## Stimulated emission of surface plasmon polaritons by lead-sulphide quantum dots at near infra-red wavelengths |

Optics Express, Vol. 18, Issue 18, pp. 18633-18641 (2010)

http://dx.doi.org/10.1364/OE.18.018633

Acrobat PDF (1283 KB)

### Abstract

Amplification of surface plasmon polaritons in planar metal-dielectric structure through stimulated emission is investigated using leakage-radiation microscopy configuration. The gain medium is a thin polymethylmethacrylate layer doped with lead-sulphide nanocrystals emitting at near-infrared wavelengths. We demonstrate an optical gain of ~ 200 cm^{−1} for the mode under consideration, which corresponds to ~ 32% compensation of SPP loss.

© 2010 Optical Society of America

## 1. Introduction

5. D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. **90**, 027402 (2003). [CrossRef] [PubMed]

6. J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. **94**, 177401 (2005). [CrossRef] [PubMed]

11. M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. **8**, 3998–4001 (2008). [CrossRef] [PubMed]

12. J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, C. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. **9**, 2935–2939 (2009). [CrossRef] [PubMed]

## 2. Experimental configuration and methods

*MW*= 350K, prepared by spin-coating of a ~ 1.5 weight percent solution in toluene) with embedded PbS QDs, and air (Fig. 1a). The gold-PMMA interface supports at least one (pure plasmonic) mode, which is excited through vertical illumination of a periodic set of gold ridges with a tightly focused continuous-waveform (CW) laser beam (diameter

*d*~ 5.8

*µ*m at the 1/

*e*

^{2}level of intensity) at the wavelength of 860 nm. This SPP mode is to be amplified and hence it is referred to as probe SPP, whereas the corresponding laser beam used for its excitation is called probe laser beam. The geometry of ridges is adjusted for efficient unidirectional SPP excitation. We have thoroughly investigated a similar geometrical configuration (without a PMMA layer) previously [13

13. I. P. Radko, S. I. Bozhevolnyi, G. Brucoli, L. Martín-Moreno, F. J. García-Vidal, and A. Boltasseva, “Efficient unidirectional ridge excitation of surface plasmons,” Opt. Express **17**, 7228–7232 (2009). [CrossRef] [PubMed]

14. I. P. Radko, S. I. Bozhevolnyi, G. Brucoli, L. Martín-Moreno, F. J. García-Vidal, and A. Boltasseva, “Efficiency of local surface plasmon polariton excitation on ridges,” Phys. Rev. B **78**, 115115 (2008). [CrossRef]

*N*~ 4.6 × 10

^{19}cm

^{−3}) exhibit a fluorescence emission peak at 876 nm and were pumped at 532 nm with a CW laser beam focused into a spot with diameter

*d*~ 13.8

*µ*m at the 1/

*e*

^{2}level of intensity (Fig. 1b). Reflection of the gold-PMMA interface is close to minus unity, and consequently the field near the metal surface is rather small, which has obviously a negative effect on the maximum achievable gain [15

15. I. De Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. B **78**, 161401(R) (2008). [CrossRef]

16. I. De Leon and P. Berini, “Modeling surface plasmon-polariton gain in planar metallic structures,” Opt. Express **17**, 20191–20202 (2009). [CrossRef] [PubMed]

*λ*/(4

*n*), where

*λ*= 532 nm and

*n*≈ 1.5 (refractive index of PMMA), so that a considerable amount of pump energy is concentrated within the thin polymer layer (inset in Fig. 1a).

