Abstract

A theoretical study of the optical properties of metallic nano-strip antennas is presented. Such strips exhibit retardation-based resonances resulting from the constructive interference of counter propagating short-range surface plasmon-polaritons (SR-SPPs) that reflect from the antenna terminations. A Fabry-Pérot model was formulated that successfully predicts both the peak position and spectral shape of their optical resonances. This model requires knowledge of the SR-SPP reflection amplitude and phase pickup upon reflection from the structure terminations. These quantities were first estimated using an intuitive Fresnel reflection model and then calculated exactly using full-field simulations based on the finite-difference frequency-domain (FDFD) method. With only three dimensionless scaling parameters, the Fabry-Pérot model provides simple design rules for engineering resonant properties of such plasmonic resonator antennas.

© 2008 Optical Society of America

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2008

M. L. Brongersma, "Plasmonics: Engineering optical nanoantennas," Nat. Photon. 2, 270-272 (2008).
[CrossRef]

G. W. Bryant, F. J. García de Abajo, and J. Aizpurua, "Mapping the plasmon resonances of metallic nanoantennas," Nano Lett. 8, 631-636 (2008).
[CrossRef] [PubMed]

T. Søndergaard and S. I. Bozhevolnyi, "Strip and gap plasmon polariton optical resonators," Phys. Status Solidi B 245, 9-19 (2008).
[CrossRef]

G. Della Valle, T. Søndergaard, and S. I. Bozhevolnyi, "Plasmon-polariton nano-strip resonators: from visible to infra-red," Opt. Express 16, 6867-6876 (2008).
[CrossRef] [PubMed]

T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, "Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration," Phys. Rev. B. 77, 115420 (2008).
[CrossRef]

2007

S. I. Bozhevolnyi and T. Søndergaard, "General properties of slow-plasmon resonant nanostructures: nanoantennas and resonators," Opt. Express 15, 10869 (2007).
[CrossRef] [PubMed]

L. Novotny, "Effective wavelength scaling for optical antennas," Phys. Rev. Lett. 98, 266802 (2007).
[CrossRef] [PubMed]

S. Lal, S. Link, and N. J. Halas, "Nano-optics from sensing to waveguiding," Nat. Photon. 1, 641-648 (2007).
[CrossRef]

2006

F. Wang and Y. R. Shen, "General properties of local plasmons in metal nanostructures," Phys. Rev. Let. 97, 206806 (2006).
[CrossRef]

R. Zia, J. A. Schuller, and M. L. Brongersma, "Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides," Phys. Rev. B. 74, 165415 (2006).
[CrossRef]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mater. Today 9, 20-27 (2006).

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

R. Gordon, "Vectorial method for calculating the fresnel reflection of surface plasmon polaritons," Phys. Rev. B. 74, 153417 (2006).
[CrossRef]

R. Gordon, "Light in a subwavelength slit in a metal: Propagation and reflection," Phys. Rev. B. 73, 153405 (2006).
[CrossRef]

2005

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, "Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas," Phys. Rev. Lett. 94, 017402-4 (2005).
[CrossRef] [PubMed]

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-9 (2005).
[CrossRef] [PubMed]

N. Engheta, A. Salandrino, and A. Alú, "Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

G. Laurent, N. F�??elidj, S. Truong, J. Aubard, G. Lévi, J. Krenn, A. Hohenau, A. Leitner, and F. Aussenegg, "Imaging surface plasmon of gold nanoparticle arrays by far-field raman scattering," Nano Lett. 5, 253-258 (2005).
[CrossRef] [PubMed]

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators." Phys. Rev. Lett. 95, 257403-4 (2005).
[CrossRef] [PubMed]

R. Zia, A. Chandran, and M. L. Brongersma, "Dielectric waveguide model for guided surface polaritons," Opt. Lett. 30, 1473-1475 (2005).
[CrossRef] [PubMed]

2004

J. B. Jackson and N. J. Halas, "Surface-enhanced raman scattering on tunable plasmonic nanoparticle substrates," Proc. Nat. Acad. Sci. U.S.A. 101, 17930 - 17935 (2004).
[CrossRef]

1999

E. Anemogiannis, E. Glytsis, and T. K. Gaylord, "Determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides: reflection pole method and wavevector density method," J. Lightwave Technol. 17, 929 (1999).
[CrossRef]

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, "Spectroscopy of single hemoglobin molecules by surface enhanced raman scattering," Phys. Rev. Lett. 83, 4357-4360 (1999).
[CrossRef]

1998

1997

1994

R. K. Mongia and P. Bhartia, "Dielectric resonator antennas �??a review and general design relations for resonant frequency and bandwidth," Int.J. Microwave Millimeter-Wave Eng. 4, 230-247 (1994).
[CrossRef]

1969

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Aizpurua, J.

