Abstract

Phase resonances in compound gratings are studied in the frequency and time domains, with the gratings having two dissimilar grooves within the unit cell that each support waveguide cavity modes that couple. Described in this work are the dependence of the phase resonances’ Q on the degree of difference between the grooves in the unit cell, their optical properties, a closed-form expression describing their dispersion, their excitation, and the extraction of energy from the phase resonances into free space and into a waveguide. Application to optical filters and corrugated surface antennas are discussed.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. A. Depine, A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Phase resonances in obliquely illuminated compound gratings,” Optik 118, 42–52 (2007).
    [CrossRef]
  2. M. Beruete, M. Navarro-Ćia, M. Sorolla, and D. Skigin, “Millimeter-wave phase resonances in compound reflection gratings with subwavelength grooves.” Opt. Express 18, 23957–23964 (2010).
    [CrossRef] [PubMed]
  3. M. Navarro-Cia, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
    [CrossRef]
  4. A. Hibbins, I. Hooper, M. Lockyear, and J. Sambles, “Microwave Transmission of a Compound Metal Grating,” Phys. Rev. Lett. 96, 257402 (2006).
    [CrossRef] [PubMed]
  5. H. J. Rance, O. K. Hamilton, J. R. Sambles, and A. P. Hibbins, “Phase resonances on metal gratings of identical, equally spaced alternately tapered slits,” Appl. Phys. Lett. 95, 041905 (2009).
    [CrossRef]
  6. D. C. Skigin and R. A. Depine, “Resonances on metallic compound transmission gratings with subwavelength wires and slits,” Opt. Commun. 262, 270–275 (2006).
    [CrossRef]
  7. D. Skigin and R. Depine, “Narrow gaps for transmission through metallic structured gratings with subwavelength slits,” Phys. Rev. E 74, 046606 (2006).
    [CrossRef]
  8. D. Crouse, E. Jaquay, A. Maikal, and A. P. Hibbins, “Light circulation and weaving in periodically patterned structures,” Phys. Rev. B 77, 195437 (2008).
  9. A. Barbara, J. Le Perchec, S. Collin, C. Sauvan, J.-L. Pelouard, T. López-Ríos, and P. Quémerais, “Generation and control of hot spots on commensurate metallic gratings.” Opt. Express 16, 19127–35 (2008).
    [CrossRef]
  10. A. Barbara, S. Collin, C. Sauvan, J. Le Perchec, C. Maxime, J.-L. Pelouard, and P. Quémerais, “Plasmon dispersion diagram and localization effects in a three-cavity commensurate grating.” Opt. Express 18, 14913–25 (2010).
    [CrossRef] [PubMed]
  11. D. Smith, H. Chang, K. Fuller, A. Rosenberger, and R. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 1–6 (2004).
    [CrossRef]
  12. Q. Xu, J. Shakya, and M. Lipson, “Direct measurement of tunable optical delays on chip analogue to electromagnetically induced transparency.” Opt. Express 14, 6463–6468 (2006).
    [CrossRef] [PubMed]
  13. Y.-F. Xiao, X.-B. Zou, W. Jiang, Y.-L. Chen, and G.-C. Guo, “Analogue to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 4 (2007).
    [CrossRef]
  14. X. Yang, M. Yu, D.-L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
    [CrossRef] [PubMed]
  15. R. S. Penciu, K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Multi-gap individual and coupled split-ring resonator structures.” Opt. Express 16, 18131–18144 (2008).
    [CrossRef] [PubMed]
  16. D. Crouse, “Numerical modeling and electromagnetic resonant modes in complex grating structures and opto-electronic device applications,” IEEE Trans. Electron Dev. 52, 2365–2373 (2005).
    [CrossRef]
  17. D. Crouse and P. Keshavareddy, “Polarization independent enhanced optical transmission in one-dimensional gratings and device applications,” Opt. Express 15, 1415–1427 (2007).
    [CrossRef] [PubMed]
  18. I. M. Mandel, A. B. Golovin, and D. T. Crouse, “The dispersion relation of phase resonances in compound transmission gratings calculated using an analytic model,” Submitted (2012).
  19. M. Navarro-Cia, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
    [CrossRef]
  20. Z. Qiang, W. Zhou, and R. A. Soref, “Optical add-drop filters based on photonic crystal ring resonators.” Opt. Express 15, 1823–1831 (2007).
    [CrossRef] [PubMed]
  21. A. D. Rakić, “Algorithm for the determination of intrinsic optical constants of metal films: application to aluminum.” Appl. Opt. 34, 4755–4767 (1995).
    [CrossRef]
  22. V. V. Veremey, R. Mittra, and L. Fellow, “Scattering from structures formed by resonant elements,” IEEE Trans. Antennas Propag. 46, 494–501 (1998).
    [CrossRef]
  23. D. C. Skigin, V. V. Veremey, R. Mittra, and L. Fellow, “Superdirective radiation from finite gratings of rectangular grooves,” IEEE Trans. Antennas Propag. 47, 376–383 (1999).
    [CrossRef]
  24. C. I. Valencia and D. C. Skigin, “Anomalous reflection in a metallic plate with subwavelength grooves of circular cross section.” Appl. Opt. 48, 5863–5870 (2009).
    [CrossRef]
  25. C. C. Culter, Bell Telephone Laboratories, Report MM-44-160-218 (1944).
  26. M. Ehrlich and L. Newkirk, “Corrugated surface antennas,” (1953).
  27. R. S. Elliot, “Antenna Theory and Design,” in “Antenna Theory and Design,”, D. Dudley, ed. (Wiley-Interscience, 2003), pp. 440–452, revised ed.