*θ*

_{Kr}[17

17. A. L. Stepanov, J. R. Krenn, H. Ditlbacher, A. Hohenau, A. Drezet, B. Steinberger, A. Leitner, and F. R. Aussenegg, “Quantitative analysis of surface plasmon interaction with silver nanoparticles,” Opt. Lett. **30**, 1524–1526 (2005). [CrossRef] [PubMed]

18. A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B **149**, 220–229 (2008). [CrossRef]

*s*- (pure photonic) and

*p*-polarized (hybrid plasmonic) modes appear in an alternating sequence. The dispersion properties of such a four-layer structure are discussed in details elsewhere [20

20. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B **75**, 245405 (2007). [CrossRef]

*p*-polarized mode is essential in our consideration, since the remaining modes exist merely by virtue of the choice of a particular experimental PMMA-layer thickness that is convenient for investigation. For this reason, we kept the polymer thickness below 350 nm (cut-off thickness for the second

*p*-polarized mode) and used a polarizer to eliminate the signal from the first

*s*-polarized mode in the detected LR (Fig. 2). Additionally, we applied a narrow band-pass interference filter (centred at 860 nm, full width at half-maximum is 10 nm) upon detection to suppress background from the pump beam.

17. A. L. Stepanov, J. R. Krenn, H. Ditlbacher, A. Hohenau, A. Drezet, B. Steinberger, A. Leitner, and F. R. Aussenegg, “Quantitative analysis of surface plasmon interaction with silver nanoparticles,” Opt. Lett. **30**, 1524–1526 (2005). [CrossRef] [PubMed]

*NA*= 1.25. Hence, only those modes whose guide index is below that value can be directly observed (the configuration space below the horizontal line in Fig. 2). Others might be detected only as light scattered inside the objective.

*f*

_{1}= 280 Hz by mechanically chopping the laser beam that is used for its excitation. The pump laser beam is chopped with the same (double-frequency) wheel at

*f*

_{2}= 200 Hz (Fig. 1a). Hence, the contribution of the probe SPP into the LR is detected by a lock-in amplifier with the reference frequency being

*f*

_{1}= 280 Hz, whereas the contribution from stimulated emission is provided by setting the reference to either the sum or the difference of the frequencies

*f*

_{1}and

*f*

_{2}; we used 80 Hz in our experiment.

## 3. Results and discussions

13. I. P. Radko, S. I. Bozhevolnyi, G. Brucoli, L. Martín-Moreno, F. J. García-Vidal, and A. Boltasseva, “Efficient unidirectional ridge excitation of surface plasmons,” Opt. Express **17**, 7228–7232 (2009). [CrossRef] [PubMed]

13. I. P. Radko, S. I. Bozhevolnyi, G. Brucoli, L. Martín-Moreno, F. J. García-Vidal, and A. Boltasseva, “Efficient unidirectional ridge excitation of surface plasmons,” Opt. Express **17**, 7228–7232 (2009). [CrossRef] [PubMed]

^{−1}at the maximum available irradiance, after which the PMMA layer starts to deteriorate and results in a decreased stimulated emission (Fig. 4b). According to Fig. 2, the SPP-mode propagation length for an 85-nm-thick PMMA layer is ~ 8

*µ*m, which corresponds to an PP-mode loss of 625 cm

^{−1}or ~ 32% of SPP-loss compensation for the achieved gain. However, one must keep in mind that QDs embedded in the PMMA layer absorb at the probe wavelength too, decreasing hereby the SPP propagation length. The effect can by estimated by introducing an effective imaginary part of the dielectric permittivity of the polymer,

*ε*″, using the following expression (see, e.g., [21]):

*ε*is the (real) dielectric constant of PMMA,

*λ*is the free-space wavelength,

*N*is the concentration of those QDs (in the PMMA) that absorb at the wavelength

*λ*, i.e. the concentration of the QDs residing in the ground state, and σ

_{abs}is the QD absorption cross-section. From the producer of the QDs the latter quantity is stated to be σ

_{abs}= 9.9 × 10

^{−17}cm

^{2}for a wavelength of 751 nm and can be recalculated for 860 nm using a measured absorption spectrum (not shown), which provides an absorbance—the value directly proportional to the absorption cross-section. We obtained σ

_{abs}= 2.9 × 10

^{−17}cm

^{2}at

*λ*= 860 nm. Assuming all QDs to be in the ground state (

*N*~ 4.6 × 10

^{19}cm

^{−3}), one gets

*ε*″ = 0.027, from which the SPP-mode propagation length is evaluated as ~ 3.4

*µ*m, i.e. more than twice shorter than that calculated (Fig. 2) without taking into account QD absorption. This value corresponds to the upper bound of the SPP-mode loss of ~ 1470 cm

^{−1}[note that relative to this value, the mode-loss compensation is still ~ 32% according to Eq. (11) of Appendix], which must be substantially overestimated, since the number of QDs residing in the ground state is reduced at least twice in the case of population inversion.

