Abstract

A metal/multi-insulator/metal waveguide plasmonic Bragg grating with a large dynamic range of index modulation is investigated analytically and numerically. Theoretical formalism of the dispersion relation for the present and general one-dimensional gratings is developed for TM waves in the vicinity of each stop band. Wide-band and narrow-band designs with their respective FWHM bandwidths of 173.4 nm and < 3.4 nm in the 1550 nm band using a grating length of < 16.0 µm are numerically demonstrated. Time-average power vortexes near the silica-silicon interfaces are revealed in the stop band and are attributed to the contra-flow interaction and simultaneous satisfactions of the Bragg condition for the incident and backward-diffracted waves. An enhanced forward-propagating power is thus shown to occur over certain sections within one period due to the power coupling from the backward-diffracted waves.

© 2010 Optical Society of America

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References

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
    [CrossRef] [PubMed]
  2. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997).
    [CrossRef] [PubMed]
  3. S. A. Maier, “Plasmonics: the promise of highly integrated optical devices,” IEEE J. Sel. Top. Quantum Electron. 12, 1671–1677 (2006).
    [CrossRef]
  4. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
    [CrossRef] [PubMed]
  5. B. Wang, and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87(013), 107 (2005).
  6. S. Jetté-Charbonneau, R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of Bragg gratings based on long-ranging surface plasmon polariton waveguides,” Opt. Express 13(12), 4674–4682 (2005).
    [CrossRef] [PubMed]
  7. A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightwave Technol. 24(2), 912–918 (2006).
    [CrossRef]
  8. J.-W. Mu, and W.-P. Huang, “A low-loss surface plasmonic Bragg grating,” J. Lightwave Technol. 27(4), 436–439 (2009).
    [CrossRef]
  9. A. Hosseini, and Y. Massoud, “A low-loss metal-insulator-metal plasmonic Bragg reflector,” Opt. Express 14(23), 318–323 (2006).
    [CrossRef]
  10. Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
    [CrossRef]
  11. J.-Q. Liu, L.-L. Wang, M.-D. He, W.-Q. Huang, D. Wang, B. S. Zou, and S. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express 16(7), 4888–4894 (2008).
    [CrossRef] [PubMed]
  12. J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16(1), 413–425 (2008).
    [CrossRef] [PubMed]
  13. Z. Fu, Q. Gan, K. Gao, Z. Pan, and F. J. Bartoli, “Numerical investigation of a bidirectional wave coupler based on plasmonic Bragg gratings in the near infrared domain,” J. Lightwave Technol. 26(22), 3699–3703 (2008).
    [CrossRef]
  14. Y.-J. Chang, and G.-Y. Lo, “A narrow band metal–multi-insulator–metal waveguide plasmonic Bragg grating,” IEEE Photon. Technol. Lett. 22, 634–636 (2010).
    [CrossRef]
  15. C. Yeh, K. F. Casey, and Z. A. Kaprielian, “Transverse magnetic wave propagation in sinusoidally stratified dielectric media,” IEEE Trans. Microw. Theory Tech. 13(3), 297–302 (1965).
    [CrossRef]
  16. P. B. Johnson, and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  17. Y.-J. Chang, T. K. Gaylord, and G.-K. Chang, “Attenuation in waveguides on FR-4 boards due to periodic substrate undulations,” Appl. Opt. 46(12), 2234–2243 (2007).
    [CrossRef] [PubMed]

2010 (1)

Y.-J. Chang, and G.-Y. Lo, “A narrow band metal–multi-insulator–metal waveguide plasmonic Bragg grating,” IEEE Photon. Technol. Lett. 22, 634–636 (2010).
[CrossRef]

2009 (1)

2008 (3)

2007 (2)

Y.-J. Chang, T. K. Gaylord, and G.-K. Chang, “Attenuation in waveguides on FR-4 boards due to periodic substrate undulations,” Appl. Opt. 46(12), 2234–2243 (2007).
[CrossRef] [PubMed]

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

2006 (4)

A. Hosseini, and Y. Massoud, “A low-loss metal-insulator-metal plasmonic Bragg reflector,” Opt. Express 14(23), 318–323 (2006).
[CrossRef]

S. A. Maier, “Plasmonics: the promise of highly integrated optical devices,” IEEE J. Sel. Top. Quantum Electron. 12, 1671–1677 (2006).
[CrossRef]

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightwave Technol. 24(2), 912–918 (2006).
[CrossRef]

2005 (2)

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

1997 (1)

1972 (1)

P. B. Johnson, and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1965 (1)

C. Yeh, K. F. Casey, and Z. A. Kaprielian, “Transverse magnetic wave propagation in sinusoidally stratified dielectric media,” IEEE Trans. Microw. Theory Tech. 13(3), 297–302 (1965).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Bartoli, F. J.