2010

2009

C. I. Valencia and D. C. Skigin, “Anomalous reflection in a metallic plate with subwavelength grooves of circular cross section.” Appl. Opt. 48, 5863–5870 (2009).
[CrossRef]

M. Navarro-Cia, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

H. J. Rance, O. K. Hamilton, J. R. Sambles, and A. P. Hibbins, “Phase resonances on metal gratings of identical, equally spaced alternately tapered slits,” Appl. Phys. Lett. 95, 041905 (2009).
[CrossRef]

X. Yang, M. Yu, D.-L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

M. Navarro-Cia, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

2008

2007

Y.-F. Xiao, X.-B. Zou, W. Jiang, Y.-L. Chen, and G.-C. Guo, “Analogue to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 4 (2007).
[CrossRef]

D. Crouse and P. Keshavareddy, “Polarization independent enhanced optical transmission in one-dimensional gratings and device applications,” Opt. Express 15, 1415–1427 (2007).
[CrossRef] [PubMed]

Z. Qiang, W. Zhou, and R. A. Soref, “Optical add-drop filters based on photonic crystal ring resonators.” Opt. Express 15, 1823–1831 (2007).
[CrossRef] [PubMed]

R. A. Depine, A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Phase resonances in obliquely illuminated compound gratings,” Optik 118, 42–52 (2007).
[CrossRef]

2006

D. C. Skigin and R. A. Depine, “Resonances on metallic compound transmission gratings with subwavelength wires and slits,” Opt. Commun. 262, 270–275 (2006).
[CrossRef]

D. Skigin and R. Depine, “Narrow gaps for transmission through metallic structured gratings with subwavelength slits,” Phys. Rev. E 74, 046606 (2006).
[CrossRef]

A. Hibbins, I. Hooper, M. Lockyear, and J. Sambles, “Microwave Transmission of a Compound Metal Grating,” Phys. Rev. Lett. 96, 257402 (2006).
[CrossRef] [PubMed]

Q. Xu, J. Shakya, and M. Lipson, “Direct measurement of tunable optical delays on chip analogue to electromagnetically induced transparency.” Opt. Express 14, 6463–6468 (2006).
[CrossRef] [PubMed]

