Abstract

In this paper, we address resonant leaky-mode reflectors made with a periodic silicon layer on an insulating substrate. Our objective is to explain the physical basis for their operation and to quantify the bandwidth provided by a single resonant layer by illustrative examples for both TE and TM polarized incident light. We find that the number of participating leaky modes and their excitation conditions affect the bandwidth. We show that recently reported experimental [1, 2] wideband reflectors operate under leaky-mode resonance. These compact reflectors are new elements with many potential applications in photonic systems. The results presented explaining their physical basis will aid in their continued development.

© 2008 Optical Society of America

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  1. C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, "Broad-band mirror (1.12-1.62 ?m) using a subwavelength grating," IEEE Photon. Technol. Lett. 16, 1676-1678 (2004).
    [CrossRef]
  2. M. C. Y Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index- contrast subwavelength grating," Nature Photonics 1, 119-122 (2007).
    [CrossRef]
  3. P. Vincent and M. Neviere, "Corrugated dielectric waveguides: A numerical study of the second-order stop bands," Appl. Phys. 20, 345-351 (1979).
    [CrossRef]
  4. L. Mashev and E. Popov, "Zero order anomaly of dielectric coated gratings," Opt. Comm. 55, 377-380 (1985).
  5. E. Popov, L. Mashev, and D. Maystre, "Theoretical study of anomalies of coated dielectric gratings," Opt. Acta 33, 607-619 (1986).
  6. 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]
  7. 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).
  8. R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61,1022-1024 (1992).
    [CrossRef]
  9. S. S. Wang and R. Magnusson, "Theory and applications of guided-mode resonance filters," Appl. Opt. 32,2606-2613 (1993).
  10. Y. Ding and R. Magnusson, "Resonant leaky-mode spectral-band engineering and device applications," Opt. Express 12, 5661-5674 (2004).
    [CrossRef]
  11. H. A. Macleod, Thin-Film Optical Filters, (McGraw-Hill, New York, 1989).
  12. Q4. A. E. Willner, "All mirrors are not created equal," Nature Photonics 1, 87-88 (2007).
    [CrossRef]
  13. A. Yariv and P. Yeh., Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, New York, 2007).
  14. A. Hardy, D. F. Welch, and W. Streifer, "Analysis of second-order gratings," IEEE J. Quantum Electron. 25, 2096-2105 (1989).
    [CrossRef]
  15. Y. Ding and R. Magnusson, "Band gaps and leaky-wave effects in resonant photonic-crystal waveguides," Opt. Express 15, 680-694 (2007).
  16. D. Rosenblatt, A. Sharon, and A. A. Friesem, "Resonant grating waveguide structures," IEEE J. Quantum Electron. 33, 2038-2059 (1997).
    [CrossRef]
  17. R. F. Kazarinov and C. H. Henry, "Second-order distributed feedback lasers with mode selection provided by first-order radiation loss," IEEE J. Quantum Electron. 21, 144-150 (1985).
    [CrossRef]
  18. T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
  19. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: Enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077-1086 (1995).
  20. S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
  21. R. Eberhart and J. Kennedy, "Particle swarm optimization," in Proceedings of IEEE Conference on Neural Networks (IEEE, 1995) 1942-1948.
  22. 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]
  23. 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]

2007

M. C. Y Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index- contrast subwavelength grating," Nature Photonics 1, 119-122 (2007).
[CrossRef]

Q4. A. E. Willner, "All mirrors are not created equal," Nature Photonics 1, 87-88 (2007).
[CrossRef]

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

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]

2004

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 ?m) using a subwavelength grating," IEEE Photon. Technol. Lett. 16, 1676-1678 (2004).
[CrossRef]

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

1997

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

1995

1993

1992

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

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).

A. Hardy, D. F. Welch, and W. Streifer, "Analysis of second-order gratings," IEEE J. Quantum Electron. 25, 2096-2105 (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. Comm. 55, 377-380 (1985).

R. F. Kazarinov and C. H. Henry, "Second-order distributed feedback lasers with mode selection provided by first-order radiation loss," IEEE J. Quantum Electron. 21, 144-150 (1985).
[CrossRef]

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

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]

1975

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

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).

