Abstract

We apply inverse numerical methods to design compact wideband reflectors in which a periodic silicon layer supports resonant leaky modes. Using particle swarm optimization to determine appropriate device thickness, period, and fill factors, we arrive at example reflector designs for both TE and TM polarized input light. As a properly configured grating profile provides added design freedom, we design reflectors with two and four subparts in the period. In TM polarization, a particular single-layer two-part reflector has 520 nm bandwidth whereas the four-part device reaches 600 nm bandwidth. In TE polarization, the corresponding numbers are 125 nm and 495 nm, respectively. We provide a qualitative explanation for the smaller TE-reflector bandwidth. We quantify the effects of deviation from the design parameters and compute the angular response of the elements. As the angle of incidence deviates from normal incidence, narrow transmission channels emerge in the response yielding a bandpass filter with low sidebands. The effects of adding a silica sublayer between a silicon substrate and the periodic silicon layer is investigated. It is found that a properly designed sublayer can extend the reflection bandwidth significantly.

© 2008 Optical Society of America

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    [CrossRef]
  4. G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
    [CrossRef]
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  6. R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992).
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  7. S. S. Wang and R. Magnusson, "Theory and applications of guided-mode resonance filters," Appl. Opt. 32, 2606-2613 (1993).
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  8. Y. Ding and R. Magnusson, "Resonant leaky-mode spectral-band engineering and device applications," Opt. Express 12, 5661-5674 (2004).
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  24. Y. Ding and R. Magnusson, "Use of nondegenerate resonant leaky modes to fashion diverse optical spectra," Opt. Express 12, 1885-1891 (2004).
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    [CrossRef]
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    [CrossRef]
  27. R. Magnusson and M. Shokooh-Saremi, "Physical basis for wideband resonant reflectors," Opt. Express 16, 3456-3462 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  29. R. Magnusson, Y. Ding, K. J. Lee, D. Shin, P. S. Priambodo, P. P. Young, and T. A. Maldonado, "Photonic devices enabled by waveguide-mode resonance effect in periodically modulated films," Proc. SPIE 5225, 20-34 (2003).
    [CrossRef]
  30. Y. Ding and R. Magnusson, "Doubly resonant single-layer bandpass optical filter," Opt. Lett. 29, 1135-1137 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  35. S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
    [CrossRef]
  36. R. Magnusson and T. K. Gaylord, "Equivalence of multiwave coupled-wave theory and modal theory for periodic-media diffraction," J. Opt. Soc. Am. 68, 1777-1779 (1978).
    [CrossRef]

2008 (1)

2007 (3)

2006 (3)

2004 (7)

D. Gerace and L. C. Andreani, "Gap maps and intrinsic diffraction losses in one-dimensional photonic crystal slabs," Phys. Rev. E 69, 056603 (2004).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, "Ultrabroadband mirror using low-index cladding subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, "Broad-band mirror (1.12-1.62 μm) using a subwavelength grating," IEEE Photon. Technol. Lett. 16, 1676-1678 (2004).
[CrossRef]

W. Suh and S. Fan, "All-pass transmission or flattop reflection filters using a single photonic crystal slab," Appl. Phys. Lett. 84, 4905-4907 (2004).
[CrossRef]

Y. Ding and R. Magnusson, "Use of nondegenerate resonant leaky modes to fashion diverse optical spectra," Opt. Express 12, 1885-1891 (2004).
[CrossRef] [PubMed]

Y. Ding and R. Magnusson, "Doubly resonant single-layer bandpass optical filter," Opt. Lett. 29, 1135-1137 (2004).
[CrossRef] [PubMed]

Y. Ding and R. Magnusson, "Resonant leaky-mode spectral-band engineering and device applications," Opt. Express 12, 5661-5674 (2004).
[CrossRef] [PubMed]

2003 (1)

R. Magnusson, Y. Ding, K. J. Lee, D. Shin, P. S. Priambodo, P. P. Young, and T. A. Maldonado, "Photonic devices enabled by waveguide-mode resonance effect in periodically modulated films," Proc. SPIE 5225, 20-34 (2003).
[CrossRef]

2002 (1)

Z. S. Liu and R. Magnusson, "Concept of multiorder multimode resonant optical filters," IEEE Photon. Technol. Lett. 14, 1091-1093 (2002).
[CrossRef]

2001 (3)

1999 (1)

1998 (1)

1996 (2)

S. Peng and M. Morris, "Resonant scattering from two-dimensional gratings," J. Opt. Soc. Am. A 13, 993-1005 (1996).

O. Parriaux, V. A. Sychugov, and A. Tishchenko, "Coupling gratings as waveguide functional element," Pure Appl. Opt. 5, 453-469 (1996).
[CrossRef]