Berini, P.

Boltasseva, A.

Bozhevolnyi, S. I.

Casey, K. F.

C. Yeh, K. F. Casey, and Z. A. Kaprielian, “Transverse magnetic wave propagation in sinusoidally stratified dielectric media,” IEEE Trans. Microw. Theory Tech. 13(3), 297–302 (1965).
[CrossRef]

Chang, G.-K.

Chang, Y.-J.

Y.-J. Chang, and G.-Y. Lo, “A narrow band metal–multi-insulator–metal waveguide plasmonic Bragg grating,” IEEE Photon. Technol. Lett. 22, 634–636 (2010).
[CrossRef]

Y.-J. Chang, T. K. Gaylord, and G.-K. Chang, “Attenuation in waveguides on FR-4 boards due to periodic substrate undulations,” Appl. Opt. 46(12), 2234–2243 (2007).
[CrossRef] [PubMed]

Charbonneau, R.

Christy, R. W.

P. B. Johnson, and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Forsberg, E.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

Fu, Z.

Gan, Q.

Gao, K.

Gaylord, T. K.

Han, Z.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

He, M.-D.

He, S.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

Hosseini, A.

A. Hosseini, and Y. Massoud, “A low-loss metal-insulator-metal plasmonic Bragg reflector,” Opt. Express 14(23), 318–323 (2006).
[CrossRef]

Huang, W.-P.

Huang, W.-Q.

Jetté-Charbonneau, S.

Johnson, P. B.

P. B. Johnson, and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Kaprielian, Z. A.

C. Yeh, K. F. Casey, and Z. A. Kaprielian, “Transverse magnetic wave propagation in sinusoidally stratified dielectric media,” IEEE Trans. Microw. Theory Tech. 13(3), 297–302 (1965).
[CrossRef]

Kim, H.

Kobayashi, T.

Lahoud, N.

Lee, B.

Leosson, K.

Liu, J.-Q.

Lo, G.-Y.

Y.-J. Chang, and G.-Y. Lo, “A narrow band metal–multi-insulator–metal waveguide plasmonic Bragg grating,” IEEE Photon. Technol. Lett. 22, 634–636 (2010).
[CrossRef]

Maier, S. A.

S. A. Maier, “Plasmonics: the promise of highly integrated optical devices,” IEEE J. Sel. Top. Quantum Electron. 12, 1671–1677 (2006).
[CrossRef]

Massoud, Y.

A. Hosseini, and Y. Massoud, “A low-loss metal-insulator-metal plasmonic Bragg reflector,” Opt. Express 14(23), 318–323 (2006).
[CrossRef]

Mattiussi, G.

Morimoto, A.

Mu, J.-W.

Nikolajsen, T.

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

Pan, Z.

Park, J.

Takahara, J.

Taki, H.

Wang, B.

B. Wang, and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87(013), 107 (2005).

Wang, D.

Wang, G. P.

B. Wang, and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87(013), 107 (2005).

Wang, L.-L.

Wen, S.

Yamagishi, S.

Yeh, C.

C. Yeh, K. F. Casey, and Z. A. Kaprielian, “Transverse magnetic wave propagation in sinusoidally stratified dielectric media,” IEEE Trans. Microw. Theory Tech. 13(3), 297–302 (1965).
[CrossRef]

Zou, B. S.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

B. Wang, and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87(013), 107 (2005).

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

S. A. Maier, “Plasmonics: the promise of highly integrated optical devices,” IEEE J. Sel. Top. Quantum Electron. 12, 1671–1677 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

Y.-J. Chang, and G.-Y. Lo, “A narrow band metal–multi-insulator–metal waveguide plasmonic Bragg grating,” IEEE Photon. Technol. Lett. 22, 634–636 (2010).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

C. Yeh, K. F. Casey, and Z. A. Kaprielian, “Transverse magnetic wave propagation in sinusoidally stratified dielectric media,” IEEE Trans. Microw. Theory Tech. 13(3), 297–302 (1965).
[CrossRef]

J. Lightwave Technol. (3)

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. B (1)

P. B. Johnson, and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Science (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1.
Fig. 1.