22. P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. **35**, 1197–1199 (2010). [CrossRef] [PubMed]

22. P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. **35**, 1197–1199 (2010). [CrossRef] [PubMed]

## 4. Conclusion

## 5. Appendix: Evaluation of SPP-mode gain from LR microscopy measurements

*Leakage coefficient*Let us define a leakage coefficient

*τ*as a relative amount of SPP power being elastically radiated into the substrate in the form of LR, i.e.,

*P*

_{LR}is the power of LR and

*P*

_{SPP}is the total power guided by the SPP beam. Assuming a plane SPP wave and denoting SPP electric-field attenuation along the propagation direction

*x*due to internal loss (ohmic and, if present, absorption loss in the dielectric medium, for instance, due to QDs) by

*α*and attenuation due to radiation loss by

*β*, the amplitude of the SPP field at the metal surface can be written as

*E*(

*x*) =

*E*

_{0}

*e*

^{−αx}

*e*

^{−βx}. We can also introduce gain

*γ*into the system by writing

*E*(

*x*) =

*E*

_{0}·exp[−(

*α*+

*β*+

*γ*)

*x*]. Hence, the power transferred by the SPP beam through a plane

*x = const*is expressed as follows:

*x*= 0 and its total power (at the origin) is

*P*

_{SPP}. The value of

*β*depends on the metal-film thickness

*d*, and for an infinitely thick film it is equal to zero. By definition, the SPP propagation length

*L*

_{SPP}(

*d*) = 1/[2(

*α*+

*β*+

*γ*)]. Denoting

*l*=

*L*

_{SPP}(

*d*=

*d*

_{0}) and

*L*=

*L*

_{SPP}(

*d*= ∞), we get

*l/L*= (

*α*+

*γ*)/(

*α*+

*β*+

*γ*), and hence:

*dx*, i.e. from Eq. (3),

*P*

_{LR}=

*P*

_{SPP}·

*β*/(

*α*+

*β*+

*γ*), and hence from Eqs. (2) and (4) we finally get:

*l*) and an infinitely thick (

*L*) metal films. Analytical estimation of

*τ*using approximate expressions for

*α*and

*β*[24

24. E. Kretschmann, “The determination of the optical constants of metals by excitation of surface plasmons,” Z. Physik **241**, 313–324 (1971). [CrossRef]

25. A. Bouhelier and G. P. Wiederrecht, “Excitation of broadband surface plasmon polaritons: Plasmonic continuum spectroscopy,” Phys. Rev. B **71**, 195406 (2005). [CrossRef]

*γ*should be set to zero, i.e.,

*τ*>

*τ*′, since gain

*γ*must be of opposite to (

*α*+

*β*) sign. That means that the presence of gain effectively increases the leakage of SPP power into the substrate.

*Overlap between the SPP and the pump beams.*LR is collected from the whole visible surface imaged with an objective, whereas we pump an area covering only partially the probe SPP beam (Fig. 1b). For this reason, gain occurs at a limited distance of SPP travelling, and for quantitative estimates we will need to calculate the relative part of SPP power,

*P*

_{circ}, dissipated inside a circular surface area, where pumping is produced. This is done by calculating an overlap integral between the pump Gaussian beam and the probe SPP beam:

*x*

_{0},0) and

*R*are the position coordinate and the radius (waist) of the pump beam (Fig. 1b), and

*P*(

*x, y*) is the SPP power transferred through the point (

*x, y*) of the surface. Expression for the derivative of

*P*(

*x, y*) can be found by noticing that (∂/∂

*y*)

