Abstract

In this paper, we present a modeling and design methodology based on characteristic impedance for plasmonic waveguides with Metal-Insulator-Metal (MIM) configuration. Finite-Difference Time-Domain (FDTD) simulations indicate that the impedance matching results in negligible reflection at discontinuities in MIM heterostructures. Leveraging the MIM impedance model, we present a general Transfer Matrix Method model for MIM Bragg reflectors and validate our model against FDTD simulations. We show that both periodically stacked dielectric layers of different thickness or different material can achieve the same performance in terms of propagation loss and minimum transmission at the central bandgap frequency in the case of a finite number of periods.

© 2008 Optical Society of America

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  1. M. Rattier, H. Benisty, R. Stanley, J.-F. Carlin, R. Houdre, U. Oesterle, C. Smith, C. Weisbuch, and T. Krauss, "Toward ultrahigh-efficiency aluminum oxide microcavitylight-emitting diodes: guided mode extraction by photonic crystals," IEEE J. Sel. Top. Quantum. Electron. 8, 238-247 (2002).
    [CrossRef]
  2. J. Wierer, D. Kellogg, and N. Holonyak, "Tunnel contact junction native-oxide aperture and mirror vertical-cavity surface-emitting lasers and resonant-cavity light-emitting diodes," Appl. Phys. Lett. 74, 926-928 (1999).
    [CrossRef]
  3. D. Zhao, K. Chan, Y. Liu, L. Zhang, and I. Bennion, "Wavelength-switched optical pulse generation in a fiber ring laser with a Fabry-Perot semiconductor modulator and a sampled fiber Bragg grating," IEEE Photon. Technol. Lett. 13, 191-193 (2001).
    [CrossRef]
  4. J. Dionne, L. Sweatlock, and H. Atwater, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006).
    [CrossRef]
  5. G. Veronis and S. Fan, "Subwavelength plasmonic waveguide structures based on slots in thin metal films," Proceed. SPIE 6123 (2006).
    [CrossRef]
  6. P. Hobson, S. Wedge, J. Wasey, I. Sage, and W. Barnes, "Surface plasmon mediated emission from organic light-emitting diodes," Adv. Mater. 14, 1393-1396 (2005).
    [CrossRef]
  7. A. Tredicucci, C. Gmachl, F. Capasso, A. Hutchinson, D. Sivco, and A. Cho, "Single-mode surface-plasmon laser," Appl. Phys. Lett. 76, 2164-2166 (2000).
    [CrossRef]
  8. C. Sirtori, J. Faist, F. Capasso, D. Sivco, A. Hutchinson, and A. Cho, "Quantum cascade laser with plasmonenhanced waveguide operating at 8.4 u m wavelength," Appl. Phys. Lett. 66, 3242-3244 (1995).
    [CrossRef]
  9. H. Ditlbacher, J. Krenn, G. Schider, A. Leitner, and F. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762-1764 (2002).
    [CrossRef]
  10. J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. Gonzalez, and A.-L. Baudrion, "Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides," Phys. Rev. B 70, 235406 (2004).
    [CrossRef]
  11. B. Wang and G. P. Wang, "Plasmon Bragg reflectors and nanocavities on flat metallic surfaces," Appl. Phys. Lett. 87, 013107 (2005).
    [CrossRef]
  12. A. Hosseini and Y. Massoud, "A low-loss metal-insulator-metal plasmonic bragg reflector," Opt. Express 14, 318-323 (2006).
    [CrossRef]
  13. 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]
  14. G. Veronis and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett. 87, 131102 (2005).
    [CrossRef]
  15. I. Nusinsky and A. A. Hardy, "Band-gap analysis of one-dimensional photonic crystals and conditions for gap closing," Phys. Rev. B 73, 125104 (2006).
    [CrossRef]

2007

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

A. Hosseini and Y. Massoud, "A low-loss metal-insulator-metal plasmonic bragg reflector," Opt. Express 14, 318-323 (2006).
[CrossRef]

I. Nusinsky and A. A. Hardy, "Band-gap analysis of one-dimensional photonic crystals and conditions for gap closing," Phys. Rev. B 73, 125104 (2006).
[CrossRef]

