Abstract

We investigate optical mode tailoring in a semiconductor microcavity with a metal grating on top and a dielectric grating (DG) on the bottom. Strong coupling between microcavity and grating-diffraction modes is explained in the Fano-picture. The Fano resonance shows a weak dependence upon grating height and duty ratio, but is strong upon grating period. The microcavity transmission line shapes are “S” and anti “S”-type for the metal and DGs, respectively. Together with these two types of Fano resonances, the transmission spectra have been tailored into very sharp peaks with FWHM being up to 0.1 nm. We prove that this optical mode tailoring method is quite applicable for other waveguide-grating structures too.

© 2012 Optical Society of America

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  1. A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, Phys. Rev. Lett. 91, 183901 (2003).
    [CrossRef]
  2. S. Feng, X. Zhang, J. Song, H. Liu, and Y. Song, Opt. Express 17, 426 (2009).
    [CrossRef]
  3. X. Zhang, B. Sun, J. M. Hodgkiss, and R. H. Friend, Adv. Mater. 20, 4455 (2008).
    [CrossRef]
  4. R. R. Boye, R. W. Ziolkowski, and R. K. Kostuk, Appl. Opt. 38, 5181 (1999).
    [CrossRef]
  5. X. Zhang, H. Liu, J. Tian, Y. Song, and L. Wang, Nano Lett. 8, 2653 (2008).
    [CrossRef]
  6. G. Levy-Yurista and A. A. Friesem, Appl. Phys. Lett. 77, 1596 (2000).
    [CrossRef]
  7. A. Sharon, D. Rosenblatt, and A. A. Friesem, Appl. Phys. Lett. 69, 4154 (1996).
    [CrossRef]
  8. N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Soennichsen, and H. Giessen, Nano Lett. 10, 1103 (2010).
    [CrossRef]
  9. R. Horvath, H. C. Pedersen, N. Skivesen, D. Selmeczi, and N. B. Larsen, Opt. Lett. 28, 1233 (2003).
    [CrossRef]
  10. G. Nemova and R. Kashyap, J. Lightwave Technol. 25, 2244 (2007).
    [CrossRef]
  11. S. Feng, X. Zhang, and P. J. Klar, Appl. Phys. Lett. 99, 053119 (2011).
    [CrossRef]
  12. Y. Zhang, X. Hu, Y. Fu, H. Yang, and Q. Gong, Appl. Phys. Lett. 100, 031106 (2012).
    [CrossRef]
  13. H. Deng, H. Haug, and Y. Yamamoto, Rev. Mod. Phys. 82, 1489 (2010).
    [CrossRef]
  14. C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007).
    [CrossRef]
  15. E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).
  16. D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999).
    [CrossRef]
  17. S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
    [CrossRef]

2012 (1)

Y. Zhang, X. Hu, Y. Fu, H. Yang, and Q. Gong, Appl. Phys. Lett. 100, 031106 (2012).
[CrossRef]

2011 (1)

S. Feng, X. Zhang, and P. J. Klar, Appl. Phys. Lett. 99, 053119 (2011).
[CrossRef]

2010 (2)

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Soennichsen, and H. Giessen, Nano Lett. 10, 1103 (2010).
[CrossRef]

H. Deng, H. Haug, and Y. Yamamoto, Rev. Mod. Phys. 82, 1489 (2010).
[CrossRef]

2009 (1)

2008 (2)

X. Zhang, B. Sun, J. M. Hodgkiss, and R. H. Friend, Adv. Mater. 20, 4455 (2008).
[CrossRef]

X. Zhang, H. Liu, J. Tian, Y. Song, and L. Wang, Nano Lett. 8, 2653 (2008).
[CrossRef]

2007 (2)

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007).
[CrossRef]

G. Nemova and R. Kashyap, J. Lightwave Technol. 25, 2244 (2007).
[CrossRef]

2003 (2)

R. Horvath, H. C. Pedersen, N. Skivesen, D. Selmeczi, and N. B. Larsen, Opt. Lett. 28, 1233 (2003).
[CrossRef]

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, Phys. Rev. Lett. 91, 183901 (2003).
[CrossRef]

2002 (1)

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
[CrossRef]

2000 (1)

G. Levy-Yurista and A. A. Friesem, Appl. Phys. Lett. 77, 1596 (2000).
[CrossRef]

1999 (2)

D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999).
[CrossRef]

R. R. Boye, R. W. Ziolkowski, and R. K. Kostuk, Appl. Opt. 38, 5181 (1999).
[CrossRef]

1996 (1)

A. Sharon, D. Rosenblatt, and A. A. Friesem, Appl. Phys. Lett. 69, 4154 (1996).
[CrossRef]

Boye, R. R.

Byrnes, T.

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007).
[CrossRef]

Christ, A.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, Phys. Rev. Lett. 91, 183901 (2003).
[CrossRef]

Culshaw, I. S.

D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999).
[CrossRef]

Deng, H.

H. Deng, H. Haug, and Y. Yamamoto, Rev. Mod. Phys. 82, 1489 (2010).
[CrossRef]

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007).
[CrossRef]

Eigenthaler, U.