*P*(

*x, y*)=

*∫*

^{+∞}

_{−∞}〈

*S*(

_{x}*x, y*)〉

_{t}

*dz*with a time-averaged

*x*-component of the SPP Poynting vector under the integral:

26. T. Søndergaard and S. I. Bozhevolnyi, “Theoretical analysis of finite-size surface plasmon polariton band-gap structures,” Phys. Rev. B **71**, 125429 (2005). [CrossRef]

*P*

_{circ}with the total power of SPP beam,

*P*

_{SPP}=

*∫∫*∂

^{2}

*P*(

*x, y*)/∂

*x*∂

*y·dxdy*, gives the desired value:

*x*

_{0}= (10 ± 0.5)

*µ*m and

*R*= (6.9 ± 0.4)

*µ*m, we obtained

*k*=(0.201 ± 0.025), i.e. ~ (20 ± 3)% of the probe-SPP power is dissipated inside the dashed circle in Fig. 1b (note a highly nonlinear colour scale, which visually enhances the SPP propagation length).

*SPP-mode gain.*In the experiment on SPP amplification, the LR signal has a component corresponding to the probe-SPP beam and a component corresponding to stimulated emission from the QDs. The enhanced LR signal (as compared with the case of unamplified SPP) can be accounted for as either an additional stimulated SPP emission emerging (coherently with the probe SPP) inside the circular area (Fig. 1b) and leaking into the substrate with the leakage coefficient

*τ*′, Eq. (6a), when the gain is effectively absent, or as a probe-SPP power leaking from the circular area with an increased leakage coefficient

*τ*, Eq. (6), due to the presence of gain in the system [see also a note after Eq. (6a)]. Mathematically this can be expressed as follows:

*P*

_{st}is the total power of stimulated SPP emission and

*P*

_{circ}is given by Eq. (8). On the other hand, by virtue of the definition of the leakage coefficient and on the strength of Eq. (8),

*M*

_{st}and

*M*

_{SPP}being the measured values of stimulated SPP emission and the total SPP power detected at reference frequencies

*f*

_{1}−

*f*

_{2}= 80 Hz and

*f*

_{1}= 280 Hz, respectively. Combining Eqs. (6), (6a), (9), and (10), we finally get an expression for gain

*γ*involving the experimentally measured values:

*α*+

*β*) is evaluated from the SPP propagation length as 1/(2

*L*

_{SPP}).

## Acknowledgments

## References and links

1. | S. A. Maier, |

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

3. | J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nature Mater. |

4. | D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nature Photon. |

5. | D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. |

6. | J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. |

7. | M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmons polariton by gain in adjacent dielectric medium,” Opt. Express |

8. | M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. |

9. | M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature (London) |

10. | I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nature Photon. |

11. | M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. |

12. | J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, C. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. |

13. | I. P. Radko, S. I. Bozhevolnyi, G. Brucoli, L. Martín-Moreno, F. J. García-Vidal, and A. Boltasseva, “Efficient unidirectional ridge excitation of surface plasmons,” Opt. Express |

14. | I. P. Radko, S. I. Bozhevolnyi, G. Brucoli, L. Martín-Moreno, F. J. García-Vidal, and A. Boltasseva, “Efficiency of local surface plasmon polariton excitation on ridges,” Phys. Rev. B |

15. | I. De Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. B |

16. | I. De Leon and P. Berini, “Modeling surface plasmon-polariton gain in planar metallic structures,” Opt. Express |

17. | A. L. Stepanov, J. R. Krenn, H. Ditlbacher, A. Hohenau, A. Drezet, B. Steinberger, A. Leitner, and F. R. Aussenegg, “Quantitative analysis of surface plasmon interaction with silver nanoparticles,” Opt. Lett. |

18. | A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B |

19. | H. Raether, |

20. | T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B |

21. | M. Kerker, |

22. | P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. |

23. | J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express |

24. | E. Kretschmann, “The determination of the optical constants of metals by excitation of surface plasmons,” Z. Physik |