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).

Chang-Hasnain, C. J.

M. C. Y Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index- contrast subwavelength grating," Nature Photonics 1, 119-122 (2007).
[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 ?m) using a subwavelength grating," IEEE Photon. Technol. Lett. 16, 1676-1678 (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]

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 ?m) using a subwavelength grating," IEEE Photon. Technol. Lett. 16, 1676-1678 (2004).
[CrossRef]

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.

Friesem, A. A.

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

Gaylord, T. K.

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.

Hardy, A.

A. Hardy, D. F. Welch, and W. Streifer, "Analysis of second-order gratings," IEEE J. Quantum Electron. 25, 2096-2105 (1989).
[CrossRef]

Henry, C. H.

R. F. Kazarinov and C. H. Henry, "Second-order distributed feedback lasers with mode selection provided by first-order radiation loss," IEEE J. Quantum Electron. 21, 144-150 (1985).
[CrossRef]

Huang, M. C. Y

M. C. Y Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index- contrast subwavelength grating," Nature Photonics 1, 119-122 (2007).
[CrossRef]

Huang, M. C. 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 ?m) using a subwavelength grating," IEEE Photon. Technol. Lett. 16, 1676-1678 (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]

Kazarinov, R. F.

R. F. Kazarinov and C. H. Henry, "Second-order distributed feedback lasers with mode selection provided by first-order radiation loss," IEEE J. Quantum Electron. 21, 144-150 (1985).
[CrossRef]

Magnusson, R.

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. Comm. 55, 377-380 (1985).

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 ?m) 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.

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]

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).

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. Comm. 55, 377-380 (1985).

Rosenblatt, D.

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

Sharon, A.

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

Shokooh-Saremi, M.

Streifer, W.

A. Hardy, D. F. Welch, and W. Streifer, "Analysis of second-order gratings," IEEE J. Quantum Electron. 25, 2096-2105 (1989).
[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 ?m) 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.

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).

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]

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).

Tishchenko, A. V.

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]

Vincent, P.

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

Wang, S. S.

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]

Welch, D. F.

A. Hardy, D. F. Welch, and W. Streifer, "Analysis of second-order gratings," IEEE J. Quantum Electron. 25, 2096-2105 (1989).
[CrossRef]

Willner, A. E.

Q4. A. E. Willner, "All mirrors are not created equal," Nature Photonics 1, 87-88 (2007).
[CrossRef]

Zhou, Y.

M. C. Y Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index- contrast subwavelength grating," Nature Photonics 1, 119-122 (2007).
[CrossRef]

Appl. Opt.

Appl. Phys.

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

Appl. Phys. Lett.

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

IEEE J. Quantum Electron.

A. Hardy, D. F. Welch, and W. Streifer, "Analysis of second-order gratings," IEEE J. Quantum Electron. 25, 2096-2105 (1989).
[CrossRef]

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

R. F. Kazarinov and C. H. Henry, "Second-order distributed feedback lasers with mode selection provided by first-order radiation loss," IEEE J. Quantum Electron. 21, 144-150 (1985).
[CrossRef]

IEEE Photon. Technol. Lett.

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

IEEE Trans. Microwave Theory Tech.

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

J. Mod. Opt.

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).

J. Opt. Soc. Am. A

Nature Photonics

M. C. Y Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index- contrast subwavelength grating," Nature Photonics 1, 119-122 (2007).
[CrossRef]

Q4. A. E. Willner, "All mirrors are not created equal," Nature Photonics 1, 87-88 (2007).
[CrossRef]

Opt. Acta

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

Opt. Comm.

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

Opt. Express

Opt. Lett.

Proc. IEEE

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

Sov. J. Quantum Electron.

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]

Other

H. A. Macleod, Thin-Film Optical Filters, (McGraw-Hill, New York, 1989).

A. Yariv and P. Yeh., Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, New York, 2007).

R. Eberhart and J. Kennedy, "Particle swarm optimization," in Proceedings of IEEE Conference on Neural Networks (IEEE, 1995) 1942-1948.

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