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Soennichsen, and H. Giessen, Nano Lett. 10, 1103 (2010).
[CrossRef]

Feng, S.

S. Feng, X. Zhang, and P. J. Klar, Appl. Phys. Lett. 99, 053119 (2011).
[CrossRef]

S. Feng, X. Zhang, J. Song, H. Liu, and Y. Song, Opt. Express 17, 426 (2009).
[CrossRef]

Fraser, M. D.

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007).
[CrossRef]

Friend, R. H.

X. Zhang, B. Sun, J. M. Hodgkiss, and R. H. Friend, Adv. Mater. 20, 4455 (2008).
[CrossRef]

Friesem, A. A.

G. Levy-Yurista and A. A. Friesem, Appl. Phys. Lett. 77, 1596 (2000).
[CrossRef]

A. Sharon, D. Rosenblatt, and A. A. Friesem, Appl. Phys. Lett. 69, 4154 (1996).
[CrossRef]

Fu, Y.

Y. Zhang, X. Hu, Y. Fu, H. Yang, and Q. Gong, Appl. Phys. Lett. 100, 031106 (2012).
[CrossRef]

Fujisawa, T.

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007).
[CrossRef]

Giessen, H.

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Soennichsen, and H. Giessen, Nano Lett. 10, 1103 (2010).
[CrossRef]

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, Phys. Rev. Lett. 91, 183901 (2003).
[CrossRef]

Gippius, N. A.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, Phys. Rev. Lett. 91, 183901 (2003).
[CrossRef]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Gong, Q.

Y. Zhang, X. Hu, Y. Fu, H. Yang, and Q. Gong, Appl. Phys. Lett. 100, 031106 (2012).
[CrossRef]

Haug, H.

H. Deng, H. Haug, and Y. Yamamoto, Rev. Mod. Phys. 82, 1489 (2010).
[CrossRef]

Hirscher, M.

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Soennichsen, and H. Giessen, Nano Lett. 10, 1103 (2010).
[CrossRef]

Hodgkiss, J. M.

X. Zhang, B. Sun, J. M. Hodgkiss, and R. H. Friend, Adv. Mater. 20, 4455 (2008).
[CrossRef]

Horvath, R.

Hu, X.

Y. Zhang, X. Hu, Y. Fu, H. Yang, and Q. Gong, Appl. Phys. Lett. 100, 031106 (2012).
[CrossRef]

Ishihara, T.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Kashyap, R.

Kim, N. Y.

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007).
[CrossRef]

Klar, P. J.

S. Feng, X. Zhang, and P. J. Klar, Appl. Phys. Lett. 99, 053119 (2011).
[CrossRef]

Kostuk, R. K.

Kuhl, J.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, Phys. Rev. Lett. 91, 183901 (2003).
[CrossRef]

Kumada, N.

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007).
[CrossRef]

Lai, C. W.

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007).
[CrossRef]

Langguth, L.

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Soennichsen, and H. Giessen, Nano Lett. 10, 1103 (2010).
[CrossRef]

Larsen, N. B.

Levy-Yurista, G.

G. Levy-Yurista and A. A. Friesem, Appl. Phys. Lett. 77, 1596 (2000).
[CrossRef]

Liu, H.

S. Feng, X. Zhang, J. Song, H. Liu, and Y. Song, Opt. Express 17, 426 (2009).
[CrossRef]

X. Zhang, H. Liu, J. Tian, Y. Song, and L. Wang, Nano Lett. 8, 2653 (2008).
[CrossRef]

Liu, N.

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Soennichsen, and H. Giessen, Nano Lett. 10, 1103 (2010).
[CrossRef]

Mesch, M.

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Soennichsen, and H. Giessen, Nano Lett. 10, 1103 (2010).
[CrossRef]

Muljarov, E. A.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Nemova, G.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

Pedersen, H. C.

Recher, P.

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007).
[CrossRef]

Rosenblatt, D.

A. Sharon, D. Rosenblatt, and A. A. Friesem, Appl. Phys. Lett. 69, 4154 (1996).
[CrossRef]

Roumpos, G.

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007).
[CrossRef]

Selmeczi, D.

Sharon, A.

A. Sharon, D. Rosenblatt, and A. A. Friesem, Appl. Phys. Lett. 69, 4154 (1996).
[CrossRef]

Skivesen, N.

Soennichsen, C.

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Soennichsen, and H. Giessen, Nano Lett. 10, 1103 (2010).
[CrossRef]

Song, J.

Song, Y.

S. Feng, X. Zhang, J. Song, H. Liu, and Y. Song, Opt. Express 17, 426 (2009).
[CrossRef]

X. Zhang, H. Liu, J. Tian, Y. Song, and L. Wang, Nano Lett. 8, 2653 (2008).
[CrossRef]

Sun, B.

X. Zhang, B. Sun, J. M. Hodgkiss, and R. H. Friend, Adv. Mater. 20, 4455 (2008).
[CrossRef]

Tian, J.

X. Zhang, H. Liu, J. Tian, Y. Song, and L. Wang, Nano Lett. 8, 2653 (2008).
[CrossRef]

Tikhodeev, S. G.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, Phys. Rev. Lett. 91, 183901 (2003).
[CrossRef]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Utsunomiya, S.