G. W. Bryant, F. J. García de Abajo, and J. Aizpurua, "Mapping the plasmon resonances of metallic nanoantennas," Nano Lett. 8, 631-636 (2008).
[CrossRef] [PubMed]

Alú, A.

N. Engheta, A. Salandrino, and A. Alú, "Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

Anemogiannis, E.

Aussenegg, F. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators." Phys. Rev. Lett. 95, 257403-4 (2005).
[CrossRef] [PubMed]

Beermann, J.

T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, "Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration," Phys. Rev. B. 77, 115420 (2008).
[CrossRef]

Bhartia, P.

R. K. Mongia and P. Bhartia, "Dielectric resonator antennas �??a review and general design relations for resonant frequency and bandwidth," Int.J. Microwave Millimeter-Wave Eng. 4, 230-247 (1994).
[CrossRef]

Bjerneld, E. J.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, "Spectroscopy of single hemoglobin molecules by surface enhanced raman scattering," Phys. Rev. Lett. 83, 4357-4360 (1999).
[CrossRef]

Boltasseva, A.

T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, "Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration," Phys. Rev. B. 77, 115420 (2008).
[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 (2006).
[CrossRef]

Börjesson, L.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, "Spectroscopy of single hemoglobin molecules by surface enhanced raman scattering," Phys. Rev. Lett. 83, 4357-4360 (1999).
[CrossRef]

Bozhevolnyi, S. I.

Brongersma, M. L.

M. L. Brongersma, "Plasmonics: Engineering optical nanoantennas," Nat. Photon. 2, 270-272 (2008).
[CrossRef]

R. Zia, J. A. Schuller, and M. L. Brongersma, "Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides," Phys. Rev. B. 74, 165415 (2006).
[CrossRef]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mater. Today 9, 20-27 (2006).

R. Zia, A. Chandran, and M. L. Brongersma, "Dielectric waveguide model for guided surface polaritons," Opt. Lett. 30, 1473-1475 (2005).
[CrossRef] [PubMed]

Bryant, G. W.

G. W. Bryant, F. J. García de Abajo, and J. Aizpurua, "Mapping the plasmon resonances of metallic nanoantennas," Nano Lett. 8, 631-636 (2008).
[CrossRef] [PubMed]

Chandran, A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mater. Today 9, 20-27 (2006).

R. Zia, A. Chandran, and M. L. Brongersma, "Dielectric waveguide model for guided surface polaritons," Opt. Lett. 30, 1473-1475 (2005).
[CrossRef] [PubMed]

Della Valle, G.

Ditlbacher, H.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators." Phys. Rev. Lett. 95, 257403-4 (2005).
[CrossRef] [PubMed]

Djurisi??, A. B.

Economou, E. N.

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Eisler, H. J.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-9 (2005).
[CrossRef] [PubMed]

Elazar, J. M.

Engheta, N.

N. Engheta, A. Salandrino, and A. Alú, "Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

Fromm, D. P.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, "Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas," Phys. Rev. Lett. 94, 017402-4 (2005).
[CrossRef] [PubMed]

García de Abajo, F. J.

G. W. Bryant, F. J. García de Abajo, and J. Aizpurua, "Mapping the plasmon resonances of metallic nanoantennas," Nano Lett. 8, 631-636 (2008).
[CrossRef] [PubMed]

Gaylord, T. K.

Glytsis, E.

Gordon, R.

