Abstract

We present a rigorous numerical analysis on tunable characteristics of guided-mode resonances (GMRs) in coupled gratings. Two schemes of strong and negligible evanescent coupling of guided modes are treated. Both show wide range tunability. In the case of strong evanescent coupling, independent control of the center wavelength and the linwidth of the resonance is obtained via variations of a gap size between the gratings and lateral alignment conditions. We believe that this characteristic will provide a useful means to realize a tunable filter in conjunction with micro/nano-electromechanical system technologies. We also present a generalized theoretical analysis on the tunable characteristics of the GMRs in coupled gratings, which is qualitatively in good agreement with the numerical analysis.

© 2009 OSA

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  1. P. Vincent and M. Nerviere, “Corrugated dielectric waveguides: A numerical study of the second-order stop band,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
    [CrossRef]
  2. R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
    [CrossRef]
  3. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
    [CrossRef]
  4. Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12(23), 5661–5674 (2004).
    [CrossRef] [PubMed]
  5. C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chan-Hasnain, “Ultrabroadband mirror using low-index cladding subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
    [CrossRef]
  6. R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008).
    [CrossRef] [PubMed]
  7. K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
    [CrossRef]
  8. R. Magnusson and M. Shokooh-Saremi, “Widely tunable guided-mode resonance nanoelectromechanical RGB pixels,” Opt. Express 15(17), 10903–10910 (2007).
    [CrossRef] [PubMed]
  9. D. Wawro, S. Tibuleac, and R. Magnusson, “Optical waveguide-mode resonant biosensors Optical,” Imaging Sensors and Systems for Homeland Security Applications, (Springer New York, 2006).
  10. M. Borodisky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, “Spontaneous emission extraction and Purcell enhancement from thin-Film 2-D photonic crystal,” J. Lightwave Technol. 17(11), 2096–2112 (1999).
    [CrossRef]
  11. H. Y. Ryu, Y. H. Lee, R. L. Sellin, and D. Bimberg, “Over 30-fold enhancement of light extraction from free-standing photonic crystal slabs with InGaAs quantum dots at low temperature,” Appl. Phys. Lett. 79(22), 3573–3575 (2001).
    [CrossRef]
  12. M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
    [CrossRef]
  13. W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82(13), 1999–2001 (2003).
    [CrossRef]
  14. W. Suh and S. Fan, “Mechanically switchable photonic crystal filter with either all-pass transmission or flat-top reflection characteristics,” Opt. Lett. 28(19), 1763–1765 (2003).
    [CrossRef] [PubMed]
  15. Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006).
    [CrossRef]
  16. W. Nakagawa and Y. Fainman, “Tunable optical nanocavity based on modulation of near-field coupling between subwavelength periodic nanostructures,” IEEE J. Sel. Top. Quantum Electron. 10(3), 478–483 (2004).
    [CrossRef]
  17. H. A. Haus, Waves and Field in Optoelectronics (Englewood Cliffs, NJ: Prentice-Hall, 1984).
  18. M. Foresti, L. Menez, and A. V. Tishchenko, “Modal method in deep metal-dielectric gratings: the deceive role of hidden modes,” J. Opt. Soc. Am. 23(10), 2501 (2006).
    [CrossRef]
  19. Y. Kanamori, T. Kitani, and K. Hane, “Control of guided resonance in a photonic crystal slab using microelectromechanical actuators,” Appl. Phys. Lett. 90(3), 031911 (2007).
    [CrossRef]
  20. Y. Ding and R. Magnusson, “Use of nondegenerate resonant leaky modes to fashion diverse optical spectra,” Opt. Express 12(9), 1885–1891 (2004).
    [CrossRef] [PubMed]
  21. S. Tibuleac and R. Magnusson, “Narrow-linewidth bandpass filters with diffractive thin-film layers,” Opt. Lett. 26(9), 584–586 (2001).
    [CrossRef] [PubMed]
  22. Y. Ding and R. Magnusson, “Doubly resonant single-layer bandpass optical filters,” Opt. Lett. 29(10), 1135–1137 (2004).
    [CrossRef] [PubMed]

2008 (2)

R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008).
[CrossRef] [PubMed]

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

2007 (2)

R. Magnusson and M. Shokooh-Saremi, “Widely tunable guided-mode resonance nanoelectromechanical RGB pixels,” Opt. Express 15(17), 10903–10910 (2007).
[CrossRef] [PubMed]

Y. Kanamori, T. Kitani, and K. Hane, “Control of guided resonance in a photonic crystal slab using microelectromechanical actuators,” Appl. Phys. Lett. 90(3), 031911 (2007).
[CrossRef]

2006 (2)

Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006).
[CrossRef]