1995 (1)

1993 (1)

1992 (1)

R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992).
[CrossRef]

1990 (1)

M. T. Gale, K. Knop, and R. Morf, "Zero-order diffractive microstructures for security applications," Proc. SPIE 1210, 83-89 (1990).
[CrossRef]

1989 (1)

I. A. Avrutsky and V. A. Sychugov, "Reflection of a beam of finite size from a corrugated waveguide," J. Mod. Opt. 36, 1527-1539 (1989).
[CrossRef]

1986 (1)

E. Popov, L. Mashev, and D. Maystre, "Theoretical study of anomalies of coated dielectric gratings," Opt. Acta 33, 607-619 (1986).
[CrossRef]

1985 (3)

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
[CrossRef]

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

T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
[CrossRef]

1979 (1)

P. Vincent and M. Neviere, "Corrugated dielectric waveguides: A numerical study of the second-order stop bands," Appl. Phys. 20, 345-351 (1979).
[CrossRef]

1978 (1)

1975 (1)

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

Andreani, L. C.

D. Gerace and L. C. Andreani, "Gap maps and intrinsic diffraction losses in one-dimensional photonic crystal slabs," Phys. Rev. E 69, 056603 (2004).
[CrossRef]

Astratov, V. A.

Avrutsky, I. A.

I. A. Avrutsky and V. A. Sychugov, "Reflection of a beam of finite size from a corrugated waveguide," J. Mod. Opt. 36, 1527-1539 (1989).
[CrossRef]

Bertoni, H. L.

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

Boonruang, S.

Boyko, O.

Brundrett, D. L.

Chang, J.-Y.

Chang-Hasnain, C. J.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, "Ultrabroadband mirror using low-index cladding subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, "Broad-band mirror (1.12-1.62 μm) using a subwavelength grating," IEEE Photon. Technol. Lett. 16, 1676-1678 (2004).
[CrossRef]

Chen, L.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, "Broad-band mirror (1.12-1.62 μm) using a subwavelength grating," IEEE Photon. Technol. Lett. 16, 1676-1678 (2004).
[CrossRef]

Chou, Y.-H.

Cowan, A. R.

A. R. Cowan, P. Paddon, V. Pacradouni, and J. F. Young, "Resonant scattering and mode coupling in two-dimensional textured planar waveguides," J. Opt. Soc. Am. A. 18, 1160-1170 (2001).
[CrossRef]

Culshaw, I. S.

De La Rue, R. M.

Deng, Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, "Ultrabroadband mirror using low-index cladding subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004).
[CrossRef]

Ding, Y.

Dunn, S. C.

Fan, S.

W. Suh and S. Fan, "All-pass transmission or flattop reflection filters using a single photonic crystal slab," Appl. Phys. Lett. 84, 4905-4907 (2004).
[CrossRef]

Fehrembach, A.-L.

Gale, M. T.

M. T. Gale, K. Knop, and R. Morf, "Zero-order diffractive microstructures for security applications," Proc. SPIE 1210, 83-89 (1990).
[CrossRef]

Gaylord, T. K.

Gerace, D.

D. Gerace and L. C. Andreani, "Gap maps and intrinsic diffraction losses in one-dimensional photonic crystal slabs," Phys. Rev. E 69, 056603 (2004).
[CrossRef]

Glytsis, E. N.

Golubenko, G. A.

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
[CrossRef]

Grann, E. B.

Greenwell, A.

Hane, K.

Y. Kanamori, T. Kitani, and K. Hane, "Guided-mode resonant grating filter fabricated on silicon-on-insulator substrate," Jpn. J. Appl. Phys. 45, 1883-1885 (2006).
[CrossRef]

Hsu, C.-L.

Huang, M. C. Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, "Ultrabroadband mirror using low-index cladding subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, "Broad-band mirror (1.12-1.62 μm) using a subwavelength grating," IEEE Photon. Technol. Lett. 16, 1676-1678 (2004).
[CrossRef]

Jacob, D. K.

Kanamori, Y.

Y. Kanamori, T. Kitani, and K. Hane, "Guided-mode resonant grating filter fabricated on silicon-on-insulator substrate," Jpn. J. Appl. Phys. 45, 1883-1885 (2006).
[CrossRef]

Kitani, T.

Y. Kanamori, T. Kitani, and K. Hane, "Guided-mode resonant grating filter fabricated on silicon-on-insulator substrate," Jpn. J. Appl. Phys. 45, 1883-1885 (2006).
[CrossRef]

Knop, K.

