Abstract

Three figures of merit, useful as quality measures for 2D surface plasmon waveguides, are discussed and applied to help trade-off mode confinement against attenuation for the symmetric mode propagating along metal stripes. Different stripe geometries are considered, and Au, Ag and Al are compared as the stripe metal over the wavelength range from 200 to 2000 nm. Depending on which figure of merit is used, and on how mode confinement is measured, different preferred designs emerge. For instance, given a mode area, narrow thick stripes are better than wide thin ones, but given a distance from the light line, the opposite is true. Each of the metals analyzed show wavelength regions where their performance is best. The figures of merit are generally applicable and should be useful to help compare, assess and optimize designs in other 2D surface plasmon waveguides or in other absorbing waveguides.

© 2007 Optical Society of America

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References

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    [CrossRef]

2007 (2)

2006 (8)

I. Breukelaar, R. Charbonneau, and P. Berini, "Long-range surface plasmon-polariton mode cutoff and radiation in embedded strip waveguides," J. Appl. Phys. 100, 043104 (2006).
[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]

P. Berini, "Figures of merit for surface plasmon waveguides," Opt. Express 14, 13030-13042 (2006).
[CrossRef] [PubMed]

J. Guo and R. Adato, "Extended long range plasmon waves in finite thickness metal film and layered dielectric materials," Opt. Express 14, 12409-12418 (2006).
[CrossRef] [PubMed]

W. L. Barnes, "Surface plasmon-polaritons length scales: a route to sub-wavelength optics," J. Opt. A: Pure Appl. Opt. 8, S87-S93 (2006).
[CrossRef]

A. Degiron and D. Smith, "Numerical simulations of long-range plasmons", Opt. Express 14,1611-1625 (2006).
[CrossRef] [PubMed]

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, "Passive integrated optics elements based on long-range surface plasmon polaritons," J. Lightwave Technol. 24, 447-494 (2006).
[CrossRef]

A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, "Compact Bragg Gratings for Long-Range Surface Plasmon Polaritons," J. Lightwave Technol. 24, 912-918 (2006).
[CrossRef]

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, 4674-4682 (2005).
[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).
[CrossRef]

R. Charbonneau, N. Lahoud, G. Mattiussi and P. Berini, "Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons," Opt. Express 13, 977-984 (2005).
[CrossRef] [PubMed]

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005).
[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]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, "Characterization of long-range surface-plasmon-polariton waveguides," J. Appl. Phys. 98, 043109 (2005).
[CrossRef]

2004 (2)

2003 (1)

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

2002 (1)

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

2001 (2)

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidj, A. Leitner and F.R. Aussenegg, "Surface plasmon propagation in microscale metal stripes," Appl. Phys. Lett. 79,51-53 (2001).
[CrossRef]

J.-C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J.-P. Goudonnet, "Near-field observation of surface plasmon polariton propagation on thin metal stripes," Phys. Rev. B 64, 045411 (2001).
[CrossRef]

2000 (2)

P. Berini, "Plasmon polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures," Phys. Rev. B 61, 10484-10503 (2000).
[CrossRef]

C. Chen, P. Berini, D. Feng, S. Tanev, and V. Tzolov, "Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media," Opt. Express 7, 260-272 (2000).
[CrossRef] [PubMed]

1999 (2)

P. Berini, "Plasmon-polariton modes guided by a metal film of a finite width," Opt. Lett. 24, 1011-1013 (1999).
[CrossRef]

J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn and J.-P. Goudonnet, "Plasmon polaritons of metallic nanowires for controlling submicron propagation of light," Phys. Rev. B 60, 9061-9068 (1999).
[CrossRef]

1991 (1)

K. Welford, "Surface plasmon-polaritons and their uses," Opt. Quantum Electron. 23, 1-27 (1991).
[CrossRef]

1988 (1)

K. R. Welford and J. R. Sambles, "Coupled Surface Plasmons in a Symmetric System", J. Mod. Opt. 35, 1467-1483 (1988).
[CrossRef]

1986 (1)

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

1981 (1)

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

Appl. Phys. Lett. (1)

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidj, A. Leitner and F.R. Aussenegg, "Surface plasmon propagation in microscale metal stripes," Appl. Phys. Lett. 79,51-53 (2001).
[CrossRef]

