Abstract

Recently researchers have demonstrated ultra high quality factor (Q) resonances in one-dimensional (1D) dielectric gratings. Here we theoretically investigate a new class of subwavelength 1D gratings, namely “diatomic” gratings with two nonequivalent subcells in one period, and utilize their intrinsic dark modes to achieve robust ultra high Q resonances. Such “diatomic” gratings provide extra design flexibility, and enable high Q resonators using thinner geometry with smaller filling factors compared to conventional designs like the high contrast gratings (HCGs). More importantly, we show that these high Q resonances can be efficiently tuned in situ, making the design appealing in various applications including optical sensing, filtering and displays.

© 2015 Optical Society of America

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References

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2014 (1)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

2013 (1)

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

2012 (2)

V. Karagodsky and C. J. Chang-Hasnain, “Physics of near-wavelength high contrast gratings,” Opt. Express 20(10), 10888–10895 (2012).
[Crossref] [PubMed]

A. Chandran, E. S. Barnard, J. S. White, and M. L. Brongersma, “Metal-dielectric-metal surface plasmon-polariton resonators,” Phys. Rev. B 85(8), 085416 (2012).
[Crossref]

2011 (1)

2010 (6)

E.-H. Cho, H.-S. Kim, J.-S. Sohn, C.-Y. Moon, N.-C. Park, and Y.-P. Park, “Nanoimprinted photonic crystal color filters for solar-powered reflective displays,” Opt. Express 18(26), 27712–27722 (2010).
[Crossref] [PubMed]

M. El Beheiry, V. Liu, S. Fan, and O. Levi, “Sensitivity enhancement in photonic crystal slab biosensors,” Opt. Express 18(22), 22702–22714 (2010).
[Crossref] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, “Theoretical analysis of subwavelength high contrast grating reflectors,” Opt. Express 18(16), 16973–16988 (2010).
[Crossref] [PubMed]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

2009 (2)

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9(4), 1663–1667 (2009).
[Crossref] [PubMed]

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref] [PubMed]

2008 (3)

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

T.-C. Lu, S.-W. Chen, L.-F. Lin, T.-T. Kao, C.-C. Kao, P. Yu, H.-C. Kuo, S.-C. Wang, and S. Fan, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92(1), 011129 (2008).
[Crossref]

L. Shi, P. Pottier, Y.-A. Peter, and M. Skorobogatiy, “Guided-mode resonance photonic crystal slab sensors based on bead monolayer geometry,” Opt. Express 16(22), 17962–17971 (2008).
[Crossref] [PubMed]

2007 (2)

2006 (2)

F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97(20), 206806 (2006).
[Crossref] [PubMed]

P. C. Slabs, T. Asano, B. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q nanocavities in two-dimensional photonic crystal slab,” IEEE J. Sel. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

2004 (2)

2003 (5)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (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 (2003).
[Crossref]

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
[Crossref] [PubMed]

A. Mizutani, H. Kikuta, and K. Iwata, “Wave Localization of Doubly Periodic Guided-mode Resonant Grating Filters,” Opt. Rev. 10(1), 13–18 (2003).
[Crossref]

S. T. Thurman and G. M. Morris, “Controlling the spectral response in guided-mode resonance filter design,” Appl. Opt. 42(16), 3225–3233 (2003).
[Crossref] [PubMed]

2002 (1)

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

2001 (2)

M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Localization versus delocalization of surface plasmons in nanosystems: can one state have both characteristics?” Phys. Rev. Lett. 87(16), 167401 (2001).
[Crossref] [PubMed]

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63(12), 125107 (2001).
[Crossref]

2000 (1)

1999 (2)

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, “Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals,” Appl. Phys. Lett. 75(8), 1036 (1999).
[Crossref]

F. Lemarchand, A. Sentenac, E. Cambril, and H. Giovannini, “Study of the resonant behaviour of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1(4), 545–551 (1999).
[Crossref]

1998 (1)

1997 (2)

S. Tibuleac and R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A 14(7), 1617 (1997).
[Crossref]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
[Crossref]

1996 (2)

S. Peng and G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A 13(5), 993 (1996).
[Crossref]

A. Sharon, D. Rosenblatt, and A. A. Friesem, “Narrow spectral bandwidths with grating waveguide structures,” Appl. Phys. Lett. 69(27), 4154 (1996).
[Crossref]

1995 (2)

1994 (1)

1993 (1)

1992 (1)

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

1989 (1)

1987 (1)

R. Zengerle, “Light Propagation in Singly and Doubly Periodic Planar Waveguides,” J. Mod. Opt. 34(12), 1589–1617 (1987).
[Crossref]

Akahane, Y.