R. Gordon, "Vectorial method for calculating the fresnel reflection of surface plasmon polaritons," Phys. Rev. B. 74, 153417 (2006).
[CrossRef]

R. Gordon, "Light in a subwavelength slit in a metal: Propagation and reflection," Phys. Rev. B. 73, 153405 (2006).
[CrossRef]

Halas, N. J.

S. Lal, S. Link, and N. J. Halas, "Nano-optics from sensing to waveguiding," Nat. Photon. 1, 641-648 (2007).
[CrossRef]

J. B. Jackson and N. J. Halas, "Surface-enhanced raman scattering on tunable plasmonic nanoparticle substrates," Proc. Nat. Acad. Sci. U.S.A. 101, 17930 - 17935 (2004).
[CrossRef]

Hecht, B.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-9 (2005).
[CrossRef] [PubMed]

Hofer, F.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators." Phys. Rev. Lett. 95, 257403-4 (2005).
[CrossRef] [PubMed]

Hohenau, A.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators." Phys. Rev. Lett. 95, 257403-4 (2005).
[CrossRef] [PubMed]

Jackson, J. B.

J. B. Jackson and N. J. Halas, "Surface-enhanced raman scattering on tunable plasmonic nanoparticle substrates," Proc. Nat. Acad. Sci. U.S.A. 101, 17930 - 17935 (2004).
[CrossRef]

Käll, M.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, "Spectroscopy of single hemoglobin molecules by surface enhanced raman scattering," Phys. Rev. Lett. 83, 4357-4360 (1999).
[CrossRef]

Kino, G. S.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, "Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas," Phys. Rev. Lett. 94, 017402-4 (2005).
[CrossRef] [PubMed]

Kobayashi, T.

Kreibig, U.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators." Phys. Rev. Lett. 95, 257403-4 (2005).
[CrossRef] [PubMed]

Krenn, J. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators." Phys. Rev. Lett. 95, 257403-4 (2005).
[CrossRef] [PubMed]

Lal, S.

S. Lal, S. Link, and N. J. Halas, "Nano-optics from sensing to waveguiding," Nat. Photon. 1, 641-648 (2007).
[CrossRef]

Laurent, G.

G. Laurent, N. F�??elidj, S. Truong, J. Aubard, G. Lévi, J. Krenn, A. Hohenau, A. Leitner, and F. Aussenegg, "Imaging surface plasmon of gold nanoparticle arrays by far-field raman scattering," Nano Lett. 5, 253-258 (2005).
[CrossRef] [PubMed]

Leosson, K.

Link, S.

S. Lal, S. Link, and N. J. Halas, "Nano-optics from sensing to waveguiding," Nat. Photon. 1, 641-648 (2007).
[CrossRef]

Majewski, M. L.

Martin, O. J. F.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-9 (2005).
[CrossRef] [PubMed]

Moerner, W. E.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, "Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas," Phys. Rev. Lett. 94, 017402-4 (2005).
[CrossRef] [PubMed]

Mongia, R. K.

R. K. Mongia and P. Bhartia, "Dielectric resonator antennas �??a review and general design relations for resonant frequency and bandwidth," Int.J. Microwave Millimeter-Wave Eng. 4, 230-247 (1994).
[CrossRef]

Morimoto, A.

Mühlschlegel, P.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-9 (2005).
[CrossRef] [PubMed]

Nikolajsen, T.

Novotny, L.

L. Novotny, "Effective wavelength scaling for optical antennas," Phys. Rev. Lett. 98, 266802 (2007).
[CrossRef] [PubMed]

Pohl, D. W.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-9 (2005).
[CrossRef] [PubMed]

Rakiíc, A. D.

Rogers, M.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators." Phys. Rev. Lett. 95, 257403-4 (2005).
[CrossRef] [PubMed]

Salandrino, A.

N. Engheta, A. Salandrino, and A. Alú, "Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

Schuck, P. J.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, "Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas," Phys. Rev. Lett. 94, 017402-4 (2005).
[CrossRef] [PubMed]

Schuller, J. A.

R. Zia, J. A. Schuller, and M. L. Brongersma, "Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides," Phys. Rev. B. 74, 165415 (2006).
[CrossRef]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mater. Today 9, 20-27 (2006).

Shen, Y. R.

