## Bouncing surface plasmons

Optics Express, Vol. 15, Issue 21, pp. 13757-13767 (2007)

http://dx.doi.org/10.1364/OE.15.013757

Acrobat PDF (268 KB)

### Abstract

Employing an interferometric cavity ring-down technique we study the launching, propagation and reflection of surface plasmons on a smooth gold-air interface that is intersected by two parallel, sub-wavelength wide slits. Inside the low-finesse optical cavity defined by these slits the surface plasmon is observed to make multiple bounces. Our experimental data allow us to determine the surface-plasmon group velocity (*v*_{group} = 2.7 ± 0.3 × 10^{-8} m/s at λ = 770 nm) and the reflection coefficient (*R* ≈ 0.04) of each of our slits for an incident surface plasmon. Moreover, we find that the phase jump upon reflection off a slit is equal to the scattering phase acquired when light is converted into a plasmon at one slit and back-converted to light at the other slit. This allows us to explain fine details in the transmission spectrum of our double slits.

© 2007 Optical Society of America

## 1. Introduction

*et al*. [1

1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature **391**, 667 (1998). [CrossRef]

2. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. **66**, 163 (1944). [CrossRef]

3. I. I. Smolyaninov, J. Elliott, G. Wurtz, A. V. Zayats, and C. C. Davis, “Digital resolution enhancement in surface plasmon microscopy,” Appl. Phys. B **84**, 253 (2006). [CrossRef]

4. B. Liedberg, C. Nylander, and I. Lundstrom, “Biosensing with surface plasmon resonance – how it all started,” Biosens. and Bioelectron. **10**, i (1995). [CrossRef]

5. F. Yu, S. Tian, D. Yao, and W. Knoll, “Surface plasmon enhanced diffraction for label-free biosensing,” Anal. Chem. **76**, 3530 (2004). [CrossRef] [PubMed]

7. M. L. Brongersma and P. G. Kik, *Surface plasmon nanophotonics*, (Springer, 2007). [CrossRef]

8. L. Cao, N. C. Panoiu, and R. M. Osgood, “Surface second-harmonic generation from surface plasmon waves scattered by metallic nanostructures,” Phys. Rev. B **75**, 205401 (2007). [CrossRef]

9. D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. **97**, 053002 (2006). [CrossRef] [PubMed]

10. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature **445**, 39 (2007). [CrossRef] [PubMed]

11. H. F. Schouten, N. V. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. **94**, 053901 (2005). [CrossRef] [PubMed]

15. C. H. Gan, G. Gbur, and T. D. Visser, “Surface plasmons modulate the spatial coherence of light in Young’s interference experiment,” Phys. Rev. Lett. **98**, 043908 (2007). [CrossRef] [PubMed]

16. N. V. Kuzmin, H. F. Schouten, G. Gbur, G. W. ’t Hooft, E. R. Eliel, and T. D. Visser, “Enhancement of spatial coherence by surface plasmons,” Opt. Lett. **32**, 445 (2007). [CrossRef] [PubMed]

*π*/2 to +

*π*/2; ii) a surface plasmon field travelling away from the slit along the metal-dielectric interface; iii) evanescent modes. A second, nearby slit can act as a receiver for the surface plasmon field and scatter it into, e.g., free space or into a backward-travelling / transmitted plasmon (Fig. 1(b)).

11. H. F. Schouten, N. V. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. **94**, 053901 (2005). [CrossRef] [PubMed]

17. 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 (2005). [CrossRef] [PubMed]

## 2. Experiment

*t*

_{ax}=

*L*/

*v*

_{group}and the cavity decay time

*τ*

_{cav}= -

*t*

_{ax}/ln(

*R*), with

*R*the mirror reflectivity. The former measures the time it takes a pulse to make a round trip through the cavity of length

*L*, while the latter equals the 1/

*e*decay time of the intracavity power. The equivalent parameters in the frequency domain are the free spectral range

*ω*

_{ax}= 2

*π*/

*t*

_{ax}and the

*finesse*ℱ; the finesse measures the ratio of the free spectral range and the cavity linewidth. Round-trip losses are the dominant factor that determine the finesse, and in conventional stable optical resonators the round-trip loss is usually determined by the reflectivity of the mirrors.

