## Spectral properties of plasmonic resonator antennas

Optics Express, Vol. 16, Issue 21, pp. 16529-16537 (2008)

http://dx.doi.org/10.1364/OE.16.016529

Acrobat PDF (486 KB)

### 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

## 1. Introduction

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

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

3. M. L. Brongersma, “Plasmonics: Engineering optical nanoantennas,” Nat. Photon. **2**, 270–272 (2008). [CrossRef]

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

6. 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]

7. 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]

8. G. Laurent, N. Félidj, 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]

9. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter.” Opt. Lett. **22**, 475–7 (1997). [CrossRef] [PubMed]

10. 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]

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

12. 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]

14. 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]

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

16. T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B **245**, 9–19 (2008). [CrossRef]

16. T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B **245**, 9–19 (2008). [CrossRef]

18. R. K. Mongia and P. Bhartia, “Dielectric resonator antennas — a review and general design relations for resonant frequency and bandwidth,” Int. J. of Microwave Millimeter-Wave Eng. **4**, 230–247 (1994). [CrossRef]

19. 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]

20. 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]

21. 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]

22. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. **182**, 539–554 (1969). [CrossRef]

23. 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]

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

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

21. 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]

26. 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]

## 2. Optical properties of metallic films and strips

16. T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B **245**, 9–19 (2008). [CrossRef]

28. 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]

## 3. Fabry-Pérot resonator model

*t*to a width

*w*. When top-illuminated with the electric field polarized along the

*x*-direction, SR-SPPs will be excited at the truncations and start propagating back and forth between the antenna end-faces. When the SR-SPP encounters an end-face it will partially reflect and partially scatter into free-space modes. For a properly chosen strip width, constructive interference of multiply-reflected SR-SPPs will occur and generate resonantly enhanced fields in the vicinity of the strip.

**245**, 9–19 (2008). [CrossRef]

*w*/

*λ*,

_{o}*t*/

*λ*, and

_{o}*ε*/

_{m}*ε*), it also enables a complete description of the resonant optical properties of metal strips in terms of these normalized quantities. For example, the resonant width of a metal strip can be written in terms of the SR-SPP wavelength (

_{d}*λ*

_{spp}=

*λ*/

_{o}*n*′

_{spp}) and reflection phase which only depend on

*t*/

*λ*and

_{o}*ε*/

_{m}*ε*. On resonance, the round trip phase must be equal to an integer multiple of 2

_{d}*π*. For the case of the metal strip this implies that (2

*π*/

*λ*

_{spp})2

^{w}_{res},

*m*+2

*ϕ*=

*m*2

*π*where

*m*is the order of the resonance. This then leads to

*n*′

_{spp}or a larger

*ϕ*will result in a shorter

*w*. It is worth noting that for structures exhibiting large reflection phases, our microwave intuition that suggests

_{res,m}*w*

_{res,1}=

*λ*/2 is insufficient to predict their resonant widths. Below we will show that reflection phases exceeding

_{o}*π*/2 can be expected in this system which can cause shifts in the resonance width,

*w*

_{res,1}, from

*λ*

_{spp}/2 to less than

*λ*

_{spp}/4.

*w*

_{res,m}. With the Fabry-Pérot model, the dependence of the field intensity at the end-faces, |

*E*

_{end}|

^{2}, can be found by summing contributions from the multiply-reflected SR-SPPs that were launched onto the strip. A simple addition of these fields gives

*E*

_{end}|

^{2}as a proportionality rather than an equality since the (possibly frequency-dependent) coupling efficiency of the incident wave into SR-SPPs is unknown. Note that for symmetry reasons only odd modes (

*m*=1,3,5…) can be excited in the considered top-illumination geometry. Through a careful comparison to full-field simulations, we will show that the frequency dependence of the coupling efficiency is weak and the Fabry-Pérot resonances occur where exp[

*i*2

*k*

_{spp}

*+*

^{w}*i2ϕ*] is close to unity, i.e. where Eq. (1) holds, and the quantity in Eq. (2) is maximized. Note that the numerator in Eq. (2) gives rise to an asymmetric line-shape as a function of

*w*and slightly shifts (by less than 5%) the resonance maximum from the

*w*

_{res,m}predicted by Eq. (1). Interestingly, the weak frequency dependence of the coupling also enables an accurate prediction of the resonant line-shape and thus the quality factor, Q.

