## Elongation of surface plasmon polariton propagation length without gain

Optics Express, Vol. 16, Issue 20, pp. 15576-15583 (2008)

http://dx.doi.org/10.1364/OE.16.015576

Acrobat PDF (1059 KB)

### Abstract

We have demonstrated that an addition of highly concentrated rhodamine 6G chloride dye to the PMMA film adjacent to a silver film can cause 30% elongation of the propagation length of surface plasmon polaritons (SPPs). The possibility to elongate the SPP propagation length without optical gain opens a new technological dimension to low-loss nanoplasmonic and metamaterials.

© 2008 Optical Society of America

## 1. Introduction and model predictions

1. M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. **57**, 783–826 (1985). [CrossRef]

3. S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science **275**, 1102–1104 (1997). [CrossRef] [PubMed]

4. S. I. Bozhevolnyi, V. S. Volkov, and K. Leosson, “Localization and Waveguiding of Surface Plasmon Polaritons in Random Nanostructures,” Phys. Rev. Lett. **89**, 186801 (2002). [CrossRef] [PubMed]

9. C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (λ ~8-11.5 µm) semiconductor lasers with waveguides based on surface plasmons,” Opt. Lett. **23**, 1366–1368 (1998). [CrossRef]

10. Thomas A. Klar, Alexander V. Kildishev, Vladimir P. Drachev, and Vladimir M. Shalaev, “Negative-index metamaterials: going optical,” IEEE J. Sel. Top. Quantum Electron. **12**, 1106–1115 (2006). [CrossRef]

12. J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. **90**, 191109 (2007) (3 pages). [CrossRef]

15. M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express **12**, 4072–4079 (2004). [CrossRef] [PubMed]

16. N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. **85**, 5040–5042 (2004). [CrossRef]

17. M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium,” Opt. Lett. **31**, 3022–3024 (2006). [CrossRef] [PubMed]

18. J. Seidel, S. Grafstroem, 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]

19. 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 plasmon polariton by gain in adjacent dielectric medium,” Opt. Express **16**, 1385–1392 (2008). [CrossRef] [PubMed]

^{3}cm

^{-1}) is a technologically difficult task, which often requires a Q-switched laser [17

17. M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium,” Opt. Lett. **31**, 3022–3024 (2006). [CrossRef] [PubMed]

19. 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 plasmon polariton by gain in adjacent dielectric medium,” Opt. Express **16**, 1385–1392 (2008). [CrossRef] [PubMed]

^{-1}).

## 2. Experimental results and discussion

^{-1}M).

*R*(

*θ*), the prism was mounted on a motorized goniometer stage. The reflectivity was probed with

*p*polarized 594.1 nm He-Ne laser light. Reflected light was detected by a photomultiplier tube connected to an integrating sphere, which was moved during the scan to follow the walk of the reflected beam. The reflectivity profile

*R*(

*θ*) had a characteristic dip [25] at the angle at which the wave vector of the SPP matched the projection of the photon wave vector to the plane of metal-dielectric interface, Fig. 3. It is described by the known formula

*p*polarized light at the interface between media

*i*and

*k*(

*i*,

*k*=0,1,2),

*ε*is the dielectric constant,

_{i, k}*d*is the thickness of the metallic film,

*k*=

_{x}*k*sin

_{phot}*θ*

_{0}is the wave vector in the direction of the SPP propagation,

*k*is the wave vector of a photon in the glass prism, and

_{phot}*q*is the angle of incidence; the subscripts 0, 1, and 2 correspond to glass, silver, and PMMA, respectively. Here it is assumed that each of the three media (glass/silver/polymer with dye) is spatially uniform, the boundaries between media are sharply defined, and effects of hybrid states at the interfaces are neglected.

*″*

_{2}, calculated at λ=594 nm from the absorption data, is plotted as a function of concentration of R6G (in log-log scale) in Fig. 4. At high concentration of dye, the slope of the curve approached 2, which indicated dimerization of dye molecules. Large scatter of the data was due to the known relatively low reproducibility of PMMA films.