*L*we can tune the ratio of these two loss mechanisms. Measurements of the spectrum of a surface-plasmon resonator consisting of a smooth metal film bounded by two sub-wavelength slits demonstrate that its finesse is small (ℱ ≈ 2) [11

11. H. F. Schouten, N. V. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. **94**, 053901 (2005). [CrossRef] [PubMed]

*πR*

^{1/2}/(1 -

*R*), but by ℱ =

*π*/{arccos[2

*R*/(1 +

*R*

^{2})]} ≈ 2(1 + 4

*R*/

*π*). We therefore have chosen to measure in the time domain, essentially using a cavity ring-down technique [20

20. J. J. Scherer, J. B. Paul, A. O’Keefe, and R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. **97**, 25 (1997). [CrossRef] [PubMed]

*λ*≈ 800 nm) propagates along a flat and unstructured air-gold interface its amplitude decays over a length of order 100

*μ*m [21, 22]. Unless a gain medium is present [23

23. M. Z. Alam, J. Meier, J. S. Aitchison, and M. Mojahedi, “Gain assisted surface plasmon polariton in quantum wells structures,” Opt. Exp. **15**, 176 (2007). [CrossRef]

20. J. J. Scherer, J. B. Paul, A. O’Keefe, and R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. **97**, 25 (1997). [CrossRef] [PubMed]

*μ*m long and 100 nm wide slits, separated by distances ranging from 25 to 90

*μ*m. The titanium adhesion layer is strongly dissipative to surface plasmons [11

**94**, 053901 (2005). [CrossRef] [PubMed]

*l*

_{coh}≈ 16–20

*μ*m. The Michelson interferometer serves to generate a time-delayed copy of the laser pulse and, together, these two pulses illuminate both slits of our sample. We image the double-slit output on a low-noise detector (New Focus model 2001-FS) and measure its output as a function of the delay Δ

*t*between the two pulses incident on the sample. We collect the data on a computer using a 24-bit A/D converter (National Instruments PCI 5911) while slowly changing Δ

*t*using a motorized translation stage (Newport model CMA-25CCCL). Note that our experimental approach is slightly unusual in that we send

*both*the original pulse, henceforth called pump,

*and*its copy, called probe, onto our sample, instead of illuminating the sample with just one of the pulses [25

25. M. Galli, F. Marabelli, and G. Guizzetti, “Direct measurement of refractive-index dispersion of transparent media by white-light interferometry,” Appl. Opt. **42**, 3910 (2003). [CrossRef] [PubMed]

^{-6}for a spot size of 50

*μ*m diameter) and considerations of signal to noise.

## 3. Results

*λ*= 770 nm are shown in Fig. 3. The upper frame shows the autocorrelation trace obtained in the absence of a sample, yielding information on the instrumental response function of our setup. At a pump-probe delay of ≈ 50 fs the signal is essentially constant and remains so when the delay is increased. The lower frame shows the measured interferogram as recorded in the presence of our sample, using a double slit with a slit separation of 25

*μ*m and TM-polarized incident light. The interference fringes show a quite different behavior here: most noticeably one observes the signal to partially recover after the initial collapse (peak B, Fig. 3(b)). This “echo” has an amplitude of order 10% of the initial signal. Upon careful observation one notices that the signal goes through an additional cycle of collapse and recovery (peak C). When the polarization of the incident light is chosen to be TE, we observe no revivals; the signal is indistinguishable from that measured with the double slit absent (Fig. 3(a)).

*t*; the second, weaker, echo (C) arises because a surface plasmon that is launched at one of the slits, can be back-scattered by the other slit to return to its place of birth with a delay equal to 2Δ

*t*.

*five*interference maxima (peaks A-E), spanning four decades of signal. The interference maxima are equidistant with a peak-to-peak separation of 93 fs. The two additional peaks that show up in the carrier envelope (D,E) are then identified with the case that a surface plasmon is back-scattered

*twice*and

*three times*, respectively. Altogether, the surface plasmon is seen to make two full round trips through the cavity. Figure 4(b) shows the carrier envelope for the case that a double slit with a slit separation of 50

*μ*m is studied. Here we observe essentially the same features as before, except that, naturally, the subsidiary maxima are farther apart and thus better resolved.