2005

D. Crouse, “Numerical modeling and electromagnetic resonant modes in complex grating structures and opto-electronic device applications,” IEEE Trans. Electron Dev. 52, 2365–2373 (2005).
[CrossRef]

2004

D. Smith, H. Chang, K. Fuller, A. Rosenberger, and R. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 1–6 (2004).
[CrossRef]

1999

D. C. Skigin, V. V. Veremey, R. Mittra, and L. Fellow, “Superdirective radiation from finite gratings of rectangular grooves,” IEEE Trans. Antennas Propag. 47, 376–383 (1999).
[CrossRef]

1998

V. V. Veremey, R. Mittra, and L. Fellow, “Scattering from structures formed by resonant elements,” IEEE Trans. Antennas Propag. 46, 494–501 (1998).
[CrossRef]

1995

Aydin, K.

Barbara, A.

Beruete, M.

M. Beruete, M. Navarro-Ćia, M. Sorolla, and D. Skigin, “Millimeter-wave phase resonances in compound reflection gratings with subwavelength grooves.” Opt. Express 18, 23957–23964 (2010).
[CrossRef] [PubMed]

M. Navarro-Cia, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

M. Navarro-Cia, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

Boyd, R.

D. Smith, H. Chang, K. Fuller, A. Rosenberger, and R. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 1–6 (2004).
[CrossRef]

Chang, H.

D. Smith, H. Chang, K. Fuller, A. Rosenberger, and R. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 1–6 (2004).
[CrossRef]

Chen, Y.-L.

Y.-F. Xiao, X.-B. Zou, W. Jiang, Y.-L. Chen, and G.-C. Guo, “Analogue to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 4 (2007).
[CrossRef]

Collin, S.

Crouse, D.

D. Crouse and P. Keshavareddy, “Polarization independent enhanced optical transmission in one-dimensional gratings and device applications,” Opt. Express 15, 1415–1427 (2007).
[CrossRef] [PubMed]

D. Crouse, “Numerical modeling and electromagnetic resonant modes in complex grating structures and opto-electronic device applications,” IEEE Trans. Electron Dev. 52, 2365–2373 (2005).
[CrossRef]

D. Crouse, E. Jaquay, A. Maikal, and A. P. Hibbins, “Light circulation and weaving in periodically patterned structures,” Phys. Rev. B 77, 195437 (2008).

Crouse, D. T.

I. M. Mandel, A. B. Golovin, and D. T. Crouse, “The dispersion relation of phase resonances in compound transmission gratings calculated using an analytic model,” Submitted (2012).

Culter, C. C.

C. C. Culter, Bell Telephone Laboratories, Report MM-44-160-218 (1944).

Depine, R.

D. Skigin and R. Depine, “Narrow gaps for transmission through metallic structured gratings with subwavelength slits,” Phys. Rev. E 74, 046606 (2006).
[CrossRef]

Depine, R. A.

R. A. Depine, A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Phase resonances in obliquely illuminated compound gratings,” Optik 118, 42–52 (2007).
[CrossRef]

D. C. Skigin and R. A. Depine, “Resonances on metallic compound transmission gratings with subwavelength wires and slits,” Opt. Commun. 262, 270–275 (2006).
[CrossRef]

Economou, E. N.

Ehrlich, M.

M. Ehrlich and L. Newkirk, “Corrugated surface antennas,” (1953).

Elliot, R. S.

R. S. Elliot, “Antenna Theory and Design,” in “Antenna Theory and Design,”, D. Dudley, ed. (Wiley-Interscience, 2003), pp. 440–452, revised ed.

Fantino, A. N.

R. A. Depine, A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Phase resonances in obliquely illuminated compound gratings,” Optik 118, 42–52 (2007).
[CrossRef]

Fellow, L.