*R*(

*θ*) in pure glass prism, without any deposited films. By fitting the function

*R*(

*θ*) with Eq. (1) at

*d*=0 and

*e*=1, we determined the index of refraction of glass

_{2}*n*

_{0}=(

*ε*)

_{0}^{1/2}to be equal to 1.7835 at 594.1 nm, in a very good agreement with the data provided by the manufacturer.

*R*(

*θ*) was fitted with Eq. (1) at

*d*=0 to determine the dielectric constant of the PMMA/R6G film, Fig. 5.

*R*(

*θ*) characteristic of SPPs [25], Fig. 3. The most remarkable result of this measurement is that the width W of the dip of the angular profile

*R*(

*θ*) decreased with an addition of R6G to PMMA, up to the concentration of dye N!30 g/l, and then increased again when the concentration of dye was increased further (compare widths

*W*

_{1}and

*W*

_{2}in Fig. 3). According to Ref. [19

19. 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 plasmon polariton by gain in adjacent dielectric medium,” Opt. Express **16**, 1385–1392 (2008). [CrossRef] [PubMed]

*W*is inversely proportional to the SPP propagation length

*L*. Correspondingly, the obtained experimental result implies that an addition of R6G dye to PMMA helps to reduce the loss and elongate the propagation length of SPPs.

*R*(

*θ*) using Eq. (1), with the fitting parameters being real and imaginary parts of the dielectric constant of silver,

*ε*’ and

_{1}*ε*”. The real and imaginary parts of the dielectric constants of PMMA/R6G,

_{1}*ε*’ and

_{2}*ε*”, were chosen in accord with the measurements presented in Figs. 4 and 5. The determined this way values

_{2}*ε*’ and

_{1}*ε*” (at λ=594.1 nm) are plotted against the concentration of R6G in Fig. 6. In the absence of R6G, the value of e1’ coincided within 5% with those published in Refs. [20,21]. The value of

_{1}*ε*” was smaller than that in Ref. [21] and larger than that in Ref. [20].

_{1}*ε*’ and

_{1}*ε*” were strongly influenced by the presence of R6G dye in the PMMA film, Fig. 6. A particularly strong effect (40% reduction) has been observed in the dependence

_{1}*ε*”(

_{1}*N*) with the increase of the concentration of dye from 0 g/l to 30 g/l.

*ε*” would be required to account for the change in the SPP propagation length observed experimentally.

_{1}*L*of SPPs can be calculated as [19

**16**, 1385–1392 (2008). [CrossRef] [PubMed]

*γ*is the internal SPP loss,

_{i}*γ*is the radiation loss caused by the decoupling of SPPs back to the prism

_{r}*ω*is the oscillation frequency,

*d*

_{1}is the thickness of the metallic film,

*k*

^{0}

*is the value of*

_{z}*k*at the resonance angle, and

_{z}*c*is the speed of light.

*L*(

*N*) for two different thicknesses of the metallic film,

*d*

_{1}=40 nm and

*d*

_{1}=80 nm (Fig. 7), we substituted to Eq. (2) functions

*ε*(

_{1}*N*) and ε2(N) obtained by interpolation of the experimental data in Figs. 4–6 with the second order polynomials. Because the values of the radiative loss

*γ*and, correspondingly, the SPP propagation lengths

_{r}*L*are different at

*d*

_{1}=80 nm and

*d*

_{1}=40 nm, the data sets

*L*(

*N*) (squares and triangles in Fig. 7) were normalized to unity at

*N*=0 for convenience of presentation.

*L*(

*N*) calculated at

*d*

_{1}=80 nm and

*d*

_{1}=40 nm (solid squares and triangles) are close to each other suggests that the

*relative*change of the SPP propagation length with the concentration of dye is not strongly dependent on the thickness of the silver film. This justifies the comparison of the calculated values

*L*(

*N*) with the inverse widths

*W*

^{-1}of the reflectivity profiles

*R*(

*θ*) (circles in Fig. 7) measured in different samples with the thickness of the silver film varying between 35 and 91 nm and the average thickness being equal to 70 nm, Fig. 7. Not surprisingly (since

*W*

^{-1}is proportional to

*L*[19

**16**, 1385–1392 (2008). [CrossRef] [PubMed]

*N*=30 g/l (6.3x10

^{-2}M). (The slight difference between the experimental and the calculated curves in Fig. 7 is not clearly understood. However, the former one appears to be more accurate since it is based on direct measurements rather than recalculated data.)

