Abstract

We computationally study a subwavelength dielectric grating structure, show that slab waveguide modes can be used to obtain broadband high reflectivity, and analyze how slab waveguide modes influence reflection. A structure showing interference between Fabry-Perot modes, slab waveguide modes, and waveguide array modes is designed with ultra-broadband high reflectivity. Owing to the coupling of guided modes, the region with reflectivity R > 0.99 has an ultra-high bandwidth (Δf / ̅f > 30%). The incident-angle region with R > 0.99 extends over a range greater than 40°. Moreover, an asymmetric waveguide structure with a semiconductor substrate is studied.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  13. B. Zhang, S. Brodbeck, Z. Wang, M. Kamp, C. Schneider, S. Hofling, and H. Deng, “Coupling polariton quantum boxes in sub-wavelength grating microcavities,” Appl. Phys. Lett. 106(5), 051104 (2015).
    [Crossref]

2015 (4)

2012 (3)

D. Bajoni, “Polariton lasers. Hybrid light–matter lasers without inversion,” J. Phys. D 45(31), 313001 (2012).
[Crossref]

V. Liu and S. Fan, “S-4: A free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun. 183(10), 2233–2244 (2012).
[Crossref]

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

2011 (1)

Y.-J. Lin, K. Jiménez-García, and I. B. Spielman, “Spin-orbit-coupled Bose-Einstein condensates,” Nature 471(7336), 83–86 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (1)

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326(5956), 1074–1077 (2009).
[Crossref] [PubMed]

2004 (1)

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

2002 (1)

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

1989 (1)

S. Haroche and D. Kleppner, “Cavity quantum electrodynamics,” Phys. Today 42(1), 24–30 (1989).
[Crossref]

Antoni, T.

Bajoni, D.

D. Bajoni, “Polariton lasers. Hybrid light–matter lasers without inversion,” J. Phys. D 45(31), 313001 (2012).
[Crossref]

Beaudoin, G.

Boyd, R. W.

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326(5956), 1074–1077 (2009).
[Crossref] [PubMed]

Braive, R.

Briant, T.

Brodbeck, S.

B. Zhang, S. Brodbeck, Z. Wang, M. Kamp, C. Schneider, S. Hofling, and H. Deng, “Coupling polariton quantum boxes in sub-wavelength grating microcavities,” Appl. Phys. Lett. 106(5), 051104 (2015).
[Crossref]

Cagnoli, G.

Chang-Hasnain, C. J.

Cohadon, P.-F.

Deléglise, S.

Deng, H.

Z. Wang, B. Zhang, and H. Deng, “Dispersion engineering for vertical microcavities using subwavelength gratings,” Phys. Rev. Lett. 114(7), 073601 (2015).
[Crossref] [PubMed]

B. Zhang, S. Brodbeck, Z. Wang, M. Kamp, C. Schneider, S. Hofling, and H. Deng, “Coupling polariton quantum boxes in sub-wavelength grating microcavities,” Appl. Phys. Lett. 106(5), 051104 (2015).
[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 cladded subwavelength grating,” IEEE Photonics Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Dolique, V.

Fan, S.

V. Liu and S. Fan, “S-4: A free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun. 183(10), 2233–2244 (2012).
[Crossref]

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

Ferrara, J.

Flaminio, R.

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326(5956), 1074–1077 (2009).
[Crossref] [PubMed]

Haroche, S.

S. Haroche and D. Kleppner, “Cavity quantum electrodynamics,” Phys. Today 42(1), 24–30 (1989).
[Crossref]

Heidmann, A.

Hofling, S.

B. Zhang, S. Brodbeck, Z. Wang, M. Kamp, C. Schneider, S. Hofling, and H. Deng, “Coupling polariton quantum boxes in sub-wavelength grating microcavities,” Appl. Phys. Lett. 106(5), 051104 (2015).
[Crossref]

Huang, M. C. Y.

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

Jiménez-García, K.

Y.-J. Lin, K. Jiménez-García, and I. B. Spielman, “Spin-orbit-coupled Bose-Einstein condensates,” Nature 471(7336), 83–86 (2011).
[Crossref] [PubMed]

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]

Kamp, M.

B. Zhang, S. Brodbeck, Z. Wang, M. Kamp, C. Schneider, S. Hofling, and H. Deng, “Coupling polariton quantum boxes in sub-wavelength grating microcavities,” Appl. Phys. Lett. 106(5), 051104 (2015).
[Crossref]

Karagodsky, V.

Kleppner, D.

S. Haroche and D. Kleppner, “Cavity quantum electrodynamics,” Phys. Today 42(1), 24–30 (1989).
[Crossref]

Kuhn, A. G.

Lin, Y.-J.

Y.-J. Lin, K. Jiménez-García, and I. B. Spielman, “Spin-orbit-coupled Bose-Einstein condensates,” Nature 471(7336), 83–86 (2011).
[Crossref] [PubMed]

Liu, V.

V. Liu and S. Fan, “S-4: A free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun. 183(10), 2233–2244 (2012).
[Crossref]

Makles, K.

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 cladded subwavelength grating,” IEEE Photonics Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Michel, C.