M. T. Gale, K. Knop, and R. Morf, "Zero-order diffractive microstructures for security applications," Proc. SPIE 1210, 83-89 (1990).
[CrossRef]

Krauss, T. F.

Lee, C.-C.

Lee, K. J.

R. Magnusson, Y. Ding, K. J. Lee, D. Shin, P. S. Priambodo, P. P. Young, and T. A. Maldonado, "Photonic devices enabled by waveguide-mode resonance effect in periodically modulated films," Proc. SPIE 5225, 20-34 (2003).
[CrossRef]

Lemarchand, F.

Liu, Y.-C.

Liu, Z. S.

Z. S. Liu and R. Magnusson, "Concept of multiorder multimode resonant optical filters," IEEE Photon. Technol. Lett. 14, 1091-1093 (2002).
[CrossRef]

Magnusson, R.

R. Magnusson and M. Shokooh-Saremi, "Physical basis for wideband resonant reflectors," Opt. Express 16, 3456-3462 (2008).
[CrossRef] [PubMed]

Y. Ding and R. Magnusson, "Band gaps and leaky-wave effects in resonant photonic-crystal waveguides," Opt. Express 15, 680-694 (2007).
[CrossRef] [PubMed]

M. Shokooh-Saremi and R. Magnusson, "Particle swarm optimization and its application to the design of diffraction grating filters," Opt. Lett. 32, 894-896 (2007).
[CrossRef] [PubMed]

Y. Ding and R. Magnusson, "Doubly resonant single-layer bandpass optical filter," Opt. Lett. 29, 1135-1137 (2004).
[CrossRef] [PubMed]

Y. Ding and R. Magnusson, "Resonant leaky-mode spectral-band engineering and device applications," Opt. Express 12, 5661-5674 (2004).
[CrossRef] [PubMed]

Y. Ding and R. Magnusson, "Use of nondegenerate resonant leaky modes to fashion diverse optical spectra," Opt. Express 12, 1885-1891 (2004).
[CrossRef] [PubMed]

R. Magnusson, Y. Ding, K. J. Lee, D. Shin, P. S. Priambodo, P. P. Young, and T. A. Maldonado, "Photonic devices enabled by waveguide-mode resonance effect in periodically modulated films," Proc. SPIE 5225, 20-34 (2003).
[CrossRef]

Z. S. Liu and R. Magnusson, "Concept of multiorder multimode resonant optical filters," IEEE Photon. Technol. Lett. 14, 1091-1093 (2002).
[CrossRef]

S. Tibuleac and R. Magnusson, "Narrow-linewidth bandpass filters with diffractive thin-film layers," Opt. Lett. 26, 584-586 (2001).
[CrossRef]

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

R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992).
[CrossRef]

R. Magnusson and T. K. Gaylord, "Equivalence of multiwave coupled-wave theory and modal theory for periodic-media diffraction," J. Opt. Soc. Am. 68, 1777-1779 (1978).
[CrossRef]

Maldonado, T. A.

R. Magnusson, Y. Ding, K. J. Lee, D. Shin, P. S. Priambodo, P. P. Young, and T. A. Maldonado, "Photonic devices enabled by waveguide-mode resonance effect in periodically modulated films," Proc. SPIE 5225, 20-34 (2003).
[CrossRef]

Mashev, L.

E. Popov, L. Mashev, and D. Maystre, "Theoretical study of anomalies of coated dielectric gratings," Opt. Acta 33, 607-619 (1986).
[CrossRef]

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

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, "Ultrabroadband mirror using low-index cladding subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, "Broad-band mirror (1.12-1.62 μm) using a subwavelength grating," IEEE Photon. Technol. Lett. 16, 1676-1678 (2004).
[CrossRef]

Maystre, D.

E. Popov, L. Mashev, and D. Maystre, "Theoretical study of anomalies of coated dielectric gratings," Opt. Acta 33, 607-619 (1986).
[CrossRef]

Moharam, M. G.

Morf, R.

M. T. Gale, K. Knop, and R. Morf, "Zero-order diffractive microstructures for security applications," Proc. SPIE 1210, 83-89 (1990).
[CrossRef]

Morris, M.

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, "Ultrabroadband mirror using low-index cladding subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004).
[CrossRef]

Neviere, M.

P. Vincent and M. Neviere, "Corrugated dielectric waveguides: A numerical study of the second-order stop bands," Appl. Phys. 20, 345-351 (1979).
[CrossRef]

Pacradouni, V.