## 4. Discussion

*v*

_{group}, the complex SP coupling factor

*α*, and the (complex) SP amplitude reflection coefficient

*r*. When the subsequent peaks in the interferogram are well separated and the group-velocity dispersion of the SP is small or negligible, the group velocity can be determined directly from the separation between subsequent peaks in the signal envelope. Both

*v*

_{group}and its dispersion can be calculated from the dispersion relation of the SP travelling along the plane interface between a metal and a dielectric [22],

*ε*

_{m}(

*ω*) and

*ε*

_{d}(

*ω*) the dielectric coefficients of the metal and the dielectric, respectively. We use the tabulated values for

*ε*

_{m}(

*ω*) [21] and set

*ε*

_{d}(

*ω*) = 1, the dielectric being air. At

*λ*= 770 nm we calculate

*v*

_{group}= d

*ω*/d

*k*

_{sp}≃ 2.72 × 10

^{8}m/s and a value for the group velocity dispersion d

^{2}

*k*

_{sp}/d

*ω*

^{2}≃ 0.76 fs

^{2}/

*μ*m equivalent to a group delay dispersion d(

*v*

^{-1}

_{group})/d

*λ*≃ -2.4 as/nm∙

*μ*m. For the experiment with as lit separation of 50

*μ*m and the pulse spectral width Δ

*λ*= 27 nm (corresponding to a Fourier-limited cosh

^{-1}pulse duration of 32 fs) the group delay dispersion leads to a pulse broadening of only 5 fs and can therefore be neglected. It is therefore perfectly allowed to extract an experimental value of the SP group velocity directly from the separation between successive peaks in the interferogram (Fig. 5(a)), provided that they are well separated, as in the case of 50

*μ*m slit separation. This yields

*v*

_{group}= 2.70 ± 0.03 × 10

^{8}m/s. This result is in excellent agreement with the calculated value and with [14

14. V. V. Temnov, U. Woggon, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon interferometry: measuring group velocity of surface plasmons,” Opt. Lett. **32**, 1235 (2007). [CrossRef] [PubMed]

*et al*. [26

26. M. Bai, C. Guerrero, S. Ioanid, E. Paz, M. Sanz, and N. Garcia, “Measuring the speed of a surface plasmon,” Phys. Rev. B **69**, 115416 (2004). [CrossRef]

*α*and of the SP reflection coefficient

*r*. The peak-height ratio (B/A) of the first echo and the peak at zero delay is given by |

*α*|exp(-

*k*″

_{sp}

*L*), while that of the second and first echo’s (C/B) is given by |

*r*|exp(-

*k*″

_{sp}

*L*). By determining these peak-height ratio’s from measurements performed on double-slit systems with different inter-slit separations

*L*, and plotting these ratio’s on a logarithmic scale versus

*L*, as shown in Fig. 5, we can extract |

*α*| and |

*r*| from the line intercepts and

*k*″

_{sp}from the slope of the lines. This yields |

*α*| = 0.19 ± 0.02, |

*r*| = 0.18 ± 0.01 and

*k*″

_{sp}= 0.02

*μ*m

^{-1}. The damping constant is approximately twice the value that one calculates from the surface-plasmon dispersion relation (Eq. (1)) using Palik’s data for the dielectric coefficient of gold [21]. We attribute the additional damping to the fact that our gold film has deteriorated over a period of a year of use, giving rise to scattering loss in the film. The value for

*α*is in good agreement with the prediction by Lalanne

*et al*. [12

12. P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. **95**, 263902 (2005). [CrossRef]

*R*= |

*r*|

^{2}of the slit is quite small (

*R*≈ 0.04); consequently the cavity finesse is very small: ℱ = 2.1. Similar values for the reflection coefficients from edges and subwavelength-wide groves and barriers have been reported [27–32

27. R. F. Wallis, A. A. Maradudin, and G. I. Stegeman, “Surface polariton reflection and radiation at end faces,” Appl. Phys. Lett. **42**, 764 (1983). [CrossRef]

*α*and

*r*, and to illustrate that point we return to the resonator picture discussed earlier. The output of the “resonator” consists of a sequence of pulses, the first one (A) simply being the light directly transmitted through the slits, the second (B) due to the SP being excited at one slit and scattered back into light at the other slit, the third (C) due to the reflected SP being back-scattered into light at the first slit, etc.