D. C. Skigin, V. V. Veremey, R. Mittra, and L. Fellow, “Superdirective radiation from finite gratings of rectangular grooves,” IEEE Trans. Antennas Propag. 47, 376–383 (1999).
[CrossRef]

V. V. Veremey, R. Mittra, and L. Fellow, “Scattering from structures formed by resonant elements,” IEEE Trans. Antennas Propag. 46, 494–501 (1998).
[CrossRef]

Fuller, K.

D. Smith, H. Chang, K. Fuller, A. Rosenberger, and R. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 1–6 (2004).
[CrossRef]

Golovin, A. B.

I. M. Mandel, A. B. Golovin, and D. T. Crouse, “The dispersion relation of phase resonances in compound transmission gratings calculated using an analytic model,” Submitted (2012).

Grosz, S. I.

R. A. Depine, A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Phase resonances in obliquely illuminated compound gratings,” Optik 118, 42–52 (2007).
[CrossRef]

Guo, G.-C.

Y.-F. Xiao, X.-B. Zou, W. Jiang, Y.-L. Chen, and G.-C. Guo, “Analogue to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 4 (2007).
[CrossRef]

Hamilton, O. K.

H. J. Rance, O. K. Hamilton, J. R. Sambles, and A. P. Hibbins, “Phase resonances on metal gratings of identical, equally spaced alternately tapered slits,” Appl. Phys. Lett. 95, 041905 (2009).
[CrossRef]

Hibbins, A.

A. Hibbins, I. Hooper, M. Lockyear, and J. Sambles, “Microwave Transmission of a Compound Metal Grating,” Phys. Rev. Lett. 96, 257402 (2006).
[CrossRef] [PubMed]

Hibbins, A. P.

H. J. Rance, O. K. Hamilton, J. R. Sambles, and A. P. Hibbins, “Phase resonances on metal gratings of identical, equally spaced alternately tapered slits,” Appl. Phys. Lett. 95, 041905 (2009).
[CrossRef]

D. Crouse, E. Jaquay, A. Maikal, and A. P. Hibbins, “Light circulation and weaving in periodically patterned structures,” Phys. Rev. B 77, 195437 (2008).

Hooper, I.

A. Hibbins, I. Hooper, M. Lockyear, and J. Sambles, “Microwave Transmission of a Compound Metal Grating,” Phys. Rev. Lett. 96, 257402 (2006).
[CrossRef] [PubMed]

Jaquay, E.

D. Crouse, E. Jaquay, A. Maikal, and A. P. Hibbins, “Light circulation and weaving in periodically patterned structures,” Phys. Rev. B 77, 195437 (2008).

Jiang, W.

Y.-F. Xiao, X.-B. Zou, W. Jiang, Y.-L. Chen, and G.-C. Guo, “Analogue to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 4 (2007).
[CrossRef]

Kafesaki, M.

Keshavareddy, P.

Koschny, T.

Kwong, D.-L.

X. Yang, M. Yu, D.-L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

Le Perchec, J.

Lipson, M.

Lockyear, M.

A. Hibbins, I. Hooper, M. Lockyear, and J. Sambles, “Microwave Transmission of a Compound Metal Grating,” Phys. Rev. Lett. 96, 257402 (2006).
[CrossRef] [PubMed]

López-Ríos, T.

Maikal, A.

D. Crouse, E. Jaquay, A. Maikal, and A. P. Hibbins, “Light circulation and weaving in periodically patterned structures,” Phys. Rev. B 77, 195437 (2008).

Mandel, I. M.

I. M. Mandel, A. B. Golovin, and D. T. Crouse, “The dispersion relation of phase resonances in compound transmission gratings calculated using an analytic model,” Submitted (2012).

Maxime, C.

Mittra, R.

D. C. Skigin, V. V. Veremey, R. Mittra, and L. Fellow, “Superdirective radiation from finite gratings of rectangular grooves,” IEEE Trans. Antennas Propag. 47, 376–383 (1999).
[CrossRef]

V. V. Veremey, R. Mittra, and L. Fellow, “Scattering from structures formed by resonant elements,” IEEE Trans. Antennas Propag. 46, 494–501 (1998).
[CrossRef]

Navarro-Cia, M.