## 4. Determination of reflection amplitude and phase

*n*

_{spp}=

*k*

_{spp}/

*k*, where

_{o}*k*

_{spp}is the in-plane wave vector of the SR-SPP supported by the film. Reflections from a termination are then obtained by considering a plane wave propagating in a uniform medium of

*n*

_{spp}and reflecting off a dielectric with an index equal to that of the embedding medium (

*n*=1 in our case). The reflection amplitude, |

*r*|, and phase pickup,

*ϕ*, for the SR-SPP wave can now be calculated based on this effective index contrast using the well-known Fresnel equations [29]:

*ε*values as in Fig. 1(a) and (b). For sufficiently thick films, the reflection parameters asymptote as the SR-SPP becomes more like a SPP on a semi-infinite metal film. However, as the film thickness is decreased, the increase in the SR-SPP mode index leads to a larger reflection amplitude that tend towards unity for films that are thinner than just a few percent of the free-space wavelength. Within the confines of the Fresnel reflection model, the reflection phase would be equal to zero for the case of a lossless metal. However, real metals exhibit loss and give rise to a non-negligible phase pickup. For low-loss noble metals this Fresnel reflection model predicts a small phase pickup as seen in Fig. 1(d) for silver.

_{m}27. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for verticalcavity optoelectronic devices,” Appl. Opt. **37**, 5271 (1998). [CrossRef]

*r*| and

*ϕ*at a frequency and film thickness of interest, we launch an analytically-derived SR-SPP mode [22

22. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. **182**, 539–554 (1969). [CrossRef]

*x*towards the end-face of the slab at

_{o}*x*and monitor its reflection at

_{e}*x*.

_{m}*E*(

_{x,i}*x,y*) for a 30 nmthick silver film at an excitation (free-space) wavelength of 550 nm. Upon reaching the end-face, the SR-SPP scatters and produces a total field

*E*

_{x,tot}(

*x*,

*y*) as shown in Fig. 2(c). Fig. 2(d) shows that near the strip the difference field,

*E*

_{x,tot}(

*x,y*)-

*E*(

_{x,i}*x,y*), is dominated by contributions from a backward-propagating, reflected SR-SPP, as is expected for such a strongly bound mode. For this reason we call this difference field the reflected field

*E*(

_{x,r}*x,y*). Sufficiently far from the end-face and within the metal film

*E*only has contributions from the reflected SR-SPP wave. In those locations, (

_{x,r}*x*), the phase and amplitude of the SR-SPP reflections can be directly computed from our simulated field patterns. To determine the reflection amplitude, |

_{m},y_{m}*r*|, and phase,

*ϕ*, we first write out the incident,

*E*, and reflected,

_{x,i}*E*, SR-SPP fields:

_{x,r}*r*, for the SR-SPP is given by the ratio of the incident and reflected fields as

*r*| with increasing film thickness can be explained by both the decrease in the SPP effective index and the concurrent spreading of the SR-SPP mode into the surrounding dielectric. The increased mode overlap of the now larger SR-SPP mode gives rise to better coupling to freespace modes and thus a reduced reflection.

*ϕ*, in some cases exceeding

*π*/2. Similar to the Fresnel reflection model, the reflection phase pickup again tends towards zero as the metal thickness is decreased. This limit can be explained by the fact that the reflection becomes almost perfect (

*r*→ 1). For large film thicknesses (

*t*/

*λ*) the reflection phase increases and approaches the phase pickup of a single-interface (semi-infinite) SPP reflection as the surface modes decouple.