*L*with the increase of

*N*above 30 g/l is due to (

*i*) the increase of the absorption losses

*ε*” and

_{1}*ε*” and (ii) the increase of

_{2}*ε*’, which becomes less negative, Figs. 4,6. Figure 7 demonstrates the strong difference between the values of

_{1}*L*calculated under the assumption of

*ε*”=0 (no loss in dielectric, open squares and triangles) and at the experimental values of

_{2}*ε*

_{2}” (solid squares and triangles).

*ε*

_{1}” by the modification of electronic states in silver layer adjacent to the metal-dielectric interface, including possible formation of the AgCl phase. The preliminary results of

*ab initio*modeling show that the formation of AgCl film can, indeed, affect the absorption loss at the surface. The results of these studies will be reported elsewhere.

## 3. Summary

## Acknowledgements

## References

1. | M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. |

2. | K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. |

3. | S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science |

4. | S. I. Bozhevolnyi, V. S. Volkov, and K. Leosson, “Localization and Waveguiding of Surface Plasmon Polaritons in Random Nanostructures,” Phys. Rev. Lett. |

5. | A. Boltasseva, S. Bozhevolnyi, T. Søndergaard, T. Nikolajsen, and K. Leosson, “Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons,” Opt. Express |

6. | S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Hare, B. E. Koe, and A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Materials |

7. | A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Solja, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. |

8. | M. Stockman, “Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides,” Phys. Rev. Lett. |

9. | C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (λ ~8-11.5 µm) semiconductor lasers with waveguides based on surface plasmons,” Opt. Lett. |

10. | Thomas A. Klar, Alexander V. Kildishev, Vladimir P. Drachev, and Vladimir M. Shalaev, “Negative-index metamaterials: going optical,” IEEE J. Sel. Top. Quantum Electron. |

11. | R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, “Nonmagnetic nanocomposites for optical and infrared negative-refractive-index media,” J. Opt. Soc. Am. |

12. | J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. |

13. | A. N. Sudarkin and P. A. Demkovich, “Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys. Tech. Phys. |

14. | I. Avrutsky, “Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain,” Phys. Rev. |

15. | M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express |

16. | N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. |

17. | M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium,” Opt. Lett. |

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

19. | 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 plasmon polariton by gain in adjacent dielectric medium,” Opt. Express |

20. | P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. |

21. | D. W. Lynch and W. R. Hunter, “Comments on the Optical Constants of Metals and an Introduction to Data for Several Metals”, In Handbook of optical constants of solids, Part II, ed. by E. D. Palik, Academic Press, NY,1985. |

22. | M. V. Klein and T. E. Furtak, Optics, 2nd ed. (Wiley, New York,1986). |

23. | Calculations are performed with ab initio norm-conserving pseudopotentials within standard Density Functional Theory. Optical functions are calculated in Random Phase Approximation using the lattice constant of 4.023 Å generated within Local Density Approximation. |

24. | K. Stahrenberg, T. Herrmann, N. Esser, J. Sahm, W. Richter, S. V. Hoffmann, and Ph. Hofmann. “Surface state contrubution of the optical anisotropy of Ag(110) surface: a reflectance anisotropy spectroscopy and photoemission study,” Phys. Rev. |

25. | H. Raether, “Surface plasmons on smooth and rough surfaces and on gratings”, Springer-Verlag, (Berlin, 1988). |

**OCIS Codes**

(240.5420) Optics at surfaces : Polaritons

(240.6680) Optics at surfaces : Surface plasmons

(250.5403) Optoelectronics : Plasmonics

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: December 11, 2007

Revised Manuscript: May 2, 2008

Manuscript Accepted: May 26, 2008

Published: September 18, 2008

**Citation**

G. Zhu, M. Mayy, M. Bahoura, B. A. Ritzo, H. V. Gavrilenko, V. I. Gavrilenko, and M. A. Noginov, "Elongation of surface plasmon polariton propagation length without gain," Opt. Express **16**, 15576-15583 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15576