M. Beruete, M. Navarro-Ćia, M. Sorolla, and D. Skigin, “Millimeter-wave phase resonances in compound reflection gratings with subwavelength grooves.” Opt. Express 18, 23957–23964 (2010).
[CrossRef] [PubMed]

M. Navarro-Cia, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

M. Navarro-Cia, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

Newkirk, L.

M. Ehrlich and L. Newkirk, “Corrugated surface antennas,” (1953).

Ozbay, E.

Pelouard, J.-L.

Penciu, R. S.

Qiang, Z.

Quémerais, P.

Rakic, A. D.

Rance, H. J.

H. J. Rance, O. K. Hamilton, J. R. Sambles, and A. P. Hibbins, “Phase resonances on metal gratings of identical, equally spaced alternately tapered slits,” Appl. Phys. Lett. 95, 041905 (2009).
[CrossRef]

Rosenberger, A.

D. Smith, H. Chang, K. Fuller, A. Rosenberger, and R. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 1–6 (2004).
[CrossRef]

Sambles, J.

A. Hibbins, I. Hooper, M. Lockyear, and J. Sambles, “Microwave Transmission of a Compound Metal Grating,” Phys. Rev. Lett. 96, 257402 (2006).
[CrossRef] [PubMed]

Sambles, J. R.

H. J. Rance, O. K. Hamilton, J. R. Sambles, and A. P. Hibbins, “Phase resonances on metal gratings of identical, equally spaced alternately tapered slits,” Appl. Phys. Lett. 95, 041905 (2009).
[CrossRef]

Sauvan, C.

Shakya, J.

Skigin, D.

M. Beruete, M. Navarro-Ćia, M. Sorolla, and D. Skigin, “Millimeter-wave phase resonances in compound reflection gratings with subwavelength grooves.” Opt. Express 18, 23957–23964 (2010).
[CrossRef] [PubMed]

D. Skigin and R. Depine, “Narrow gaps for transmission through metallic structured gratings with subwavelength slits,” Phys. Rev. E 74, 046606 (2006).
[CrossRef]

Skigin, D. C.

C. I. Valencia and D. C. Skigin, “Anomalous reflection in a metallic plate with subwavelength grooves of circular cross section.” Appl. Opt. 48, 5863–5870 (2009).
[CrossRef]

M. Navarro-Cia, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

M. Navarro-Cia, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

R. A. Depine, A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Phase resonances in obliquely illuminated compound gratings,” Optik 118, 42–52 (2007).
[CrossRef]

D. C. Skigin and R. A. Depine, “Resonances on metallic compound transmission gratings with subwavelength wires and slits,” Opt. Commun. 262, 270–275 (2006).
[CrossRef]

D. C. Skigin, V. V. Veremey, R. Mittra, and L. Fellow, “Superdirective radiation from finite gratings of rectangular grooves,” IEEE Trans. Antennas Propag. 47, 376–383 (1999).
[CrossRef]

Smith, D.

D. Smith, H. Chang, K. Fuller, A. Rosenberger, and R. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 1–6 (2004).
[CrossRef]

Soref, R. A.

Sorolla, M.

M. Beruete, M. Navarro-Ćia, M. Sorolla, and D. Skigin, “Millimeter-wave phase resonances in compound reflection gratings with subwavelength grooves.” Opt. Express 18, 23957–23964 (2010).
[CrossRef] [PubMed]

M. Navarro-Cia, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

M. Navarro-Cia, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

Soukoulis, C. M.

Valencia, C. I.

Veremey, V. V.

