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]
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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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  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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  25. 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]
  26. 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]
  27. R. Magnusson and M. Shokooh-Saremi, "Physical basis for wideband resonant reflectors," Opt. Express 16, 3456-3462 (2008).
    [CrossRef]
  28. S. Tibuleac and R. Magnusson, "Narrow-linewidth bandpass filters with diffractive thin-film layers," Opt. Lett. 26, 584-586 (2001).
    [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).
  30. Y. Ding and R. Magnusson, "Doubly resonant single-layer bandpass optical filter," Opt. Lett. 29, 1135-1137 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [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).

2008

2007

2006

2004

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]

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

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

2003

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).

2002

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

2001

1999

1998

1996

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

1993

1992

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

1990

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

1989

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

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

1985

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

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

1975

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).

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).

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).

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]

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]

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

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

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

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).

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).

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).

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).

Mashev, L.

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

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).

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).

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).

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).

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).

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.

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]

Sychugov, V. A.

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

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]

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]

Talneau, A.

Tamir, T.

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