A. R. Cowan, P. Paddon, V. Pacradouni, and J. F. Young, "Resonant scattering and mode coupling in two-dimensional textured planar waveguides," J. Opt. Soc. Am. A. 18, 1160-1170 (2001).
[CrossRef]

Paddon, P.

A. R. Cowan, P. Paddon, V. Pacradouni, and J. F. Young, "Resonant scattering and mode coupling in two-dimensional textured planar waveguides," J. Opt. Soc. Am. A. 18, 1160-1170 (2001).
[CrossRef]

Parriaux, O.

O. Parriaux, V. A. Sychugov, and A. Tishchenko, "Coupling gratings as waveguide functional element," Pure Appl. Opt. 5, 453-469 (1996).
[CrossRef]

Peng, S.

Peng, S. T.

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

Pommet, D. A.

Popov, E.

E. Popov, L. Mashev, and D. Maystre, "Theoretical study of anomalies of coated dielectric gratings," Opt. Acta 33, 607-619 (1986).
[CrossRef]

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

Priambodo, P. S.

R. Magnusson, Y. Ding, K. J. Lee, D. Shin, P. S. Priambodo, P. P. Young, and T. A. Maldonado, "Photonic devices enabled by waveguide-mode resonance effect in periodically modulated films," Proc. SPIE 5225, 20-34 (2003).
[CrossRef]

Sentenac, A.

Shin, D.

R. Magnusson, Y. Ding, K. J. Lee, D. Shin, P. S. Priambodo, P. P. Young, and T. A. Maldonado, "Photonic devices enabled by waveguide-mode resonance effect in periodically modulated films," Proc. SPIE 5225, 20-34 (2003).
[CrossRef]

Shokooh-Saremi, M.

Skolnick, M. C.

Stevenson, R. M.

Suh, W.

W. Suh and S. Fan, "All-pass transmission or flattop reflection filters using a single photonic crystal slab," Appl. Phys. Lett. 84, 4905-4907 (2004).
[CrossRef]

Suzuki, Y.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, "Broad-band mirror (1.12-1.62 μm) using a subwavelength grating," IEEE Photon. Technol. Lett. 16, 1676-1678 (2004).
[CrossRef]

Svakhin, A. S.

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Talneau, A.

Tamir, T.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
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G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
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R. Magnusson, Y. Ding, K. J. Lee, D. Shin, P. S. Priambodo, P. P. Young, and T. A. Maldonado, "Photonic devices enabled by waveguide-mode resonance effect in periodically modulated films," Proc. SPIE 5225, 20-34 (2003).
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Appl. Opt. (2)

Appl. Phys. (1)

P. Vincent and M. Neviere, "Corrugated dielectric waveguides: A numerical study of the second-order stop bands," Appl. Phys. 20, 345-351 (1979).
[CrossRef]

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R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992).
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W. Suh and S. Fan, "All-pass transmission or flattop reflection filters using a single photonic crystal slab," Appl. Phys. Lett. 84, 4905-4907 (2004).
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Figures (20)

Fig. 1.
Fig. 1.

Basic structure and parameters of the GMR reflector. Λ, d, and F1 to F4 denote the grating period, thickness, and fill factors, respectively. dL is the silica sublayer thickness. The incidence medium is air, substrate is silicon, nH=nSi=3.48, nL=nair=1.0, and nsilica=1.48.

Fig. 2.
Fig. 2.

Reflectance and transmittance spectra (a) linear and (b) logarithmic of a PSO-designed broadband reflector for TM polarization. The resonance wavelengths are (i) 1.495 µm, (ii) 1.620 µm, and (iii) 1.839 µm.

Fig. 3.
Fig. 3.

Amplitude of the magnetic (modal) field (Hy(z)) inside the grating structure and in the surrounding media for the three resonances in Fig. 2 at (a) 1.495 µm, (b) 1.620 µm, and (c) 1.839 µm.

Fig. 4.
Fig. 4.

(a) Reflectance map R0(λ,d) drawn versus wavelength and grating thickness. (b) Corresponding transmittance map T0(λ,d) in dB.

Fig. 5.
Fig. 5.

(a) Magnified transmission map (in dB, Fig. 4(b)) of the reflector for thicknesses between 0.2 µm and 0.9 µm around the optimum design thickness (dotted line). (b) Reflection spectra for thicknesses at two points near the optimal thickness (0.455 and 0.520 µm) in comparison to that for the optimal thickness (0.490 µm); note vertical axis scale change. Amplitude of the leaky-mode magnetic field for two points on the resonance locus in Fig. 5(a) but far from the optimal condition: (c) d=0.217 µm, λ=1.363 µm, {point (i)}, and (d) d=0.843 µm, λ=1.883 µm {point (ii)}.