_{o}## 5. Fabry-Pérot resonances in local field enhancement

*r*| and

*ϕ*in the previous section we can now assess the usefulness of the Fabry-Pérot model for predicting the spectral response of metallic strips. To this end we will directly compare full-field simulations of the field enhancement near strips with the Fabry-Pérot model. For our simulations we consider a generic silver strip, shown schematically in Fig. 3(a), with a given thickness (

*t*=30nm) in

*y*, a width (

*w*) in

*x*, and is infinite in

*z*. The strip is top-illuminated under normal incidence by a plane wave with an

*E*-field parallel to the

*x*-axis. Fig. 3(f) shows the simulated local field intensity enhancement, |

*E*

_{end}/

*E*|

_{o}^{2}, 4 nm outside of the end of the strip as a function of the strip width and incident wavelength. As predicted by the Fabry-Pérot model, this near-field intensity map indeed shows first-, third- and fifth-order resonances. Representative horizontal and vertical cuts of this resonance map (dashed green lines in Fig. 3(c) and (e) respectively) were made for a detailed comparison to the Fabry-Pérot model. The field intensity distributions corresponding to the resonant peaks in Fig. 3(c) show the odd order resonant modes and the high field enhancement at the PRA end-faces (Fig. 4).

*w*

_{res,m}is expected to match the SR-SPP wavelength of

*λ*

_{spp}=465 nm for the considered excitation wavelength of

*λ*=550 nm. The differences between

_{o}*w*

_{res,1}and

*w*

_{res,3}is 445 nm, just 4.3% smaller than the SR-SPP wavelength. This similarity to the surface plasmon wavelength was used previously to argue that metal strips behave as SR-SPP resonators [31

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

*m*=3 and

*m*=5 resonance widths is less than 1 nm from the SR-SPP wavelength. This indicates that for wide strips the local field intensity enhancement can fully be attributed to resonating SR-SPPs and that narrow strips are dominantly, but not purely SR-SPP resonators.

*r*| and

*ϕ*from the Fresnel reflection model. For this simple model the Fabry-Pérot resonance peaks occur at too large a width or too short a wavelength when compared to the full-field simulations because this model significantly underestimates the phase pickup upon reflection. The solid red curves in these Figs. were obtained by taking |

*r*| and

*φ*from full-field reflection simulations as shown in Fig. 2. With these more accurate reflection parameters the Fabry-Pérot model predicts peak positions and spectral shapes that are in agreement with full-field simulations of strips. The small observed deviations in the line-shape and peak position may be attributed to minor contributions on the local intensity from other modes as well as to the frequency-dependence of the coupling efficiency for free-space waves into SR-SPPs. The close agreement between the full-field simulations and the Fabry-Pérot model further confirm that wavelength-scale strips behave as resonators for SR-SPPs. It also shows that intuitive Fabry-Pérot models can effectively be used to predict not only the resonance positions, but also their line-shapes.

## 6. Conclusions

*w*/

*λ*/

_{o}, t*λ*, and

_{o}*ε*/

_{m}*ε*). Moreover, it allows for the SR-SPP reflection amplitudes and phases to be described in terms of these parameters. This in-turn enables the construction of an intuitive Fabry-Pérot model capable of predicting the position and line-shapes of resonant metallic structures for a wide variety of choices for the metal, surrounding dielectric, and structure geometries. Although we have only verified applicability for strips, it is expected that these models can effectively be extended to other wavelengths-scale structures of different cross-sectional shape. We anticipate that the presented concepts will provides optical engineers with a powerful framework for designing the properties of this exciting new class of resonators.

