Prokhorov, E. T. N. A. M.

I. A. Avrutskiı̌, V. P. Duraev, E. T. N. A. M. Prokhorov, A. S. Svakhin, V. A. Sychugov, A. V. Tishchenko, “Optimization of the characteristics of a dispersive element based on a corrugated wavguide,” Sov. J. Quantum Electron. 18, 362–365 (1988).
[CrossRef]

Reinisch, R.

Rosenblatt, D.

Saarinen, J.

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Sharon, A.

Sohn, A.

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antennas Propag. 42, 567–569 (1994).
[CrossRef]

Steingrueber, R.

Svakhin, A. S.

I. A. Avrutskiı̌, V. P. Duraev, E. T. N. A. M. Prokhorov, A. S. Svakhin, V. A. Sychugov, A. V. Tishchenko, “Optimization of the characteristics of a dispersive element based on a corrugated wavguide,” Sov. J. Quantum Electron. 18, 362–365 (1988).
[CrossRef]

Sychugov, V. A.

I. A. Avrutskiı̌, V. P. Duraev, E. T. N. A. M. Prokhorov, A. S. Svakhin, V. A. Sychugov, A. V. Tishchenko, “Optimization of the characteristics of a dispersive element based on a corrugated wavguide,” Sov. J. Quantum Electron. 18, 362–365 (1988).
[CrossRef]

I. A. Avrutskiı̌, V. A. Sychugov, “Interference between waveguide modes on reflection of light from the surface of a corrugated waveguide,” Sov. J. Quantum Electron. 18, 366–368 (1988).
[CrossRef]

Tamir, T.

T. Tamir, S. Zhang, “Resonant scattering by multilayered dielectric gratings,” J. Opt. Soc. Am. A 14, 1607–1616 (1997).
[CrossRef]

H. L. Bertoni, L. S. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
[CrossRef]

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

S. T. Peng, H. L. Bertoni, T. Tamir, “Analysis of thin-film structures with rectangular profiles,” Opt. Commun. 10, 91–94 (1974).
[CrossRef]

Tibuleac, S.

S. Tibuleac, R. Magnusson, “Diffractive narrow-band transmission filters based on guided-mode resonance effects in thin-film multilayers,” IEEE Photon. Technol. Lett. 9, 464–466 (1997).
[CrossRef]

S. Tibuleac, R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A 14, 1617–1626 (1997).
[CrossRef]

Tishchenko, A. V.

I. A. Avrutskiı̌, V. P. Duraev, E. T. N. A. M. Prokhorov, A. S. Svakhin, V. A. Sychugov, A. V. Tishchenko, “Optimization of the characteristics of a dispersive element based on a corrugated wavguide,” Sov. J. Quantum Electron. 18, 362–365 (1988).
[CrossRef]

Turunen, J.

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Vincent, P.

M. Nevière, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of the resonances of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

Wang, S. S.

R. W. Day, S. S. Wang, R. Magnusson, “Filter response lineshapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815–1824 (1996).
[CrossRef]

R. Magnusson, S. S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Opt. 34, 8106–8109 (1995).
[CrossRef] [PubMed]

S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Opt. Lett. 34, 2414–2420 (1995).

S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994).
[CrossRef] [PubMed]

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antennas Propag. 42, 567–569 (1994).
[CrossRef]

S. S. Wang, R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993).
[CrossRef] [PubMed]

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[CrossRef]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990).
[CrossRef]

R. Magnusson, S. S. Wang, “Optical filter elements based on waveguide gratings,” in Holographics International ’92, Y. N. Denisyuk, F. Wyrowski, eds., Proc. SPIE1732, 7–18 (1993).
[CrossRef]

Weber, H. G.

Zhang, S.

Appl. Opt. (5)

Appl. Phys. Lett. (1)

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Tibuleac, R. Magnusson, “Diffractive narrow-band transmission filters based on guided-mode resonance effects in thin-film multilayers,” IEEE Photon. Technol. Lett. 9, 464–466 (1997).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antennas Propag. 42, 567–569 (1994).
[CrossRef]

H. L. Bertoni, L. S. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

J. Lightwave Technol. (1)

R. W. Day, S. S. Wang, R. Magnusson, “Filter response lineshapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815–1824 (1996).
[CrossRef]

J. Opt. Soc. Am. A (10)

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Grating structure considered in this paper. The refractive index of the semi-infinite lossless cover region is nc, and that of the semi-infinite substrate region is ns. The grating is defined by its period Λ, its groove depth d, the refractive indices nr and ng of the ridge and groove materials, and the filling factor F, which represents the fraction of each period filled with the ridge material. The grating vector is K=xˆ2π/Λ. For the cases considered in this paper the electric field is polarized in the yˆ direction.  