J. Dionne, L. Sweatlock, and H. Atwater, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

G. Veronis and S. Fan, "Subwavelength plasmonic waveguide structures based on slots in thin metal films," Proceed. SPIE 6123 (2006).
[CrossRef]

2005

P. Hobson, S. Wedge, J. Wasey, I. Sage, and W. Barnes, "Surface plasmon mediated emission from organic light-emitting diodes," Adv. Mater. 14, 1393-1396 (2005).
[CrossRef]

G. Veronis and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

B. Wang and G. P. Wang, "Plasmon Bragg reflectors and nanocavities on flat metallic surfaces," Appl. Phys. Lett. 87, 013107 (2005).
[CrossRef]

2004

J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. Gonzalez, and A.-L. Baudrion, "Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides," Phys. Rev. B 70, 235406 (2004).
[CrossRef]

2002

M. Rattier, H. Benisty, R. Stanley, J.-F. Carlin, R. Houdre, U. Oesterle, C. Smith, C. Weisbuch, and T. Krauss, "Toward ultrahigh-efficiency aluminum oxide microcavitylight-emitting diodes: guided mode extraction by photonic crystals," IEEE J. Sel. Top. Quantum. Electron. 8, 238-247 (2002).
[CrossRef]

H. Ditlbacher, J. Krenn, G. Schider, A. Leitner, and F. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762-1764 (2002).
[CrossRef]

2001

D. Zhao, K. Chan, Y. Liu, L. Zhang, and I. Bennion, "Wavelength-switched optical pulse generation in a fiber ring laser with a Fabry-Perot semiconductor modulator and a sampled fiber Bragg grating," IEEE Photon. Technol. Lett. 13, 191-193 (2001).
[CrossRef]

2000

A. Tredicucci, C. Gmachl, F. Capasso, A. Hutchinson, D. Sivco, and A. Cho, "Single-mode surface-plasmon laser," Appl. Phys. Lett. 76, 2164-2166 (2000).
[CrossRef]

1999

J. Wierer, D. Kellogg, and N. Holonyak, "Tunnel contact junction native-oxide aperture and mirror vertical-cavity surface-emitting lasers and resonant-cavity light-emitting diodes," Appl. Phys. Lett. 74, 926-928 (1999).
[CrossRef]

1995

C. Sirtori, J. Faist, F. Capasso, D. Sivco, A. Hutchinson, and A. Cho, "Quantum cascade laser with plasmonenhanced waveguide operating at 8.4 u m wavelength," Appl. Phys. Lett. 66, 3242-3244 (1995).
[CrossRef]

Adv. Mater.

P. Hobson, S. Wedge, J. Wasey, I. Sage, and W. Barnes, "Surface plasmon mediated emission from organic light-emitting diodes," Adv. Mater. 14, 1393-1396 (2005).
[CrossRef]

Appl. Phys. Lett.

A. Tredicucci, C. Gmachl, F. Capasso, A. Hutchinson, D. Sivco, and A. Cho, "Single-mode surface-plasmon laser," Appl. Phys. Lett. 76, 2164-2166 (2000).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. Sivco, A. Hutchinson, and A. Cho, "Quantum cascade laser with plasmonenhanced waveguide operating at 8.4 u m wavelength," Appl. Phys. Lett. 66, 3242-3244 (1995).
[CrossRef]

H. Ditlbacher, J. Krenn, G. Schider, A. Leitner, and F. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762-1764 (2002).
[CrossRef]

J. Wierer, D. Kellogg, and N. Holonyak, "Tunnel contact junction native-oxide aperture and mirror vertical-cavity surface-emitting lasers and resonant-cavity light-emitting diodes," Appl. Phys. Lett. 74, 926-928 (1999).
[CrossRef]

B. Wang and G. P. Wang, "Plasmon Bragg reflectors and nanocavities on flat metallic surfaces," Appl. Phys. Lett. 87, 013107 (2005).
[CrossRef]

G. Veronis and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum. Electron.

M. Rattier, H. Benisty, R. Stanley, J.-F. Carlin, R. Houdre, U. Oesterle, C. Smith, C. Weisbuch, and T. Krauss, "Toward ultrahigh-efficiency aluminum oxide microcavitylight-emitting diodes: guided mode extraction by photonic crystals," IEEE J. Sel. Top. Quantum. Electron. 8, 238-247 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