Fig. 6.
Fig. 6.

(a) R0(λ,d) map for a low-refractive-index contrast structure (nH=2.0 and nL=1.3417). (b) Calculated modal curves for the first four leaky modes excited by the first diffraction order in an equivalent homogenous film with refractive index of 1.92. (c,d) Magnetic modal field amplitudes corresponding to curves I (at λ=1.1849 µm and d=0.3293 µm (TM0)) and IV (at λ =1.1466 µm and d=1.913 µm (TM3)) in Fig. 6(a), respectively.

Fig. 7.
Fig. 7.

(a) Angular sensitivity of the reflection spectra of the broadband reflector. ~ ±1° deviation from normal incidence induces a transmission channel in the reflection band. (b) Samples of reflection spectra under normal and off-normal incidence.

Fig. 8.
Fig. 8.

Sensitivity of the reflectance R0 to the structural parameters. In each part only one parameter is variable and the other two parameters are kept at their optimal values (a) Reflectivity map with period deviation, (b) Reflectivity map with thickness deviation, and (c) Reflectivity map with fill factor deviation. In each case, the optimum value is shown by a dotted line.

Fig. 9.
Fig. 9.

(a) Reflectance and transmittance spectra of a broadband reflector for TE polarization on linear and logarithmic scales. (b) Map of the amplitude of the total electric field (Ey(z)) in the grating and surrounding media at the resonance wavelength (λ=1.558 µm).

Fig. 10.
Fig. 10.

(a) Color-coded R0(λ,d) map for the TE reflector. (b) Reflectance map for reduced refractive contrast with nH=3.0 and nL=1.5898. (c) Reflectance map for reduced contrast with nH=2.3 and nL=2.0856, and (d) Modal characteristic curves for the equivalent homogeneous slab waveguide corresponding to (c) with the layer’s refractive index set to 2.167. The optimal thickness is shown by the dotted line in part (a).

Fig.11.
Fig.11.

a) Modal curves for equivalent homogeneous slab waveguides corresponding to the high-contrast reflectors in Figs. 2 (TM) and 9 (TE) using second-order effective indices. (a) TE reflector (nf=3.365), and (b) TM reflector (nf=3.1577).

Fig.12.
Fig.12.

a) Angular sensitivity of the spectra of the TE reflector. (b) Samples of the reflection spectra for normal (θ=0°) and off-normal (θ=+3°) incidence.

Fig. 13.
Fig. 13.

Maps showing the sensitivity of the reflection spectra to (a) period, (b) thickness, and (c) fill factor for TE polarization. The optimal parameters are denoted by the dotted line in each case.

Fig. 14.
Fig. 14.

(a) Reflectance and transmittance of a resonant reflector with a silica sublayer for TM polarization (logarithmic scale). (b) Reflection spectra with and without the sublayer.

Fig. 15.
Fig. 15.

(a) Reflectance and transmittance spectra of the TE reflector with silica sublayer on a logarithmic scale. (b) Reflection spectra with and without the sublayer.

Fig. 16.
Fig. 16.

(a) Reflectance (solid line) and transmittance (dashed line) spectra of the four-part broadband reflector for TM polarization. (b) R0(λ,d) map for this device. (c) Transmittance map T0(λ,d) in dB. (d-f) Magnetic field amplitude distribution in the device and surrounding media for three leaky-mode resonances at 1.627 µm, 1.744 µm, and 2.015 µm, respectively.

Fig. 17.
Fig. 17.

(a) Angular sensitivity of the four-part broadband reflector for TM polarization. (b) Samples of reflection spectra for normal and off-normal incidence.

Fig. 18.
Fig. 18.

(a) Reflectance and transmittance spectra of the four-part broadband reflector for TE polarization. (b) Color-coded R0(λ,d) map. (c) T0(λ,d) map in dB. (d–f) Amplitudes of electric field modal profiles for the three resonance leaky-modes at 1.489 µm, 1.642 µm, and 1.872 µm, respectively.

Fig. 19.
Fig. 19.

(a) Angular sensitivity of the four-part broadband reflector. (b) Samples of reflection spectra for normal (θ=0°) and oblique (θ=+3°) incidence.

Fig. 20.
Fig. 20.

(a) Color-coded R0(λ,dL) map showing the effect of adding a silica sublayer to the fourpart reflector designed in section 4.2 for TM polarization. (b) Same for TE polarization.

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