Fig. 2
Fig. 2

Scattering resonances as a function of (a) groove depth, (b) wavelength, and (c) angle of incidence, for a weakly modulated silicon-on-sapphire grating with nc=1.0, ng=3.46, nr=3.48, ns=1.746, F=0.5, d=0.2233 μm, and Λ=0.5431 μm. The design is for λ0=1.55 μm and θ=0° with E ⊥ K. Note that there are two peaks in (a), corresponding to groove depths for TE0 and TE1 waveguide modes in the grating; the insets show the shapes of these resonances, which have half-widths in groove depth of less than 0.05 nm. The resonances in (b) and (c) are those associated with the TE0 mode.

Fig. 3
Fig. 3

Spectral instability of resonances with angles of incidence around normal is typical of weakly modulated structures with filling factors of F=0.5.

Fig. 4
Fig. 4

Spectral instability of the resonance with angles of incidence around normal, even in the case in which a maximum angular linewidth is predicted for F=1/3.

Fig. 5
Fig. 5

Similar spectral instability of the resonance with the angles of incidence around normal in the second case of maximum angular linewidth (F=2/3).

Fig. 6
Fig. 6

Brillouin diagrams for the grating of Fig. 2, showing (a) βR/K dependence and (b) β1/K dependence on k0. Solid curves are for TE0, and dashed curves are for TE1.

Fig. 7
Fig. 7

Stop-band details for the grating of Fig. 2. Solid curves are for βR and dotted curves are for βI. (a) First stop band. (b) Second stop band. A scaled version of the scattering resonance is included as the long-dashed curve in (b). The open-dotted curve in (b) is a reflection of the βI curve across a line through the peak of the band, and the thin construction lines are included to aid in visualizing the band edges.

Fig. 8
Fig. 8

Stop-band details for the weakly modulated grating with F=1/3. The scattering resonance is seen to fall at the lower band edge.

Fig. 9
Fig. 9

Stop-band details for the weakly modulated grating with F=2/3. The scattering resonance is seen to fall at the upper band edge.

Fig. 10
Fig. 10

Evolution of resonances in the Fd plane as index modulation is increased. Dark areas in the gray scale correspond to regions of low reflectance, and light areas correspond to high reflectance.

Fig. 11
Fig. 11

With increase of the period from Λ=0.5431 μm to Λ=0.80 μm, the effective index of the gratings of Fig. 10(d) is increased, pushing the resonances out into the Fd plane as shown in (a). As in Fig. 10, dark areas in the gray scale correspond to regions of low reflectance, and light areas correspond to high reflectance. The contour lines indicate reflectances ranging from 80% to 100% in steps of 5%. In (b), the reflectance as a function of wavelength is plotted for two points in the Fd plane for normal incidence and for θ=2°. The angular stability of the strongly modulated grating is apparent.

Fig. 12
Fig. 12

Brillouin diagrams for the grating of Fig. 11, showing (a) βR/K dependence and (b) βI/K dependence on k0. Solid curves are for TE0, and dashed curves are for TE1.

Fig. 13
Fig. 13

Second stop-band details for the grating of Fig. 11. The solid and the dotted curves are for TE0 βR and βI, respectively, and the short-dashed and the open-dotted curves are for TE1 βR and βI, respectively. The stop bands of these modes overlap, and the scattering resonance (long-dashed curve) that was associated with the TE0 mode is now found to lie on the upper band edge of the TE1 mode.

Fig. 14
Fig. 14

Extended wavelength plot of the reflectance of the strongly modulated grating of F=0.57 and d=0.53 μm. At an angle of incidence of 2° the originally designed resonance around 1.55 μm remains stable. However, other reflection resonances appear in the region of 1.6823 μm and 2.1384 μm.

Equations (2)

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-I¯¯0¯¯W¯¯W¯¯E¯¯jkzc¯¯/k00¯¯W¯¯Q¯¯-W¯¯Q¯¯E¯¯0¯¯-I¯¯W¯¯E¯¯W¯¯0¯¯-jkzs¯¯/k0W¯¯Q¯¯E¯¯-W¯¯Q¯¯ RTC+C-
=Ijkz,0cI/k000.

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