D. C. Skigin, V. V. Veremey, R. Mittra, and L. Fellow, “Superdirective radiation from finite gratings of rectangular grooves,” IEEE Trans. Antennas Propag. 47, 376–383 (1999).
[CrossRef]

V. V. Veremey, R. Mittra, and L. Fellow, “Scattering from structures formed by resonant elements,” IEEE Trans. Antennas Propag. 46, 494–501 (1998).
[CrossRef]

Wong, C. W.

X. Yang, M. Yu, D.-L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

Xiao, Y.-F.

Y.-F. Xiao, X.-B. Zou, W. Jiang, Y.-L. Chen, and G.-C. Guo, “Analogue to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 4 (2007).
[CrossRef]

Xu, Q.

Yang, X.

X. Yang, M. Yu, D.-L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

Yu, M.

X. Yang, M. Yu, D.-L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

Zhou, W.

Zou, X.-B.

Y.-F. Xiao, X.-B. Zou, W. Jiang, Y.-L. Chen, and G.-C. Guo, “Analogue to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 4 (2007).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. Navarro-Cia, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

M. Navarro-Cia, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

H. J. Rance, O. K. Hamilton, J. R. Sambles, and A. P. Hibbins, “Phase resonances on metal gratings of identical, equally spaced alternately tapered slits,” Appl. Phys. Lett. 95, 041905 (2009).
[CrossRef]

IEEE Trans. Antennas Propag.

V. V. Veremey, R. Mittra, and L. Fellow, “Scattering from structures formed by resonant elements,” IEEE Trans. Antennas Propag. 46, 494–501 (1998).
[CrossRef]

D. C. Skigin, V. V. Veremey, R. Mittra, and L. Fellow, “Superdirective radiation from finite gratings of rectangular grooves,” IEEE Trans. Antennas Propag. 47, 376–383 (1999).
[CrossRef]

IEEE Trans. Electron Dev.

D. Crouse, “Numerical modeling and electromagnetic resonant modes in complex grating structures and opto-electronic device applications,” IEEE Trans. Electron Dev. 52, 2365–2373 (2005).
[CrossRef]

Opt. Commun.

D. C. Skigin and R. A. Depine, “Resonances on metallic compound transmission gratings with subwavelength wires and slits,” Opt. Commun. 262, 270–275 (2006).
[CrossRef]

Opt. Express

Optik

R. A. Depine, A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Phase resonances in obliquely illuminated compound gratings,” Optik 118, 42–52 (2007).
[CrossRef]

Phys. Rev. A

D. Smith, H. Chang, K. Fuller, A. Rosenberger, and R. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 1–6 (2004).
[CrossRef]

Y.-F. Xiao, X.-B. Zou, W. Jiang, Y.-L. Chen, and G.-C. Guo, “Analogue to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 4 (2007).
[CrossRef]

Phys. Rev. B

D. Crouse, E. Jaquay, A. Maikal, and A. P. Hibbins, “Light circulation and weaving in periodically patterned structures,” Phys. Rev. B 77, 195437 (2008).

Phys. Rev. E

D. Skigin and R. Depine, “Narrow gaps for transmission through metallic structured gratings with subwavelength slits,” Phys. Rev. E 74, 046606 (2006).
[CrossRef]

Phys. Rev. Lett.

A. Hibbins, I. Hooper, M. Lockyear, and J. Sambles, “Microwave Transmission of a Compound Metal Grating,” Phys. Rev. Lett. 96, 257402 (2006).
[CrossRef] [PubMed]

X. Yang, M. Yu, D.-L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

Other

C. C. Culter, Bell Telephone Laboratories, Report MM-44-160-218 (1944).

M. Ehrlich and L. Newkirk, “Corrugated surface antennas,” (1953).

R. S. Elliot, “Antenna Theory and Design,” in “Antenna Theory and Design,”, D. Dudley, ed. (Wiley-Interscience, 2003), pp. 440–452, revised ed.

