Abstract

Effective-index approach is applied for modeling of channel plasmon polaritons (CPPs) propagating in rectangular grooves (trenches) and triangular (V-shaped) grooves in gold, accounting for the main features of CPP guiding and elucidating its underlying physics. The effective indexes of CPP modes along with the corresponding propagation lengths are calculated for different configurations and wavelengths while varying the groove depth. The results obtained allow one to identify the parameter range for realizing the single-mode CPP guiding featuring subwavelength confinement and moderate propagation loss at telecom wavelengths.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]

2006 (5)

C. Reinhardt, S. Passinger, B. N. Chichkov, C. Marquart, I. P. Radko, and S. I. Bozhevolnyi, "Laser-fabricated dielectric optical components for surface plasmon polaritons, " Opt. Lett. 31, 1307-1309 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonantors," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, "Compact gradual bends for channel plasmon polaritons," Opt. Express 14, 4494-4503 (2006).
[CrossRef] [PubMed]

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

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
[CrossRef]

2005 (4)

2004 (1)

D. K. Gramotnev, and D. F. P. Pile, "Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface," Appl. Phys. Lett. 85, 6323-6325 (2004).
[CrossRef]

2003 (2)

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

K. Tanaka, and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158-1160 (2003).
[CrossRef]

2002 (1)

I. V. Novikov, and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 035403 (2002).
[CrossRef]

2001 (3)

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078 (2001).
[CrossRef]

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidji, A. Leitner. F. R. Aussenegg, and J. C. Weeber, "Surface plasmon propagation in microscale metal stripes," Appl. Phys. Lett. 79, 51 (2001).
[CrossRef]

S. A. Maier, M. L. Brongersma, P. G. Kirk, S. Meltzer, A. A. G. Reguicha, and H. A. Atwater, "Plasmons-a route to nanoscale optical devices," Adv. Mater. 13, 1501-1505 (2001).
[CrossRef]

1999 (1)

1981 (1)

A. D. Boardman, G. C. Aers, and R. Teshima, "Retarded edge modes of a parabolic wedge," Phys. Rev. B 24, 5703-5712 (1981).
[CrossRef]

1977 (1)

1974 (1)

Aers, G. C.

A. D. Boardman, G. C. Aers, and R. Teshima, "Retarded edge modes of a parabolic wedge," Phys. Rev. B 24, 5703-5712 (1981).
[CrossRef]

Atwater, H. A.

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

S. A. Maier, M. L. Brongersma, P. G. Kirk, S. Meltzer, A. A. G. Reguicha, and H. A. Atwater, "Plasmons-a route to nanoscale optical devices," Adv. Mater. 13, 1501-1505 (2001).
[CrossRef]

Barnes, W. L.

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

Boardman, A. D.

A. D. Boardman, G. C. Aers, and R. Teshima, "Retarded edge modes of a parabolic wedge," Phys. Rev. B 24, 5703-5712 (1981).
[CrossRef]

Boltasseva, A.

Bozhevolnyi, S. I.

C. Reinhardt, S. Passinger, B. N. Chichkov, C. Marquart, I. P. Radko, and S. I. Bozhevolnyi, "Laser-fabricated dielectric optical components for surface plasmon polaritons, " Opt. Lett. 31, 1307-1309 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonantors," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, "Compact gradual bends for channel plasmon polaritons," Opt. Express 14, 4494-4503 (2006).
[CrossRef] [PubMed]

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, "Integrated optical components utilizing long-range surface plasmon polaritons," J. Lightwave Technol. 23, 413-422 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=JLT-23-1-413
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078 (2001).
[CrossRef]

Brongersma, M. L.

R. Zia, A. Chandran, and M. L. Brongersma, "Dielectric waveguide model for guided surface polaritons," Opt. Lett. 30, 1473-1475 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=ol-30-12-1473
[CrossRef]

S. A. Maier, M. L. Brongersma, P. G. Kirk, S. Meltzer, A. A. G. Reguicha, and H. A. Atwater, "Plasmons-a route to nanoscale optical devices," Adv. Mater. 13, 1501-1505 (2001).
[CrossRef]

Burns, W. K.

Chandran, A.

Chiang, K. S.

Chichkov, B. N.

Dereux, A.

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

Devaux, E.