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### References

- M. Moskovits, "Surface-enhanced spectroscopy," Rev. Mod. Phys. 57, 783-826 (1985). [CrossRef]
- K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, "Single molecule detection using surface-enhanced Raman scattering (SERS)," Phys. Rev. Lett. 78, 1667-1670 (1997). [CrossRef]
- S. Nie and S. R. Emory, "Probing single molecules and single nanoparticles by surface-enhanced Raman scattering," Science 275, 1102-1104 (1997). [CrossRef] [PubMed]
- S. I. Bozhevolnyi, V. S. Volkov, and K. Leosson, "Localization and Waveguiding of Surface Plasmon Polaritons in Random Nanostructures," Phys. Rev. Lett. 89, 186801 (2002). [CrossRef] [PubMed]
- A. Boltasseva, S. Bozhevolnyi, T. Søndergaard, T. Nikolajsen, and K. Leosson, "Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons," Opt. Express 13, 4237-4243 (2005). [CrossRef] [PubMed]
- S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Hare, B. E. Koe and A. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003). [CrossRef] [PubMed]
- A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Solja, "Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air," Phys. Rev. Lett. 95, 063901 (2005). [CrossRef] [PubMed]
- M. Stockman, "Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides," Phys. Rev. Lett. 93, 137404 (2004). [CrossRef] [PubMed]
- C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, "Long-wavelength (? ~ 8-11.5 µm) semiconductor lasers with waveguides based on surface plasmons," Opt. Lett. 23, 1366-1368 (1998). [CrossRef]
- T. A. Klar; A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, "Negative-index metamaterials: going optical," IEEE J. Sel. Top. Quantum Electron. 12, 1106-1115 (2006). [CrossRef]
- R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, "Nonmagnetic nanocomposites for optical and infrared negative-refractive-index media," J. Opt. Soc. Am. B 23, 498-505 (2006).
- J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, "Nonlocal effects in effective-medium response of nanolayered metamaterials," Appl. Phys. Lett. 90, 191109 (2007). [CrossRef]
- A. N. Sudarkin and P. A. Demkovich, "Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium," Sov. Phys. Tech. Phys. 34, 764-766 (1989).
- I. Avrutsky, "Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain," Phys. Rev. B 70, 155416 (2004).
- M. P. Nezhad, K. Tetz and Y. Fainman, "Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides," Opt. Express 12, 4072-4079 (2004). [CrossRef] [PubMed]
- N. M. Lawandy, "Localized surface plasmon singularities in amplifying media," Appl. Phys. Lett. 85, 5040-5042 (2004). [CrossRef]
- M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, "Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium," Opt. Lett. 31, 3022-3024 (2006). [CrossRef] [PubMed]
- J. Seidel, S. Grafstroem, 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 plasmon polariton by gain in adjacent dielectric medium," Opt. Express 16, 1385-1392 (2008). [CrossRef] [PubMed]
- P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
- D. W. Lynch and W. R. Hunter, "Comments on the Optical Constants of Metals and an Introduction to Data for Several Metals," in Handbook of Optical Constants of Solids, Part II, E. D. Palik, ed., (Academic Press, NY, 1985).
- M. V. Klein and T. E. Furtak, Optics, 2nd ed. (Wiley, New York, 1986).
- Calculations are performed with ab initio norm-conserving pseudopotentials within standard Density Functional Theory. Optical functions are calculated in Random Phase Approximation using the lattice constant of 4.023 ?? generated within Local Density Approximation.
- K. Stahrenberg, T. Herrmann, N. Esser, J. Sahm, W. Richter, S. V. Hoffmann, and Ph. Hofmann. "Surface state contrubution of the optical anisotropy of Ag (110) surface: a reflectance anisotropy spectroscopy and photoemission study," Phys. Rev. B 58, R10207 (1998).
- H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, Berlin, 1988).

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