M. Foresti, L. Menez, and A. V. Tishchenko, “Modal method in deep metal-dielectric gratings: the deceive role of hidden modes,” J. Opt. Soc. Am. 23(10), 2501 (2006).
[CrossRef]

2004 (5)

W. Nakagawa and Y. Fainman, “Tunable optical nanocavity based on modulation of near-field coupling between subwavelength periodic nanostructures,” IEEE J. Sel. Top. Quantum Electron. 10(3), 478–483 (2004).
[CrossRef]

Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12(23), 5661–5674 (2004).
[CrossRef] [PubMed]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chan-Hasnain, “Ultrabroadband mirror using low-index cladding subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Y. Ding and R. Magnusson, “Use of nondegenerate resonant leaky modes to fashion diverse optical spectra,” Opt. Express 12(9), 1885–1891 (2004).
[CrossRef] [PubMed]

Y. Ding and R. Magnusson, “Doubly resonant single-layer bandpass optical filters,” Opt. Lett. 29(10), 1135–1137 (2004).
[CrossRef] [PubMed]

2003 (2)

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82(13), 1999–2001 (2003).
[CrossRef]

W. Suh and S. Fan, “Mechanically switchable photonic crystal filter with either all-pass transmission or flat-top reflection characteristics,” Opt. Lett. 28(19), 1763–1765 (2003).
[CrossRef] [PubMed]

2002 (1)

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

2001 (2)

H. Y. Ryu, Y. H. Lee, R. L. Sellin, and D. Bimberg, “Over 30-fold enhancement of light extraction from free-standing photonic crystal slabs with InGaAs quantum dots at low temperature,” Appl. Phys. Lett. 79(22), 3573–3575 (2001).
[CrossRef]

S. Tibuleac and R. Magnusson, “Narrow-linewidth bandpass filters with diffractive thin-film layers,” Opt. Lett. 26(9), 584–586 (2001).
[CrossRef] [PubMed]

1999 (2)

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

M. Borodisky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, “Spontaneous emission extraction and Purcell enhancement from thin-Film 2-D photonic crystal,” J. Lightwave Technol. 17(11), 2096–2112 (1999).
[CrossRef]

1992 (1)

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[CrossRef]

1979 (1)

P. Vincent and M. Nerviere, “Corrugated dielectric waveguides: A numerical study of the second-order stop band,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[CrossRef]

Bhat, R.

Bimberg, D.

H. Y. Ryu, Y. H. Lee, R. L. Sellin, and D. Bimberg, “Over 30-fold enhancement of light extraction from free-standing photonic crystal slabs with InGaAs quantum dots at low temperature,” Appl. Phys. Lett. 79(22), 3573–3575 (2001).
[CrossRef]

Borodisky, M.

Britton, B.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Chan-Hasnain, C. J.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chan-Hasnain, “Ultrabroadband mirror using low-index cladding subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Coccioli, R.

Deng, Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chan-Hasnain, “Ultrabroadband mirror using low-index cladding subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Ding, Y.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006).
[CrossRef]

Y. Ding and R. Magnusson, “Use of nondegenerate resonant leaky modes to fashion diverse optical spectra,” Opt. Express 12(9), 1885–1891 (2004).
[CrossRef] [PubMed]

Y. Ding and R. Magnusson, “Doubly resonant single-layer bandpass optical filters,” Opt. Lett. 29(10), 1135–1137 (2004).
[CrossRef] [PubMed]

Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12(23), 5661–5674 (2004).
[CrossRef] [PubMed]

Dodabalapur, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

Donkor, E.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Fainman, Y.

W. Nakagawa and Y. Fainman, “Tunable optical nanocavity based on modulation of near-field coupling between subwavelength periodic nanostructures,” IEEE J. Sel. Top. Quantum Electron. 10(3), 478–483 (2004).
[CrossRef]

Fan, S.

W. Suh and S. Fan, “Mechanically switchable photonic crystal filter with either all-pass transmission or flat-top reflection characteristics,” Opt. Lett. 28(19), 1763–1765 (2003).
[CrossRef] [PubMed]

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82(13), 1999–2001 (2003).
[CrossRef]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Foresti, M.

M. Foresti, L. Menez, and A. V. Tishchenko, “Modal method in deep metal-dielectric gratings: the deceive role of hidden modes,” J. Opt. Soc. Am. 23(10), 2501 (2006).
[CrossRef]

Hane, K.

Y. Kanamori, T. Kitani, and K. Hane, “Control of guided resonance in a photonic crystal slab using microelectromechanical actuators,” Appl. Phys. Lett. 90(3), 031911 (2007).
[CrossRef]

Huang, M. C. Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chan-Hasnain, “Ultrabroadband mirror using low-index cladding subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Joannopoulos, J. D.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

Kanamori, Y.