I. M. Mandel, A. B. Golovin, and D. T. Crouse, “The dispersion relation of phase resonances in compound transmission gratings calculated using an analytic model,” Submitted (2012).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

(a) A cross-sectional schematic of the two-groove-per-unit-cell CTG that supports PRs. If the grooves are identical and uniformly spaced, then the CTG reverts to the parent simple lamellar grating (SLG) that does not support PRs. Mirror symmetry about Plane A needs to be broken for the structure to support PRs. (b) The simulated transmittance (solid) and re-flectance (dashed) for normal incident light for a CTG with WCMs with moderate Q and with the structure’s dimensions tuned to produce a PR at what was initially (i.e., before a dissimilarity between the grooves is introduced) the very peak of the transmittance. Again, note that before any groove dissimilarity is introduced, the transmission peak produced by the WCMs is a smoothly varying Gaussian shaped peak from 10 GHz to 14 GHz. The PR introduces a complete inversion of the transmissivity/opacity of the film. The structure has a period Λ = 19.05 mm, both grooves have widths of w1 = w2 = 1.905 mm, but with Groove 1 having ε1 = 1 and Groove 2 having ε2 = 1.5; the height of the grooves is h = 9.525 mm, and the width of the aluminum wire with Groove 1 on the left and Groove 2 on the left is s12 = 2 mm, the substrate and superstrate is vacuum. A RCWA algorithm is used to simulate the optical properties of the structure shown in this figure [16].

Fig. 2
Fig. 2

The dispersion curve calculated using the RCWA for a CTG with Λ = 19.05 mm, h = 9.525 mm, w1 = 11.43 mm, w2 = 5.08 mm, s12 = 0.3175 mm, εt = εb = ε1 = ε2 = 1, and for p-polarized incident light. The dispersion curve shows the transmittance of the structure for p-polarized light, showing that the PR inverts the transmissivity/opacity of the film, has a large Q, and has a negative group velocity. Also shown is the PR dispersion curve predicted by Eq. (1) for a perturbed SLG with Λ = 19.05 mm (Λ is actually twice the period of the SLG), h = 9.525 mm, wg = 8.255 mm, s12 = 1.27 mm, εt = εb = ε1 = ε2 = 1. The frequencies of the PRs predicted by Eq. (1) differ from what is obtained using the RCWA because the CTG is significantly perturbed away from the parent SLG for which Eq. (1) is most accurate.

Fig. 3
Fig. 3

(a) A cross-section of one period of the CTG described in Fig. 2 showing |Hz|2 for the p-polarized phase resonance (point (+) in Fig. 2 (ν = 8.46 GHz, kx/K = 0.38)) for a p-polarized incident beam |Hz,incident| = 1 and 45° incident angle. The intensity amplification (i.e., |Hz,max| // |Hz,incident|2) is only ∼ 87 for this structure and at this angle of incidence. (b) The Poynting vector showing that energy is propagating in the −x̂ direction along the surfaces of the grating even though the Poynting vector for the incident beam has a positive kx value. This difference in the direction of the flow of energy of the incident beam and the PR is in agreement with the negative group velocity shown in Fig. 2.

Fig. 4
Fig. 4

The Q of the phase resonance for p-polarized, normal incidence light. The starting structure (when f = 1) structure has the dimensions: Λ = 19.05 mm (actually the true period for the structure when f = 1 is Λ/2), h = 9.525 mm, w1 = w2 = 8.89 mm, s12 = s21 = 0.635 mm, ε1 = 1, and ε2 = f · ε1 with f being the asymmetry factor that introduces a dissimilarity between the grooves. It is seen that as f → 1, the Q of the structure becomes infinitely large.