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, "Compact gradual bends for channel plasmon polaritons," Opt. Express 14, 4494-4503 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonantors," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

Dionne, J. A.

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

Ditlbacher, H.

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidji, A. Leitner. F. R. Aussenegg, and J. C. Weeber, "Surface plasmon propagation in microscale metal stripes," Appl. Phys. Lett. 79, 51 (2001).
[CrossRef]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonantors," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, "Compact gradual bends for channel plasmon polaritons," Opt. Express 14, 4494-4503 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

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

Felidji, N.

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidji, A. Leitner. F. R. Aussenegg, and J. C. Weeber, "Surface plasmon propagation in microscale metal stripes," Appl. Phys. Lett. 79, 51 (2001).
[CrossRef]

Fukui, M.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
[CrossRef]

Gramotnev, D. K.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
[CrossRef]

D. K. Gramotnev, and D. F. P. Pile, "Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface," Appl. Phys. Lett. 85, 6323-6325 (2004).
[CrossRef]

Han, Z.

Haraguchi, M.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
[CrossRef]

He, S.

Hocker, G. B.

Kaminow, I. P.

Kirk, P. G.

S. A. Maier, M. L. Brongersma, P. G. Kirk, S. Meltzer, A. A. G. Reguicha, and H. A. Atwater, "Plasmons-a route to nanoscale optical devices," Adv. Mater. 13, 1501-1505 (2001).
[CrossRef]

Kjaer, K.

Krenn, J. R.

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidji, A. Leitner. F. R. Aussenegg, and J. C. Weeber, "Surface plasmon propagation in microscale metal stripes," Appl. Phys. Lett. 79, 51 (2001).
[CrossRef]

Kwan, C. H.

Laluet, J.-Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonantors," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

Lamprecht, B.

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidji, A. Leitner. F. R. Aussenegg, and J. C. Weeber, "Surface plasmon propagation in microscale metal stripes," Appl. Phys. Lett. 79, 51 (2001).
[CrossRef]

Larsen, M. S.

Leitner, A.

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidji, A. Leitner. F. R. Aussenegg, and J. C. Weeber, "Surface plasmon propagation in microscale metal stripes," Appl. Phys. Lett. 79, 51 (2001).
[CrossRef]

Leosson, K.

Liu, L.

Lo, K. M.

Maier, S. A.

S. A. Maier, M. L. Brongersma, P. G. Kirk, S. Meltzer, A. A. G. Reguicha, and H. A. Atwater, "Plasmons-a route to nanoscale optical devices," Adv. Mater. 13, 1501-1505 (2001).
[CrossRef]

Mammel, W. L.

Maradudin, A. A.

I. V. Novikov, and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 035403 (2002).
[CrossRef]

Marquart, C.

Meltzer, S.

S. A. Maier, M. L. Brongersma, P. G. Kirk, S. Meltzer, A. A. G. Reguicha, and H. A. Atwater, "Plasmons-a route to nanoscale optical devices," Adv. Mater. 13, 1501-1505 (2001).
[CrossRef]

Nikolajsen, T.

Novikov, I. V.

I. V. Novikov, and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 035403 (2002).
[CrossRef]

Okamoto, T.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
[CrossRef]

Passinger, S.

Pile, D. F. P.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
[CrossRef]

D. K. Gramotnev, and D. F. P. Pile, "Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface," Appl. Phys. Lett. 85, 6323-6325 (2004).
[CrossRef]

Polman, A.

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

Radko, I. P.

Reguicha, A. A. G.

S. A. Maier, M. L. Brongersma, P. G. Kirk, S. Meltzer, A. A. G. Reguicha, and H. A. Atwater, "Plasmons-a route to nanoscale optical devices," Adv. Mater. 13, 1501-1505 (2001).
[CrossRef]

Reinhardt, C.

Salerno, M.

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidji, A. Leitner. F. R. Aussenegg, and J. C. Weeber, "Surface plasmon propagation in microscale metal stripes," Appl. Phys. Lett. 79, 51 (2001).
[CrossRef]

Schider, G.

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidji, A. Leitner. F. R. Aussenegg, and J. C. Weeber, "Surface plasmon propagation in microscale metal stripes," Appl. Phys. Lett. 79, 51 (2001).
[CrossRef]

Sweatlock, L. A.

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

Tanaka, K.

K. Tanaka, and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158-1160 (2003).
[CrossRef]

Tanaka, M.