F. Wang and Y. R. Shen, "General properties of local plasmons in metal nanostructures," Phys. Rev. Let. 97, 206806 (2006).
[CrossRef]

Søndergaard, T.

T. Søndergaard and S. I. Bozhevolnyi, "Strip and gap plasmon polariton optical resonators," Phys. Status Solidi B 245, 9-19 (2008).
[CrossRef]

T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, "Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration," Phys. Rev. B. 77, 115420 (2008).
[CrossRef]

G. Della Valle, T. Søndergaard, and S. I. Bozhevolnyi, "Plasmon-polariton nano-strip resonators: from visible to infra-red," Opt. Express 16, 6867-6876 (2008).
[CrossRef] [PubMed]

S. I. Bozhevolnyi and T. Søndergaard, "General properties of slow-plasmon resonant nanostructures: nanoantennas and resonators," Opt. Express 15, 10869 (2007).
[CrossRef] [PubMed]

Sundaramurthy, A.

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[CrossRef] [PubMed]

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[CrossRef]

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, "Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas," Phys. Rev. Lett. 94, 017402-4 (2005).
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Figures (4)

Fig. 1.
Fig. 1.

Trends in the guiding and reflection properties of short range surface plasmonpolaritions (SR-SPPs) supported by truncated silver films with normalized metal thickness, t/λo . The blue dotted, green dashed, and red solid curves show the trends for εm values that correspond to silver at 500, 600, and 700 nm free-space wavelengths respectively. (a) Real part of the effective index, nspp, of SR-SPP mode. (b) Mode size of the SR-SPP. (c) Reflection amplitude for an SR-SPP reflecting off of a silver film truncation. (d) Phase pickup for an SR-SPP reflecting off of a silver film truncation. (c) & (d): The thin lines were calculated with the Fresnel reflection model and the thick lines were obtained from full-field simulations.

Fig. 2.
Fig. 2.

Full-field simulation of an SR-SPP reflecting off of a metal film truncation. (a) Schematic of the simulation geometry showing the truncated metal film with the SR-SPP launch point (xo ), end-face (xe ), and measurement point (xm ). (b) Incident, (c) total, and (d) reflected (total minus incident) tangential electric field, Ex , for a 30 nm thick silver film excited with a SR-SPP mode with a wavelength of λ spp=465 nm (free-space λo =550nm).

Fig. 3.
Fig. 3.

Resonance behavior of 30 nm thick silver strips and comparison with Fabry-Pérot models. Dashed blue lines correspond to the Fresnel reflection Fabry-Pérot model and solid red lines correspond to Fabry-Pérot model with phase and reflection coefficient from fullfield simulations. The dashed green indicates cuts from the full-field strip resonance map. (a) Schematic of the simulated strip geometry. (b) Slice of resonance map and (c) Fabry-Pérot model vs. strip width, w, at λo =550 nm. (d) Slice of resonance map and (e) Fabry-Pérot model vs. excitation wavelength, λo , at w=0.8µm. (f) Resonance map of 30 nm thick silver strips from full-field simulations. |E end|2 is shown as a density plot, overlayed with predicted resonance peaks from Fabry-Pérot models.

Fig. 4.
Fig. 4.

Field intensity distributions (|E|2/|Eo |2) for the lowest order resonances (m=1,3, 5) of 30 nm thick silver strips at an illumination wavelength of λo =550 nm. For this excitation wavelength w res,1=130 nm is shown in (a), w res,3=575 nm is shown in (b), and w res,5=1040 nm is shown in (c).

Equations (6)

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w res , m = m π ϕ ( t λ o , ε m ε d ) 2 π λ o n spp ( t λ o , ε m ε d )
E end 2 ( 1 r e i ϕ e i k spp w ) ( 1 e i k spp w ) 1 r 2 e i 2 ϕ e i 2 k spp w 2 .
r = r e i ϕ = n spp 1 n spp + 1 .
E x , i ( x , y ) = E x , o ( y ) e i k spp ( x x o )
E x , r ( x , y ) = E x , o ( y ) r e i k spp ( x e x o ) e i ϕ e i k spp ( x e x ) .
r = r e i ϕ = E x , r ( x m , y m ) E x , i ( x m , y m ) e i 2 k spp ( x m x e ) .

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