*G*(

*ω*) of the double slit can thus be written as:

*k*=

*k*

_{sp}(

*ω*) the complex surface-plasmon wave vector (see Eq. (1)); here the coefficients

*α*and

*r*are assumed to be frequency independent. In the limit that

*r*= 0 this transfer function gives rise to a sinusoidally modulated two-slit spectrum [11

**94**, 053901 (2005). [CrossRef] [PubMed]

*kL*± arg(

*α*) = 2

*πm*, with

*m*integer. Various theoretical studies suggest that arg(

*α*) =

*π*[11

**94**, 053901 (2005). [CrossRef] [PubMed]

12. P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. **95**, 263902 (2005). [CrossRef]

33. O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, “On the phase of plasmons excited by slits in a metal film,” Opt. Exp. **14**, 11823 (2006). [CrossRef]

*r*of the resonator mirrors, the reflectivity spectrum |

*R*(

*ω*)|

^{2}of a Fabry-Pérot displays deep dips whenever 2

*k*

_{0}

*L*= 2

*πm*′, with

*m*′ an integer, on an otherwise constant background. These resonances occur when the denominator in Eq. (4) reaches its minimum value. Because of the strong similarities between Eqs. (2) and (4) we conclude that the resonances of the transmission spectrum |

*G*(

*ω*)|

^{2}of our double slit appear when

*kL*+ arg(

*r*) = 2

*πn*, with

*n*an integer. The shape of the resonance (dip, peak, or asymmetric Fano-type [35

35. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. **124**, 1866 (1961). [CrossRef]

*α*exp [

*ikL*], i.e., by

*u*= arg(

*r*) – arg(

*α*). When

*u*= 0 the spectrum shows peaks, when

*u*= ±

*π*, the spectrum carries dips, and Fano-type features arise when

*u*≈ ±

*π*/2. Experimental results for the plasmon-induced modulation of the two-slit transmission spectrum hint at a value for

*u*close to zero [11

**94**, 053901 (2005). [CrossRef] [PubMed]

36. R. H. J. Kop and R. Sprik, “Phase-sensitive interferometry with ultrashort optical pulses,” Rev. Sci. Instrum. **66**, 5459 (1995). [CrossRef]

*E*(

*ω*) the field incident on both slits. We assume here that our Michelson interferometer is symmetric, i.e. that the transfer functions of both interferometer arms are equal. If the spectrum of

*E*(

*ω*) is much broader than the separation ΔΩ of modulation features in

*G*(

*ω*) (see Fig. 6(a)), the interferometer signal will approximately equal the Fourier transform of |

*G*(

*ω*)|

^{2}, i.e., the interferometer signal will consist of a rapidly decaying series of equidistant bursts, separated by an interval equal to

*L*/

*v*

_{group}, representing the subsequent round trips through the cavity. The duration of these bursts (in units of pump-probe delay) is determined by the coherence time of the incident light

*τ*

_{coh}. In this limit one thus observes well separated individual pulses; Fig. 4(b) serves as an example. When the slit separation is reduced the modulation features in

*G*(

*ω*) lie further apart so that

*E*(

*ω*) and

*G*(

*ω*) are modulated on the same scale (see Fig. 6(b)). In that limit the interferometer signal consists of more or less overlapping peaks and, in the overlap regions is quite sensitive to the value of the parameter

*u*, as we shall see below. The limit where the spectral width of

*E*(

*ω*) is much smaller than a single modulation feature of

*G*(

*ω*) (see Fig. 6(c)) is uninteresting, corresponding to a situation where the coherence time of the incident light is much larger than the memory time of the two-slit cavity. In this limit, time-domain experiments are ineffective.