_{d}## Acknowledgments

## References and links

1. | S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photon. |

2. | N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. |

3. | M. L. Brongersma, “Plasmonics: Engineering optical nanoantennas,” Nat. Photon. |

4. | F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Let. |

5. | U. Kreibig and M. Vollmer, |

6. | H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced raman scattering,” Phys. Rev. Lett. |

7. | J. B. Jackson and N. J. Halas, “Surface-enhanced raman scattering on tunable plasmonic nanoparticle substrates,” Proc. Nat. Acad. Sci. U.S.A. |

8. | G. Laurent, N. Félidj, 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. |

9. | J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter.” Opt. Lett. |

10. | 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. |

11. | R. Zia, A. Chandran, and M. L. Brongersma, “Dielectric waveguide model for guided surface polaritons,” Opt. Lett. |

12. | 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. |

13. | R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today |

14. | G. W. Bryant, F. J. García de Abajo, and J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett. |

15. | L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. |

16. | T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B |

17. | C. A. Balanis, |

18. | R. K. Mongia and P. Bhartia, “Dielectric resonator antennas — a review and general design relations for resonant frequency and bandwidth,” Int. J. of Microwave Millimeter-Wave Eng. |

19. | 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. |

20. | P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas.” Science |

21. | G. Della Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Plasmon-polariton nano-strip resonators: from visible to infra-red,” Opt. Express |

22. | E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. |

23. | 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. |

24. | R. Gordon, “Vectorial method for calculating the fresnel reflection of surface plasmon polaritons,” Phys. Rev. B. |

25. | R. Gordon, “Light in a subwavelength slit in a metal: Propagation and reflection,” Phys. Rev. B. |

26. | T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, “Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration,” Phys. Rev. B. |

27. | A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for verticalcavity optoelectronic devices,” Appl. Opt. |

28. | A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightwave Technol. |

29. | E. Hecht, |

30. | G. Veronis and S. Fan, “Overview of simulation techniques for plasmonic devices,” in “Surface Plasmon Nanophotonics,”, |

31. | S. I. Bozhevolnyi and T. Søndergaard, “General properties of slow-plasmon resonant nanostructures: nanoantennas and resonators,” Opt. Express |

**OCIS Codes**

(050.2230) Diffraction and gratings : Fabry-Perot

(140.4780) Lasers and laser optics : Optical resonators

(240.6680) Optics at surfaces : Surface plasmons

(260.3910) Physical optics : Metal optics

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: September 16, 2008

Revised Manuscript: September 26, 2008

Manuscript Accepted: September 28, 2008

Published: October 1, 2008

**Citation**

Edward S. Barnard, Justin S. White, Anu Chandran, and Mark L. Brongersma, "Spectral properties of plasmonic resonator antennas," Opt. Express **16**, 16529-16537 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-16529

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### References

- S. Lal, S. Link, and N. J. Halas, "Nano-optics from sensing to waveguiding," Nat. Photon. 1, 641-648 (2007). [CrossRef]
- N. Engheta, A. Salandrino, and A. Alú, "Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005). [CrossRef] [PubMed]
- M. L. Brongersma, "Plasmonics: Engineering optical nanoantennas," Nat. Photon. 2, 270-272 (2008). [CrossRef]
- F. Wang and Y. R. Shen, "General properties of local plasmons in metal nanostructures," Phys. Rev. Let. 97, 206806 (2006). [CrossRef]
- U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).
- 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]
- 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]
- 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]
- J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, "Guiding of a one-dimensional optical beam with nanometer diameter." Opt. Lett. 22, 475-7 (1997). [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]
- 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).
- 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]
- L. Novotny, "Effective wavelength scaling for optical antennas," Phys. Rev. Lett. 98, 266802 (2007). [CrossRef] [PubMed]
- T. Søndergaard and S. I. Bozhevolnyi, "Strip and gap plasmon polariton optical resonators," Phys. Status Solidi B 245, 9-19 (2008). [CrossRef]
- C. A. Balanis, Antenna Theory : Analysis and Design (John Wiley, 2005), 3rd ed.
- 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]
- 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]
- 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]
- E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969). [CrossRef]
- 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]
- 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]
- 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]
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