J. Appl. Phys. (3)

I. Breukelaar, R. Charbonneau, and P. Berini, "Long-range surface plasmon-polariton mode cutoff and radiation in embedded strip waveguides," J. Appl. Phys. 100, 043104 (2006).
[CrossRef]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, "Characterization of long-range surface-plasmon-polariton waveguides," J. Appl. Phys. 98, 043109 (2005).
[CrossRef]

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

J. Lightwave Technol. (3)

J. Mod. Opt. (1)

K. R. Welford and J. R. Sambles, "Coupled Surface Plasmons in a Symmetric System", J. Mod. Opt. 35, 1467-1483 (1988).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

W. L. Barnes, "Surface plasmon-polaritons length scales: a route to sub-wavelength optics," J. Opt. A: Pure Appl. Opt. 8, S87-S93 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nano Lett. (1)

P. Berini, R. Charbonneau, and N. Lahoud, "Long-Range Surface Plasmons on Ultrathin Membranes," Nano Lett. 7, 1376-1380 (2007).
[CrossRef] [PubMed]

Nat. (1)

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

Opt. Express (6)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

K. Welford, "Surface plasmon-polaritons and their uses," Opt. Quantum Electron. 23, 1-27 (1991).
[CrossRef]

Phys. Rev. B (6)

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

P. Berini, "Plasmon polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures," Phys. Rev. B 61, 10484-10503 (2000).
[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]

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

J.-C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J.-P. Goudonnet, "Near-field observation of surface plasmon polariton propagation on thin metal stripes," Phys. Rev. B 64, 045411 (2001).
[CrossRef]

J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn and J.-P. Goudonnet, "Plasmon polaritons of metallic nanowires for controlling submicron propagation of light," Phys. Rev. B 60, 9061-9068 (1999).
[CrossRef]

Phys. Rev. Lett. (2)

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]

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

Other (3)

M. Bass et al.(Editors), "Properties of Metals," in Handbook of Optics - Vol II, (McGraw-Hill, 2000).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, Berlin, 1988).

E. D. Palik (Editor), Handbook of Optical Constants of Solids, (Academic Press, Orlando, Florida, 1985).

Supplementary Material (4)

» Media 1: AVI (2562 KB)     
» Media 2: AVI (2415 KB)     
» Media 3: AVI (1676 KB)     
» Media 4: AVI (1539 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Cross sectional view of surface plasmon waveguides. (a) Single stripe, (b) pair of SC stripes, (c) three SC stripes, (d) cladded stripe.

Fig. 2.
Fig. 2.

(a) neff and (b) α z and k eff of the ss 0 b and s b modes. (c) Mode size for the s b mode in the slab (right axis) and the ss 0 b mode in the stripes (left axis). (d) M 1D 1 (right axis) and M 2D 1 (left axis). (e) Distance from the light line and (f) M 2. (g) Guided wavelength and (h) M 3. The gray curves are for the cladded stripe (Fig. 1(d)).

Fig. 3.
Fig. 3.

Spatial distribution of |E y | associated with the ss 0 b mode in various waveguides. Quarter symmetry is used with the origin, (x=y=0), being the center of the mode. The 1/e field contour is also plotted as the thin black curve. In all cases, the fields are normalized such that max(|E y |)=1. (a) Single stripe with w=8 µm and t=70 nm; the associated movie shows a sweep over t [Media 1]. (b) Three SC stripes with wswsws=22222 µm and t=70 nm; the associated movie shows a sweep over t [Media 2]. (c) Cladded stripe with w=4 µm, t=20 nm and d=0.8 µm; the associated movie shows a sweep over d [Media 3]. (d) Pair of SC Au stripes, wsw=222 µm, t=30 nm and λ 0 =1000 nm; the associated movie shows a sweep over λ 0 [Media 4].

Fig. 4.
Fig. 4.

(a) neff and (b) α z versus λ 0 . (c) Mode size and (d) M 2D 1. (e) Distance from the light line and (f) M 2. (g) Quality factor Q and (h) M 3. (green: Au, blue: Ag, magenta: Al)

Equations (1)

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M 1 2 D = π A e 1 α z

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