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007).
[CrossRef]

Wang, L.

X. Zhang, H. Liu, J. Tian, Y. Song, and L. Wang, Nano Lett. 8, 2653 (2008).
[CrossRef]

Weiss, T.

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Soennichsen, and H. Giessen, Nano Lett. 10, 1103 (2010).
[CrossRef]

Whittaker, D. M.

D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999).
[CrossRef]

Yablonskii, A. L.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Yamamoto, Y.

H. Deng, H. Haug, and Y. Yamamoto, Rev. Mod. Phys. 82, 1489 (2010).
[CrossRef]

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007).
[CrossRef]

Yang, H.

Y. Zhang, X. Hu, Y. Fu, H. Yang, and Q. Gong, Appl. Phys. Lett. 100, 031106 (2012).
[CrossRef]

Zhang, X.

S. Feng, X. Zhang, and P. J. Klar, Appl. Phys. Lett. 99, 053119 (2011).
[CrossRef]

S. Feng, X. Zhang, J. Song, H. Liu, and Y. Song, Opt. Express 17, 426 (2009).
[CrossRef]

X. Zhang, B. Sun, J. M. Hodgkiss, and R. H. Friend, Adv. Mater. 20, 4455 (2008).
[CrossRef]

X. Zhang, H. Liu, J. Tian, Y. Song, and L. Wang, Nano Lett. 8, 2653 (2008).
[CrossRef]

Zhang, Y.

Y. Zhang, X. Hu, Y. Fu, H. Yang, and Q. Gong, Appl. Phys. Lett. 100, 031106 (2012).
[CrossRef]

Ziolkowski, R. W.

Adv. Mater. (1)

X. Zhang, B. Sun, J. M. Hodgkiss, and R. H. Friend, Adv. Mater. 20, 4455 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

G. Levy-Yurista and A. A. Friesem, Appl. Phys. Lett. 77, 1596 (2000).
[CrossRef]

A. Sharon, D. Rosenblatt, and A. A. Friesem, Appl. Phys. Lett. 69, 4154 (1996).
[CrossRef]

S. Feng, X. Zhang, and P. J. Klar, Appl. Phys. Lett. 99, 053119 (2011).
[CrossRef]

Y. Zhang, X. Hu, Y. Fu, H. Yang, and Q. Gong, Appl. Phys. Lett. 100, 031106 (2012).
[CrossRef]

J. Lightwave Technol. (1)

Nano Lett. (2)

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Soennichsen, and H. Giessen, Nano Lett. 10, 1103 (2010).
[CrossRef]

X. Zhang, H. Liu, J. Tian, Y. Song, and L. Wang, Nano Lett. 8, 2653 (2008).
[CrossRef]

Nature (1)

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Nature 450, 529 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (2)

D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999).
[CrossRef]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, Phys. Rev. Lett. 91, 183901 (2003).
[CrossRef]

Rev. Mod. Phys. (1)

H. Deng, H. Haug, and Y. Yamamoto, Rev. Mod. Phys. 82, 1489 (2010).
[CrossRef]

Other (1)

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic illustration of the semiconductor microcavity with a metal grating on top and a dielectric grating on the bottom. (b) Geometry of diffraction waves transferred in (a).

Fig. 2.
Fig. 2.

Transmission spectra of SMC-MG [(a), (c), and (e)] and of SMC-DG [(b), (d), and (f)]. For comparison, the solid gray lines in each panel represent the SMC transmission. The parameters used are given in every panel.

Fig. 3.
Fig. 3.

Transmission spectra of the SMC-MDG structure varying (a) with the grating period L and (b) with the relative deviation fd between the Ag and GaAs gratings. In (a), hg=50nm, and fg=fd=1/3; in (b), hg=50nm, fg=1/3, and L=302.5nm. For the purpose of convenient observation, the curves of fd=0 and 1/12 in (b) are amplified.

Fig. 4.
Fig. 4.

Transmission spectra of waveguide-grating structures. The dashed line is the transmission spectrum of the AlAs waveguide without grating. The parameters defined are similar to Fig. 1(a), except the AlAs waveguide height being 4λc/nb. Other parameters are: L=302nm, hg=50nm, fg=1/3, and fd=1/4.

Equations (9)

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

Ey(j)(x,z)=μEμ(j)(x)eiμGz,
2x2e(j)+Ξ(j)·e(j)=0,
Ξ(j)=(ε0(j)k02G2ε1(j)k02ε2(j)k02ε1(j)k02ε0(j)k02ε1(j)k02ε2(j)k02ε1(j)k02ε0(j)k02G2).
M(j)=W(j)P(j)W˜(j)Q(j),
Wμμ(j)=Vμμ(j)(11ikμ(j)ikμ(j)),
Pμμ(j)=diag(eikμ(j)h(j),eikμ(j)h(j)),
Qμμ(j)=diag(eiμ2πξ(j),eiμ2πξ(j)).
M=M(N)M(N1)M(1).
T=|E0(N+1)/Ein|2,R=|E0(0)/Ein|2

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