Y. Kanamori, T. Kitani, and K. Hane, “Control of guided resonance in a photonic crystal slab using microelectromechanical actuators,” Appl. Phys. Lett. 90(3), 031911 (2007).
[CrossRef]

Kitani, T.

Y. Kanamori, T. Kitani, and K. Hane, “Control of guided resonance in a photonic crystal slab using microelectromechanical actuators,” Appl. Phys. Lett. 90(3), 031911 (2007).
[CrossRef]

Krauss, T. F.

Lacomb, R.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Lee, K. J.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Lee, Y. H.

H. Y. Ryu, Y. H. Lee, R. L. Sellin, and D. Bimberg, “Over 30-fold enhancement of light extraction from free-standing photonic crystal slabs with InGaAs quantum dots at low temperature,” Appl. Phys. Lett. 79(22), 3573–3575 (2001).
[CrossRef]

Magnusson, R.

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chan-Hasnain, “Ultrabroadband mirror using low-index cladding subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Meier, M.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

Mekis, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

Menez, L.

M. Foresti, L. Menez, and A. V. Tishchenko, “Modal method in deep metal-dielectric gratings: the deceive role of hidden modes,” J. Opt. Soc. Am. 23(10), 2501 (2006).
[CrossRef]

Nakagawa, W.

W. Nakagawa and Y. Fainman, “Tunable optical nanocavity based on modulation of near-field coupling between subwavelength periodic nanostructures,” IEEE J. Sel. Top. Quantum Electron. 10(3), 478–483 (2004).
[CrossRef]

Nalamasu, O.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

Nerviere, M.

P. Vincent and M. Nerviere, “Corrugated dielectric waveguides: A numerical study of the second-order stop band,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[CrossRef]

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chan-Hasnain, “Ultrabroadband mirror using low-index cladding subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Ryu, H. Y.

H. Y. Ryu, Y. H. Lee, R. L. Sellin, and D. Bimberg, “Over 30-fold enhancement of light extraction from free-standing photonic crystal slabs with InGaAs quantum dots at low temperature,” Appl. Phys. Lett. 79(22), 3573–3575 (2001).
[CrossRef]

Sellin, R. L.

H. Y. Ryu, Y. H. Lee, R. L. Sellin, and D. Bimberg, “Over 30-fold enhancement of light extraction from free-standing photonic crystal slabs with InGaAs quantum dots at low temperature,” Appl. Phys. Lett. 79(22), 3573–3575 (2001).
[CrossRef]

Shokooh-Saremi, M.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008).
[CrossRef] [PubMed]

R. Magnusson and M. Shokooh-Saremi, “Widely tunable guided-mode resonance nanoelectromechanical RGB pixels,” Opt. Express 15(17), 10903–10910 (2007).
[CrossRef] [PubMed]

Silva, H.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Slusher, R. E.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

Solgaard, O.

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82(13), 1999–2001 (2003).
[CrossRef]

Suh, W.

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82(13), 1999–2001 (2003).
[CrossRef]

W. Suh and S. Fan, “Mechanically switchable photonic crystal filter with either all-pass transmission or flat-top reflection characteristics,” Opt. Lett. 28(19), 1763–1765 (2003).
[CrossRef] [PubMed]

Tibuleac, S.

Timko, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

Tishchenko, A. V.

M. Foresti, L. Menez, and A. V. Tishchenko, “Modal method in deep metal-dielectric gratings: the deceive role of hidden modes,” J. Opt. Soc. Am. 23(10), 2501 (2006).
[CrossRef]

Vincent, P.

P. Vincent and M. Nerviere, “Corrugated dielectric waveguides: A numerical study of the second-order stop band,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[CrossRef]

Vrijen, R.

Wang, S. S.

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[CrossRef]

Yablonovitch, E.

Yanik, M. F.

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82(13), 1999–2001 (2003).
[CrossRef]

Appl. Phys. (Berl.) (1)

P. Vincent and M. Nerviere, “Corrugated dielectric waveguides: A numerical study of the second-order stop band,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[CrossRef]

Appl. Phys. Lett. (5)

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[CrossRef]

H. Y. Ryu, Y. H. Lee, R. L. Sellin, and D. Bimberg, “Over 30-fold enhancement of light extraction from free-standing photonic crystal slabs with InGaAs quantum dots at low temperature,” Appl. Phys. Lett. 79(22), 3573–3575 (2001).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82(13), 1999–2001 (2003).
[CrossRef]

Y. Kanamori, T. Kitani, and K. Hane, “Control of guided resonance in a photonic crystal slab using microelectromechanical actuators,” Appl. Phys. Lett. 90(3), 031911 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