P. C. Slabs, T. Asano, B. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q nanocavities in two-dimensional photonic crystal slab,” IEEE J. Sel. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[Crossref] [PubMed]

Asano, T.

P. C. Slabs, T. Asano, B. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q nanocavities in two-dimensional photonic crystal slab,” IEEE J. Sel. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

Barnard, E. S.

A. Chandran, E. S. Barnard, J. S. White, and M. L. Brongersma, “Metal-dielectric-metal surface plasmon-polariton resonators,” Phys. Rev. B 85(8), 085416 (2012).
[Crossref]

Beausoleil, R. G.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

Bergman, D. J.

M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Localization versus delocalization of surface plasmons in nanosystems: can one state have both characteristics?” Phys. Rev. Lett. 87(16), 167401 (2001).
[Crossref] [PubMed]

Bhat, R.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, “Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals,” Appl. Phys. Lett. 75(8), 1036 (1999).
[Crossref]

Bolivar, P. H.

Boroditsky, M.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, “Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals,” Appl. Phys. Lett. 75(8), 1036 (1999).
[Crossref]

Boyko, O.

Brongersma, M. L.

A. Chandran, E. S. Barnard, J. S. White, and M. L. Brongersma, “Metal-dielectric-metal surface plasmon-polariton resonators,” Phys. Rev. B 85(8), 085416 (2012).
[Crossref]

Cambril, E.

F. Lemarchand, A. Sentenac, E. Cambril, and H. Giovannini, “Study of the resonant behaviour of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1(4), 545–551 (1999).
[Crossref]

Capasso, F.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Chandran, A.

A. Chandran, E. S. Barnard, J. S. White, and M. L. Brongersma, “Metal-dielectric-metal surface plasmon-polariton resonators,” Phys. Rev. B 85(8), 085416 (2012).
[Crossref]

Chang-Hasnain, C. J.

Chen, S.-W.

T.-C. Lu, S.-W. Chen, L.-F. Lin, T.-T. Kao, C.-C. Kao, P. Yu, H.-C. Kuo, S.-C. Wang, and S. Fan, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92(1), 011129 (2008).
[Crossref]

Cho, E.-H.

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Chow, E.

Coccioli, R.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, “Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals,” Appl. Phys. Lett. 75(8), 1036 (1999).
[Crossref]

Dodabalapur, A.

El Beheiry, M.

Faleev, S. V.

M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Localization versus delocalization of surface plasmons in nanosystems: can one state have both characteristics?” Phys. Rev. Lett. 87(16), 167401 (2001).
[Crossref] [PubMed]

Fan, S.

M. El Beheiry, V. Liu, S. Fan, and O. Levi, “Sensitivity enhancement in photonic crystal slab biosensors,” Opt. Express 18(22), 22702–22714 (2010).
[Crossref] [PubMed]

T.-C. Lu, S.-W. Chen, L.-F. Lin, T.-T. Kao, C.-C. Kao, P. Yu, H.-C. Kuo, S.-C. Wang, and S. Fan, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92(1), 011129 (2008).
[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 (2003).
[Crossref]

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
[Crossref] [PubMed]

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

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
[Crossref]

Fattal, D.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

Fehrembach, A.-L.

Fiorentino, M.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

Fleischhauer, M.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref] [PubMed]

Friesem, A. A.

A. Sharon, D. Rosenblatt, and A. A. Friesem, “Narrow spectral bandwidths with grating waveguide structures,” Appl. Phys. Lett. 69(27), 4154 (1996).
[Crossref]

Gaylord, T. K.

Genevet, P.