25. | A. Bouhelier and G. P. Wiederrecht, “Excitation of broadband surface plasmon polaritons: Plasmonic continuum spectroscopy,” Phys. Rev. B |

26. | T. Søndergaard and S. I. Bozhevolnyi, “Theoretical analysis of finite-size surface plasmon polariton band-gap structures,” Phys. Rev. B |

**OCIS Codes**

(240.6680) Optics at surfaces : Surface plasmons

(250.4480) Optoelectronics : Optical amplifiers

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: June 4, 2010

Revised Manuscript: July 15, 2010

Manuscript Accepted: July 30, 2010

Published: August 16, 2010

**Citation**

Ilya Radko, Michael G. Nielsen, Ole Albrektsen, and Sergey I. Bozhevolnyi, "Stimulated emission of surface plasmon polaritons by lead-sulphide quantum dots
at near infra-red wavelengths," Opt. Express **18**, 18633-18641 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-18-18633

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### References

- S. A. Maier, Plasmonics: Fundamentals and applications (Springer, 2007).
- S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007). [CrossRef]
- J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008). [CrossRef]
- D. K. Gramotnev, and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010). [CrossRef]
- D. J. Bergman, and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003). [CrossRef] [PubMed]
- J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401 (2005). [CrossRef] [PubMed]
- M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmons polariton by gain in adjacent dielectric medium,” Opt. Express 16, 1385–1392 (2008). [CrossRef] [PubMed]
- M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008). [CrossRef] [PubMed]
- M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1113 (2009). [CrossRef] [PubMed]
- I. De Leon, and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4, 382–387 (2010). [CrossRef]
- M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8, 3998–4001 (2008). [CrossRef] [PubMed]
- J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, C. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009). [CrossRef] [PubMed]
- I. P. Radko, S. I. Bozhevolnyi, G. Brucoli, L. Martín-Moreno, F. J. García-Vidal, and A. Boltasseva, “Efficient unidirectional ridge excitation of surface plasmons,” Opt. Express 17, 7228–7232 (2009). [CrossRef] [PubMed]
- I. P. Radko, S. I. Bozhevolnyi, G. Brucoli, L. Martín-Moreno, F. J. García-Vidal, and A. Boltasseva, “Efficiency of local surface plasmon polariton excitation on ridges,” Phys. Rev. B 78, 115115 (2008). [CrossRef]
- . I. De Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. B 78, 161401(R) (2008). [CrossRef]
- I. De Leon, and P. Berini, “Modeling surface plasmon-polariton gain in planar metallic structures,” Opt. Express 17, 20191–20202 (2009). [CrossRef] [PubMed]
- A. L. Stepanov, J. R. Krenn, H. Ditlbacher, A. Hohenau, A. Drezet, B. Steinberger, A. Leitner, and F. R. Aussenegg, “Quantitative analysis of surface plasmon interaction with silver nanoparticles,” Opt. Lett. 30,Q11524–1526 (2005). [CrossRef] [PubMed]
- A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B 149, 220–229 (2008). [CrossRef]
- H. Raether, Surface plasmons on smooth and rough surfaces and on gratings (Springer, 1988).
- T. Holmgaard, and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75, 245405 (2007). [CrossRef]
- M. Kerker, The scattering of light and other electromagnetic radiation (Academic Press, 1969).
- P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35, 1197–1199 (2010). [CrossRef] [PubMed]
- J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18, 1207–1216 (2010). [CrossRef] [PubMed]
- E. Kretschmann, “The determination of the optical constants of metals by excitation of surface plasmons,” Z. Phys. 241, 313–324 (1971). [CrossRef]
- A. Bouhelier, and G. P. Wiederrecht, “Excitation of broadband surface plasmon polaritons: Plasmonic continuum spectroscopy,” Phys. Rev. B 71, 195406 (2005). [CrossRef]
- T. Søndergaard, and S. I. Bozhevolnyi, “Theoretical analysis of finite-size surface plasmon polariton band-gap structures,” Phys. Rev. B 71, 125429 (2005). [CrossRef]

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