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 cladded subwavelength grating,” IEEE Photonics Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Pinard, L.

Qiao, P.

Robert-Philip, I.

Schneider, C.

B. Zhang, S. Brodbeck, Z. Wang, M. Kamp, C. Schneider, S. Hofling, and H. Deng, “Coupling polariton quantum boxes in sub-wavelength grating microcavities,” Appl. Phys. Lett. 106(5), 051104 (2015).
[Crossref]

Sedgwick, F. G.

Spielman, I. B.

Y.-J. Lin, K. Jiménez-García, and I. B. Spielman, “Spin-orbit-coupled Bose-Einstein condensates,” Nature 471(7336), 83–86 (2011).
[Crossref] [PubMed]

Wang, Z.

Z. Wang, B. Zhang, and H. Deng, “Dispersion engineering for vertical microcavities using subwavelength gratings,” Phys. Rev. Lett. 114(7), 073601 (2015).
[Crossref] [PubMed]

B. Zhang, S. Brodbeck, Z. Wang, M. Kamp, C. Schneider, S. Hofling, and H. Deng, “Coupling polariton quantum boxes in sub-wavelength grating microcavities,” Appl. Phys. Lett. 106(5), 051104 (2015).
[Crossref]

Yang, W.

Zhang, B.

Z. Wang, B. Zhang, and H. Deng, “Dispersion engineering for vertical microcavities using subwavelength gratings,” Phys. Rev. Lett. 114(7), 073601 (2015).
[Crossref] [PubMed]

B. Zhang, S. Brodbeck, Z. Wang, M. Kamp, C. Schneider, S. Hofling, and H. Deng, “Coupling polariton quantum boxes in sub-wavelength grating microcavities,” Appl. Phys. Lett. 106(5), 051104 (2015).
[Crossref]

Zhu, L.

Appl. Phys. Lett. (1)

B. Zhang, S. Brodbeck, Z. Wang, M. Kamp, C. Schneider, S. Hofling, and H. Deng, “Coupling polariton quantum boxes in sub-wavelength grating microcavities,” Appl. Phys. Lett. 106(5), 051104 (2015).
[Crossref]

Comput. Phys. Commun. (1)

V. Liu and S. Fan, “S-4: A free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun. 183(10), 2233–2244 (2012).
[Crossref]

IEEE Photonics Technol. Lett. (1)

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

J. Phys. D (1)

D. Bajoni, “Polariton lasers. Hybrid light–matter lasers without inversion,” J. Phys. D 45(31), 313001 (2012).
[Crossref]

Nature (1)

Y.-J. Lin, K. Jiménez-García, and I. B. Spielman, “Spin-orbit-coupled Bose-Einstein condensates,” Nature 471(7336), 83–86 (2011).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

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]

Phys. Rev. Lett. (1)

Z. Wang, B. Zhang, and H. Deng, “Dispersion engineering for vertical microcavities using subwavelength gratings,” Phys. Rev. Lett. 114(7), 073601 (2015).
[Crossref] [PubMed]

Phys. Today (1)

S. Haroche and D. Kleppner, “Cavity quantum electrodynamics,” Phys. Today 42(1), 24–30 (1989).
[Crossref]

Science (1)

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326(5956), 1074–1077 (2009).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 (a) Schematic of the free-standing grating slab waveguide structure. (b) Reflectivity contour of the structure as a function of frequency and slab-layer thickness simulated using RCWA, with TM-polarized, surface-normal incident waves and the parameters h 1 =0.167Λ , ε r =11.9 , and η=0.5 . The contour map shows a dispersion shape of guided modes but with some cut-off frequencies (dashed lines), which has affinities with the dispersion of WGA modes. Intricate transmission properties occur in the Λ<λ<Λ n eff range owing to interference.
Fig. 2
Fig. 2 (a) Reflectivity contour as a function of frequency and grating-layer thickness with h1 = 0.685Λ. The thick grating layer can sustain WGA modes, which are essential for HCGs. The interference among guided modes, WGA modes, and Fabry-Perot modes leads to the broadband high reflection (dark red area). (b) Reflectivity with the parameters described in (a) for three different configurations: h2 = 0.45Λ and η = 0.5(black line), h2 = 0.5Λ and η = 0.5 (red dashed line), and h2 = 0.45Λ and η = 0.55 (blue dash-dotted line).
Fig. 3
Fig. 3 (a) Reflectivity contour as a function of frequency and incident angle with the parameters h1 = 0.685Λ and h2 = 0.45Λ. (b) Reflectivity contour as a function of frequency and incident angle with the parameters h1 = 0.685Λ and h2 = 0 (HCGs). (c) Reflectivity as a function of incident angle at a frequency of 0.5×2πc/Λ . The high reflection angle region is significantly expanded because of the slab waveguide modes.
Fig. 4
Fig. 4 (a) Schematic of the asymmetric waveguide structure. (b) Reflectivity contour of the structure with a substrate (εr = 10.8) as a function of frequency and grating thickness with h2 = 0.45Λ.

Equations (1)

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k z 2 = (2π n i /λ) 2 (2πm/Λ) 2 .

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