The schematic diagram (top view) of one unit cell of the proposed silver/multi-insulator/silver waveguide plasmonic Bragg grating.

Fig. 2.
Fig. 2.

Isometric plots of (a) real part, and (b) imaginary part of the effective mode index N eff associated with the fundamental mode with varying gap width w gap and central Si stripe width w Si at λ 0 = 1550 nm.

Fig. 3.
Fig. 3.

Transmission spectra of a wide-bandwidth design with structure parameters Λ=950 nm, AM = 90 nm, w gap = 130 nm, and different numbers of periods.

Fig. 4.
Fig. 4.

Transmission spectra of three design examples operating in 1550 nm band. Case 1: (Λ, AM , w gap, λB ) = (1405, 30, 145, 1540.1). Case 2: (Λ, AM , w gap, λB ) = (1405, 30, 150, 1550.4). Case 3: (Λ, AM , w gap, λB )=(1450, 30, 154, 1560.1). All numerical values are in units of nm and 11 periods are employed for all cases. The FWHM bandwidth for each case is 2.95 nm, 3.35 nm, 3.05 nm, respectively.

Fig. 5.
Fig. 5.

(a) Time-average norm power P norm (in units of W/m2) distributions and (b) the normalized x-directed power in the Si stripe and silica gap regions at λ 0 = 1600 nm within the 6th unit cell of case 2 shown in Fig. 4. The arrow indicates the direction of the vector sum of the x- and y-directed time-average power.

Fig. 6.
Fig. 6.

(a) Time-average norm power P norm (in units of W/m2) distributions and (b) the normalized x-directed power in the Si stripe and silica gap regions at λ 0 = 1550.4 nm within the 6th unit cell of case 2 shown in Fig. 4. The arrow indicates the direction of the vector sum of the x- and y-directed time-average power.

Fig. 7.
Fig. 7.

Plane-wave spectrum obtained at the end of the 6th unit cell at λ 0 = 1550.4 nm for case 2 shown in Fig. 4. ky is the wave vector in the y direction.

Tables (1)

Tables Icon

Table 1. Information on the 11-section staircase approximation to case 2 in Fig. 4. The structure is symmetric to section no. 6.

Equations (20)

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A ( x ) = A 0 A M cos ( 2 π x Λ ) ,
ε eff ( x ) = ε ¯ [ 1 δ M cos ( K · x ) ] ,
[ d 2 d ξ 2 + c 0 + 2 Σ n = 1 c n cos ( 2 n ξ ) ] f ( ξ ) = 0 ,
c 0 = ( k 0 Λ π ) 2 ε ¯ [ ( 1 δ M 2 ) 1 2 1 ] ,
c 1 = δ M 2 ( k 0 Λ π ) 2 ε ¯ + 4 b 3 2 b b 2 1 ,
c n = ( 3 n + 1 ) b n + 2 ( 3 n 1 ) b n b 2 1 ( n 2 ) ,
b = 1 δ M 1 δ M 1 δ M 2 .
{ d 2 d x 2 [ d ε eff ( x ) d x ] 1 ε eff ( x ) d d x + k 0 2 ε eff ( x ) } I ( x ) = 0 ,
Σ n = 1 c n F ( κ Λ π + 2 n ) + [ c 0 ( κ Λ π ) 2 ] F ( κ Λ π ) + Σ n = 1 c n F ( κ Λ π 2 n ) = 0 ,
F ( κ Λ π ± 2 n ) = F ( κ Λ π ± 2 n + 2 k ) , k .
D u D v c p 2 = 0 ,
D m = c 0 ( κ Λ π + 2 m ) 2 .
c 0 [ κ Λ π ( p + q ) ]
c 0 κ Λ π + ( p q ) ,
( c 0 p ) 2 ( κ Λ π q ) 2 = ( c p 2 c 0 ) 2 .
[ c 0 ( κ Λ π ) 2 ] [ c 0 ( κ Λ π 2 p ) 2 ] = c p 2
λ B = 2 ε ¯ Λ p + [ ( 1 δ M 2 ) 1 2 1 ] 2 p ,
P norm = 1 2 { [ Re ( E y H z * ) ] 2 + [ Re ( E x H z * ) ] 2 } 1 2 .
P x ( x ) = 1 P in · 1 2 Re [ E y ( x , y ) H z * ( x , y ) ] d y
cos ( ϕ θ ) m λ 0 2 N σ Λ = 0 ,

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