K. Tanaka, and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158-1160 (2003).
[CrossRef]

Teshima, R.

A. D. Boardman, G. C. Aers, and R. Teshima, "Retarded edge modes of a parabolic wedge," Phys. Rev. B 24, 5703-5712 (1981).
[CrossRef]

Volkov, V. S.

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, "Compact gradual bends for channel plasmon polaritons," Opt. Express 14, 4494-4503 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonantors," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078 (2001).
[CrossRef]

Weber, H. P.

Zia, R.

Adv. Mater. (1)

S. A. Maier, M. L. Brongersma, P. G. Kirk, S. Meltzer, A. A. G. Reguicha, and H. A. Atwater, "Plasmons-a route to nanoscale optical devices," Adv. Mater. 13, 1501-1505 (2001).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (4)

D. K. Gramotnev, and D. F. P. Pile, "Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface," Appl. Phys. Lett. 85, 6323-6325 (2004).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078 (2001).
[CrossRef]

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidji, A. Leitner. F. R. Aussenegg, and J. C. Weeber, "Surface plasmon propagation in microscale metal stripes," Appl. Phys. Lett. 79, 51 (2001).
[CrossRef]

K. Tanaka, and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158-1160 (2003).
[CrossRef]

J. Appl. Phys. (1)

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
[CrossRef]

J. Lightwave Technol. (2)

Nature (2)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonantors," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

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

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. B (3)

I. V. Novikov, and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 035403 (2002).
[CrossRef]

A. D. Boardman, G. C. Aers, and R. Teshima, "Retarded edge modes of a parabolic wedge," Phys. Rev. B 24, 5703-5712 (1981).
[CrossRef]

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

Phys. Rev. Lett. (1)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

Other (3)

H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1988).

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

H. Kogelnik and V. Ramaswamy, "Scaling rules for thin-film optical waveguides," Appl. Opt. 13, 1857- (1974). http://www.opticsinfobase.org/abstract.cfm?URI=ao-13-8-1857
[CrossRef] [PubMed]

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Figures (9)

Fig. 1.
Fig. 1.

Schematic of the surface plasmon waveguides under consideration.

Fig. 2.
Fig. 2.

The effective indexes of SPP modes and their propagation lengths for the configuration shown in Fig. 1(a) as a function of the metal film thickness. The results of simulations with the FD method [13] are also shown for comparison.

Fig. 3.
Fig. 3.

The gap SPP mode effective index and its propagation length as a function of the width w of air gap in gold for several light wavelengths. The insert shows the gap configuration and the SPP magnetic field orientation along with the example of field distribution across a 1-µm-wide gap (λ=1.55 µm).

Fig. 4.
Fig. 4.

The trench CPP mode effective index and its propagation length as a function of the trench depth d in gold for two trench widths w (λ=1.55 µm) in the parameter ranges corresponding to the single-mode waveguiding regime. The insert shows the trench configuration and the electric field orientation.

Fig. 5.
Fig. 5.

The trench CPP field magnitude distributions for 500-nm-wide trenches of different depths, including the close to cutoff depth of 1.5 µm (Fig. 4).

Fig. 6.
Fig. 6.

The trench parameter range ensuring the single-mode CPP guiding at the wavelength range of 0.775-1.55 µm evaluated using Eq. (2) and Fig. 3.

Fig. 7.
Fig. 7.

The effective indexes of fundamental CPP modes at 1.55 µm and their propagation lengths as a function of the groove depth d for different groove angles θ. The insert shows the groove configuration and dominant orientation of the CPP electric field. The plane SPP effective index is also indicated.

Fig. 8.
Fig. 8.

(a) The effective indexes of V-groove CPP modes and (b) the corresponding CPP propagation lengths as a function of the 250-angle groove depth d for several light wavelengths.

Fig. 9.
Fig. 9.

The CPP amplitude distributions for 250-angle V-grooves of different depths, including the close to cutoff (for TE1 mode) depth of 2.14 µm (Fig. 8).

Equations (2)

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R ( u ) exp ( u ) ( 2 u + exp ( u ) exp ( u ) ) ( 1 + exp ( u ) ) 2 .
V ( w , d ) = 2 π λ d N eff 2 ( w ) 1 = π 2 + m π , m = 0 , 1 , 2 ,

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