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Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
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Nat. Mater. (3)

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
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[Crossref]

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[Crossref]

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Figures (5)

Fig. 1
Fig. 1

Design of the “Diatomic” grating and the emergence of intrinsic “dark” modes. (a) Schematic diagram of a regular grating. Grating is excited with normal incidence and TM polarization. Thickness t , period P / 2 and filling factor γ are given as grating parameters. Incidence and Transmission interfaces of the grating are at z = 0 and z = t , respectively. Blue blocks represent dielectric bars with width s . The one dimensional grating is assumed to be infinitely long in the y direction. (b) Brillouin zone of a typical regular grating with γ = 0.2 . Red dots represent “bright” modes at the zone center and dark dots represent completely “dark” modes due to reflection symmetries in the grating. Gray dots represent “dark” modes with a small but finite κ at the zone edge. Shaded area indicates frequencies outside the subwavelength regime ( ω > 4 π c / P and ω > 2 π c / P for the regular and “diatomic” gratings respectively). (c) Schematic diagram of a “diatomic” grating with the same filling factor γ = 0.2 except for a doubled period P and finite air gap difference δ . Two subcells merge into a larger unit cell. (d) Brillouin zone of a typical “diatomic” grating with δ = 0.05 . Note the Brillouin zone is folded with half the original size. (e) Illustration of emergence of a pair of “bright” and “dark” modes after symmetry breaking. The “dark” mode has field phases difference of nearly π in its 2 subcells. (f) The field profile for E x for the 1st order “bright” and “dark” eigenmodes in the “diatomic” design.

Fig. 2
Fig. 2

Dependence of Q on filling factors for the “diatomic” design: the thin grating case. (a) Dramatic decline in Q for the dark mode resonance as a result of increased filling factor and subsequent increased mixing with “bright” modes. (b) Reflection spectrum showing resonances of varying Q for 3 different filling factors. Inset shows a unit cell of the “diatomic” grating with given design parameters assuming P = 1 and colored blocks represent silicon bars. The x axis is wavelength λ normalized by period P . For the leftmost spectrum with γ = 0.2 , scale of x axis is magnified by 5 for clarity.

Fig. 3
Fig. 3

Demonstration of the effect of filling factors on the “diatomic” design. (a) Emergence of beating patterns from additional “bright” mode resonances for large filing factor γ in a thicker grating design. x axis is wavelength ( λ ) normalized by grating period ( P ). (b) Effective | r | for the “dark” mode (color line) and “bright” modes (gray lines) with different γ . The trend in | r | for corresponds well with decline in Q for the “dark” mode. (c) Round trip phase for “bright” (gray) and “dark” modes (color). It predicts well where the first “dark” mode resonance is (color markers, when ϕ r o u n d = 2 π n , n = 1 ) and shows the emergence of new resonances from “bright” modes as γ increases.

Fig. 4
Fig. 4

The design of a typical single high Q resonance in a thin and small γ “diatomic” grating. (a) The single high Q resonance in the “diatomic” grating (red curve, zoom-in in the inset) and the moderate Q resonance in the corresponding regular grating (blue curve). (b) The mode dispersion ( ω β ) plot in the subwavelength regime showing both the 1st “bright” mode (blue solid line) and the 1st “dark” mode (blue dashed line) for the design. They are marked with red and gray dots respectively. The 2nd “dark” mode is completely dark due to the reflection symmetry of the grating and is marked by a dark dot. (c) The Electric field ( E x ) enhancement inside the “diatomic” grating at resonance. The field enhancement is as high as 6 × 10 5 . (d) Blue curve (log-log plot) depicts power law dependence of Q as a function of δ for the “dark” mode resonance. Orange curve shows the resonance wavelength barely changes with a large range of δ from 0.001 up to 0.1.

Fig. 5
Fig. 5

In situ tuning of the high Q resonance in “diatomic” gratings. (a) Solid and dashed curves represent the simulation results of a typical “di atomic” and HCG grating respectively. Blue lines are the relative resonance shift ( Δ λ / λ 0 ) while orange lines are Q factors at the corresponding resonances. Inset shows the unit cell of HCG (orange) and “diatomic” (blue) gratings reflecting their design parameters for comparison used in the simulation. P = 1 is assumed. The blocks represent silicon bars. (b) A schematic view of the structure that allows for in situ mechanical tuning of the grating period. Light is of TM polarization and normal incidence. It also gives an example of how the geometry of the grating changes after stretching from P to P + Δ P , where s and a 1 are defined previously in the text.

Equations (2)

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1 | r | 2 κ | 0 P E x d x | 2 z = 0 , t P
κ | 0 P E x d x | 2 P = | 0 s + a 1 E x d x s + a 1 P E x d x | 2 P δ 2 0

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