W. Nakagawa and Y. Fainman, “Tunable optical nanocavity based on modulation of near-field coupling between subwavelength periodic nanostructures,” IEEE J. Sel. Top. Quantum Electron. 10(3), 478–483 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chan-Hasnain, “Ultrabroadband mirror using low-index cladding subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

M. Foresti, L. Menez, and A. V. Tishchenko, “Modal method in deep metal-dielectric gratings: the deceive role of hidden modes,” J. Opt. Soc. Am. 23(10), 2501 (2006).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. B (1)

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Other (2)

D. Wawro, S. Tibuleac, and R. Magnusson, “Optical waveguide-mode resonant biosensors Optical,” Imaging Sensors and Systems for Homeland Security Applications, (Springer New York, 2006).

H. A. Haus, Waves and Field in Optoelectronics (Englewood Cliffs, NJ: Prentice-Hall, 1984).

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Figures (7)

Fig. 1
Fig. 1

(a) Coupling of two identical gratings. (b) General structure of the two resonators with both evanescent and propagation wave couplings which is equivalent to (a). The field profile of the guided-mode of each waveguide grating is depicted in (a).

Fig. 2
Fig. 2

Reflection coefficient spectra in evanescently coupled resonators as a function of a normalized frequency, (ω−ωο)τ/2 = Δωτ/2 (a) for θ = π/2, (b) and (c) for μ = 10.

Fig. 3
Fig. 3

Reflection coefficient spectra as a function of a normalized frequency, (ω−ωο)τ/2 = Δωτ/2 in the case of negligible evanescent coupling (μ = 0).

Fig. 4
Fig. 4

(a) Structure of two identical coupled grating. (b) Reflection spectrum of the single grating in (a). Reflection spectra for the coupled gratings under different alignment conditions: (c) complete alignment (s = 0), (d) quarter-period shifted (s = P/4), and (e) half-period shifted (s = P/2). The calculations are done for a normally incident TE polarized wave.

Fig. 5
Fig. 5

Field (Ey) distributions in the coupled grating shown in Fig. 4(a) for d = 0: (a) at λ = 1697.7 nm (even super-mode) and (b)at λ = 1517.1 nm(odd super-mode). Field amplitudes are normalized to the incident wave.

Fig. 6
Fig. 6

(a) Structure of two identical coupled grating. (b) Reflection spectrum of the single grating in (a). Reflection spectra for the coupled gratings under different alignment conditions: (c) complete alignment (s = 0), (d) quarter-period shifted (s = P/4), and (e) half-period shifted (s = P/2). The calculations are done for a normally incident TE polarized wave.

Fig. 7
Fig. 7

(a) Structure of two identical coupled grating. (b) Reflection spectrum of the single grating in (a). Transmission spectra for the coupled gratings for various d. The calculations are done for a normally incident TM polarized wave.

Equations (18)

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d a 1 d t = ( j ω o 2 τ ) a 1 j μ a 2 + κ s + 1 + κ s + 2 ,
d a 2 d t = ( j ω o 2 τ ) a 2 j μ a 1 + κ s + 3 + κ s + 4 ,
s 2 = s + 1 κ a 1
s 1 = s + 2 κ a 1
s 3 = s + 4 κ a 2
s 4 = s + 3 κ a 2
s + 2 = e j θ s 3 = e j θ ( s + 4 κ a 2 ) ,
s + 3 = e j θ s 2 = e j θ ( s + 1 κ a 1 ) .
d a 1 d t = ( j ω o 2 τ ) a 1 ( j μ + 2 τ e j θ ) a 2 + κ s + 1 + κ e j θ s + 4 ,
d a 2 d t = ( j ω o 2 τ ) a 2 ( j μ + 2 τ e j θ ) a 1 + κ e j θ s + 1 + κ s + 4 .
d a e v e n d t = ( j ω e v e n 2 τ e v e n ) a e v e n + 2 κ e j θ / 2 cos θ 2 ( s + 1 + s + 4 ) ,
d a o d d d t = ( j ω o d d 2 τ o d d ) a o d d + j 2 κ e j θ / 2 sin θ 2 ( s + 1 s + 4 ) ,
ω e v e n = ω o μ + 2 τ sin θ ,
ω o d d = ω o + μ 2 τ sin θ ,
1 τ e v e n = 1 τ ( 1 + cos θ ) ,
1 τ o d d = 1 τ ( 1 cos θ ) .
r = | s 1 s + 1 | = | j ( ω ω o ) τ 2 ( 1 + e j 2 θ ) + j μ τ e j θ 1 + e j 2 θ { j ( ω ω o ) τ 2 + 1 } 2 ( j μ τ 2 + e j θ ) 2 | .
( Δ ω τ / 2 ) z e r o = tan θ .

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