*τ*

_{coh}of the input pulse is comparable to the cavity round-trip time

*τ*

_{cav}. Let us further assume that the average frequency of the incident light is tuned so that

*kL*+ arg(

*α*) is an integer multiple of 2

*π*(in the approximation that the surface plasmons do

*not*reflect from the slits (

*r*= 0), the incident light is tuned to a transmission maximum). Then the first two terms in Eq. (2) are in phase; in the interferometer signal the first two peaks will then add so that the dip between these peaks will be shallow. If

*kL*+ arg(

*r*) is also an integer multiple of 2

*π*(i.e.,

*u*= 0), all terms in Eq. (2) are in phase, so that all neighboring peaks in the interferogram are separated by shallow dips (see Fig. 7(a)). If, however,

*kL*+ arg(

*r*) is an odd multiple of

*π*(

*u*=

*π*), each subsequent term in Eq. (2) is out of phase with the previous one giving rise to deep dips between second, third, fourth, fifth etc. peaks in the interferogram (see Fig. 7(b)).

*kL*± arg(

*α*) is an odd multiple of

*π*the first two terms in Eq. (2) are out of phase and give rise to a deep dip between the first two peaks in the interferogram. If now

*kL*+ arg(

*r*) is an integer multiple of 2

*π*(so that

*u*=

*π*) the subsequent terms in Eq. (2) will all be in phase with each other giving rise to shallow dips between peaks 2,3,4,… in the interferogram (see Fig. 7(c)). If, however,

*kL*+ arg(

*r*) is an odd multiple of

*π*(so that

*u*= 0) all subsequent terms in Eq. (2) will all be out of phase with each other giving rise to deep dips between all peaks in the interferogram (see Fig. 7(d)). Figures 7(e) and 7(f) show experimental results obtained for the 25

*μ*m slits at two different settings of the laser, one corresponding to the case

*kL*+ arg(

*α*) = 2

*mπ*(Fig. 7(e)) and one corresponding to the case

*kL*+ arg(

*α*) = (2

*m*+ 1)

*π*(Fig. 7(f)). These experimental results clearly suggest that

*u*≈ 0.

*u*fits well with the shape of the transmission spectrum of the double slit, as measured with TM-polarized incident light. Figure 8 shows such a spectrum together with spectra calculated on the basis that |

*α*| = |

*r*| = 0.2, one spectrum for the case that

*u*= 0, the other for the case

*u*=

*π*. Clearly, the curve with

*u*= 0 provides a much better description of the experimental data than that with

*u*=

*π*.

## 5. Conclusions

*et al*. [13

13. P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Approximate model for surface-plasmon generation at slit apertures,” J. Opt. Soc. Am. A **23**, 1608 (2006). [CrossRef]

31. F. Lopez-Tejeira, F. J. Garcia-Vidal, and L. Martin-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B **72**, 161405(R) (2005). [CrossRef]

37. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface-plasmon polaritons,” Phys. Rep. **408**, 131 (2005). [CrossRef]

28. A. Bouhelier, T. Huser, H. Tamaru, H. J. Güntherodt, D. W. Pohl, F. I. Baida, and D. V. Labeke, “Plasmon optics of structured silver films,” Phys. Rev. B **63**, 155404 (2001). [CrossRef]

30. T. Okamoto, K. Kakutani, T. Yoshizaki, M. Haraguchi, and M. Fukui, “Experimental evaluation of reflectance of surface plasmon polariton at metal step barrier,” Surf. Sci. **544**, 67 (2003). [CrossRef]

## Acknowledgments

## References and links

1. | T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature |

2. | H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. |

3. | I. I. Smolyaninov, J. Elliott, G. Wurtz, A. V. Zayats, and C. C. Davis, “Digital resolution enhancement in surface plasmon microscopy,” Appl. Phys. B |

4. | B. Liedberg, C. Nylander, and I. Lundstrom, “Biosensing with surface plasmon resonance – how it all started,” Biosens. and Bioelectron. |