Fig. 5
Fig. 5

Top: The transmittance and absorption for a scaled-down version of the device that operates in the infrared spectral region (Λ = 6 μm, w1 = w2 = 2.8 μm, h = 3 μm, s12 = s21 = 0.2 μm, ε1 = 1, ε2 = f with f = 1 → 2 in steps of 0.06, and aluminum wires with the optical parameters (n and k) obtained from [21]). Even though the PRs have a broader bandwidth and are dampened, their effects on the transmittance are still strong, especially when the asymmetry factor f is greater than 1.4. For structures with optical loss, there is an optimal value for f such that the phase resonances are strong but not overdamped (as occurs in this structure for f < 1.52). Bottom: The intensities of the ±1 order Floquet modes in the superstrate (|R±1|2), the 0th order Floquet mode (|R0|2 or specular reflection), and the 0th order cavity mode |a0|2. As f becomes greater than 1.76, the magnitudes of |R±1|2 and |a0|2 relative to |R0|2 decrease, indicating that the phase resonance is becoming weaker as f increases beyond 1.76.

Fig. 6
Fig. 6

The change in the field energy contained within structure as the incident pulse passes through the system. The initial large increase in energy is the incident beam passing through the structure while the slow decay of field energy is caused by the slow release of energy trapped within the structure by the PR. This decay rate is inversely proportional to the Q of the PR.

Fig. 7
Fig. 7

(a) The time signal response as captured by a probe above the grating structure. The initial pulse is the Gaussian time signal used for excitation, while the waveform afterwards is the energy released by the slowly decaying PR. (b) The frequency response of the reflected waveform. The maximum of the peak occurs at the same frequency as the frequency of the PR

Fig. 8
Fig. 8

(a) The time signal response as captured by a probe below the grating structure. The initial pulse is the input Gaussian time signal minus a small bandwidth of frequency components that couple to the PR. The second, longer duration waveform is the slow decay of energy released by PR. (b) The frequency response of the transmitted signal shows which frequencies pass through the grating largely unimpeded and which frequencies are reflected or scattered due to the PR.

Fig. 9
Fig. 9

The ratio of the output beam to input beam for the device studied in this work. The portions of the incident beam that do not excite the phase resonance will pass through the structure largely unimpeded, whereas the component of the incident beam that has a frequency that matches the phase resonance will excite the phase resonance, with most of the this component being reflected and some of this component going into intensifying the fields of the phase resonance.

Fig. 10
Fig. 10

A snapshot in time of the electromagnetic field profile for a 8.17 GHz incident beam with an angle of incidence of −45°. This beam excites a PR that channels the energy along the grating in a direction opposite to the in-plane wave vector component of the incident beam. Upon entering the region of the grating that has its structure perturbed such that it does not support the PR, the energy within the PR is released into the substrate at an angle the matches the angle of incidence of the incident beam.

Fig. 11
Fig. 11

A snapshot in time of the electromagnetic field profile for a 8.17 GHz incident beam with an angle of incidence of −45°. Again, this beam excites a PR that channels the energy along the grating in a direction opposite to the in-plane wave vector component of the incident beam. The PR then propagates into the waveguide and releases its energy into the waveguide at the end of the grating. The color scale is the same as in Fig. 10.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

2 i γ 0 ε g tan ( γ 0 h / 2 ) = β 1 β 1 ( Λ / ε s w ) β 1 sin c 2 ( α 1 w 2 ) + β 1 sin c 2 ( α 1 w 2 )
H z = n = n = I n e i ( α n ( x w 1 2 ) β n ( y h 2 ) ) + R n e i ( α n ( x w 1 2 ) + β n ( y h 2 ) )
H ˜ z = n = n = R ˜ n e i ( α n ( x w 1 2 ) β ˜ n ( y + h 2 ) )
α n = k x + n K
β n = ( ε t k o 2 α n 2 ) 1 / 2
β ˜ n = ( ε b k o 2 α n 2 ) 1 / 2
H z = m = 0 ( d m g sin ( μ m g ( x x o g ) ) + cos ( μ m g ( x x o g ) ) ) ( a m g e i γ m g y + b m g e i γ m g y )
tan ( μ m g w g ) = 2 μ m g η ( μ m g ) 2 η 2
γ m g = ( ε g k o 2 ( μ m g ) 2 ) 1 / 2

Metrics