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]

D. Zhao, K. Chan, Y. Liu, L. Zhang, and I. Bennion, "Wavelength-switched optical pulse generation in a fiber ring laser with a Fabry-Perot semiconductor modulator and a sampled fiber Bragg grating," IEEE Photon. Technol. Lett. 13, 191-193 (2001).
[CrossRef]

Opt. Express

A. Hosseini and Y. Massoud, "A low-loss metal-insulator-metal plasmonic bragg reflector," Opt. Express 14, 318-323 (2006).
[CrossRef]

Phys. Rev. B

I. Nusinsky and A. A. Hardy, "Band-gap analysis of one-dimensional photonic crystals and conditions for gap closing," Phys. Rev. B 73, 125104 (2006).
[CrossRef]

J. Dionne, L. Sweatlock, and H. Atwater, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. Gonzalez, and A.-L. Baudrion, "Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides," Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Proceed. SPIE

G. Veronis and S. Fan, "Subwavelength plasmonic waveguide structures based on slots in thin metal films," Proceed. SPIE 6123 (2006).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

(a) Real part and (b) imaginary part of effective index (neff) variation as a function of wavelength for d=25 nm, 50 nm, 100 nm and 200 nm, for Ag/SiO 2/Ag (solid line) and Ag/Si/Ag (circled line) waveguides. The refractive indices (n) of SiO 2 and Si are assumed to be 1.46 and 3.4, respectively. A schematic of MIM waveguide is shown in (a) inset.

Fig. 2.
Fig. 2.

FDTD simulation results for a thickness modulated waveguide designed based on (a) our characteristic impedance matching technique provided in Eq. 4 and (b) the characteristic impedance matching technique introduced in [14]. The schematic of both structures with actual physical dimensions, effective indices, and characteristic impedances are shown on top of each FDTD simulation result.

Fig. 3.
Fig. 3.

(a) Schematic of a generalized Bragg reflector with dielectric index and thickness modulations. (b) Bandgap strength variation as a function of thickness for ThM Bragg reflector [t 2=t 1/2, n 1=n 2=1.46] and InM Bragg reflector [n 1=1.46, n 2=3.4, t 1=t 2] from TMM and FDTD simulations. (c) Variation of sin -1{abs[(Z1-Z2)/(Z1+Z2)]} versus t 2.

Fig. 4.
Fig. 4.

FOM variation as a function of number of periods and (a) n 2 for InM Bragg reflector (n 1=1.46, t 1=t 2=100 nm) and (b) t 2 for ThM Bragg reflector (n 1=n 2=1.46, t 1=100 nm) for fixed central wavelength of 1550 nm. Transmission (TMM and FDTD) and Reflection (TMM) spectra versus wavelength for optimum (c) InM (n 2=2.6) and (d) ThM (t 2=50 nm) Bragg reflectors with N=6.

Equations (9)

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ε d k x 2 + ε m k x 1 coth ( i k x 1 d 2 ) = 0 ,
k x 1 , 2 2 = ε d , m ( ω c ) 2 k 2 ,
ε m ( ω ) = ε ( ) ω p 2 ω ( ω + i γ ) ,
Z = E x d H y w = β d n 2 ω ε 0 w ,
A 11 = 1 2 e j ( β r β l ) X + Z r 2 Z l e j ( β r β l ) X , A 12 = 1 2 e j ( β r + β l ) X Z r 2 Z l e j ( β r + β l ) X
A 21 = 1 2 e j ( β r + β l ) X Z r 2 Z l e j ( β r + β l ) X , A 22 = 1 2 e j ( β r β l ) X + Z r 2 Z l e j ( β r β l ) X
F = d 1 + d 2 2 k 0 [ d 1 I m ( n eff , 1 ) + d 2 I m ( n eff , 2 ) ] × 1 N ( d 1 + d 2 ) = 1 2 N k 0 [ d 1 I m ( n eff , 1 ) + d 2 I m ( n eff , 2 ) ] ,
Maximize F ( N , n 1 , n 2 , t 1 , t 2 , d 1 , d 2 )
Subject to R ( N , n 1 , n 2 , t 1 , t 2 , d 1 , d 2 ) > R 0

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