5. | F. Yu, S. Tian, D. Yao, and W. Knoll, “Surface plasmon enhanced diffraction for label-free biosensing,” Anal. Chem. |

6. | V. Shalaev and S. Kawata, |

7. | M. L. Brongersma and P. G. Kik, |

8. | L. Cao, N. C. Panoiu, and R. M. Osgood, “Surface second-harmonic generation from surface plasmon waves scattered by metallic nanostructures,” Phys. Rev. B |

9. | D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. |

10. | C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature |

11. | H. F. Schouten, N. V. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. |

12. | P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. |

13. | P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Approximate model for surface-plasmon generation at slit apertures,” J. Opt. Soc. Am. A |

14. | V. V. Temnov, U. Woggon, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon interferometry: measuring group velocity of surface plasmons,” Opt. Lett. |

15. | C. H. Gan, G. Gbur, and T. D. Visser, “Surface plasmons modulate the spatial coherence of light in Young’s interference experiment,” Phys. Rev. Lett. |

16. | N. V. Kuzmin, H. F. Schouten, G. Gbur, G. W. ’t Hooft, E. R. Eliel, and T. D. Visser, “Enhancement of spatial coherence by surface plasmons,” Opt. Lett. |

17. | 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. |

18. | C. Bohren and F. Huffman, “Absorption and scattering of light by small particles,” (Wiley, 1983). |

19. | A. E. Siegman, |

20. | J. J. Scherer, J. B. Paul, A. O’Keefe, and R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. |

21. | E. D. Palik, ed., |

22. | H. Raether, |

23. | M. Z. Alam, J. Meier, J. S. Aitchison, and M. Mojahedi, “Gain assisted surface plasmon polariton in quantum wells structures,” Opt. Exp. |

24. | J. C. Diels and W. Rudolph, |

25. | M. Galli, F. Marabelli, and G. Guizzetti, “Direct measurement of refractive-index dispersion of transparent media by white-light interferometry,” Appl. Opt. |

26. | M. Bai, C. Guerrero, S. Ioanid, E. Paz, M. Sanz, and N. Garcia, “Measuring the speed of a surface plasmon,” Phys. Rev. B |

27. | R. F. Wallis, A. A. Maradudin, and G. I. Stegeman, “Surface polariton reflection and radiation at end faces,” Appl. Phys. Lett. |

28. | A. Bouhelier, T. Huser, H. Tamaru, H. J. Güntherodt, D. W. Pohl, F. I. Baida, and D. V. Labeke, “Plasmon optics of structured silver films,” Phys. Rev. B |

29. | J. Seidel, S. Grafström, L. Eng, and L. Bischoff, “Surface plasmon transmission across narrow grooves in thin silver films,” Appl. Phys. Lett. |

30. | T. Okamoto, K. Kakutani, T. Yoshizaki, M. Haraguchi, and M. Fukui, “Experimental evaluation of reflectance of surface plasmon polariton at metal step barrier,” Surf. Sci. |

31. | F. Lopez-Tejeira, F. J. Garcia-Vidal, and L. Martin-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B |

32. | M. U. Gonzalez, J. C. Weeber, A. L. Baudrion, A. Dereux, A. L. Stepanov, J. R. K. E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors,” Phys. Rev. B |

33. | O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, “On the phase of plasmons excited by slits in a metal film,” Opt. Exp. |

34. | M. Born and E. Wolf, |

35. | U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. |

36. | R. H. J. Kop and R. Sprik, “Phase-sensitive interferometry with ultrashort optical pulses,” Rev. Sci. Instrum. |

37. | A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface-plasmon polaritons,” Phys. Rep. |

**OCIS Codes**

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(140.4780) Lasers and laser optics : Optical resonators

(240.6680) Optics at surfaces : Surface plasmons

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: July 25, 2007

Revised Manuscript: September 28, 2007

Manuscript Accepted: October 1, 2007

Published: October 4, 2007

**Citation**

Ni. V. Kuzmin, P. F. Alkemade, G. W. 't Hooft, and E. r. Eliel, "Bouncing surface plasmons," Opt. Express **15**, 13757-13767 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-21-13757

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