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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 7 — Apr. 2, 2007
  • pp: 4253–4267
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Optical near-field excitations on plasmonic nanoparticle-based structures

S. Foteinopoulou, J. P. Vigneron, and C. Vandenbem  »View Author Affiliations


Optics Express, Vol. 15, Issue 7, pp. 4253-4267 (2007)
http://dx.doi.org/10.1364/OE.15.004253


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Abstract

We investigate optical excitations on single silver nanospheres and nanosphere composites with the Finite Difference Time Domain (FDTD) method. Our objective is to achieve polarization control of the enhanced local field, pertinent to SERS applications. We employ dimer and quadrumer structures, which can display broadband and highly confined near-field-intensity enhancement comparable to or exceeding the resonant value of smaller sized isolated spheres. Our results demonstrate that the polarization of the enhanced field can be controlled by the orientation of the multimers in respect to the illumination, rather than the illumination itself. In particular, we report cases where the enhanced field shares the same polarization with the exciting field, and cases where it is predominantly perpendicular to the source field. We call the later phenomenon depolarized enhancement. Furthermore, we study a realizable nanolens based on a tapered self-similar silver nanosphere array. The time evolution of the fields in such structures show conversion of a diffraction limited Gaussian beam to a focused spot, through sequential coupling of the nano-array spheres’ Mie-plasmons. For a longitudinally excited nanolens design we observed the formation of an isolated focus with size about one tenth the vacuum wavelength. We believe such nanolens will aid scanning near-field optical microscopy (SNOM) detection and the excitation of surface plasmon based guiding devices.

© 2007 Optical Society of America

1. Introduction

Undoubtedly, metal nanoparticles will play a leading role in the rapidly developing fields of nanoscience and technology. While, Mie theory describes efficiently the scattering of a plane wave source by a single metal sphere, it becomes highly complex and maybe inappropriate for large number of particles, for particles with non-spherical shape in arbitrary arrangement, and for realistic or multiple excitation sources. Consequently, it becomes important to be able to study electromagnetic excitations on metallic particles by means of a numerical method. The Finite Difference Time domain (FDTD) method [12

12. A. Taflove and S. C. Hagness, Computational Electrodynamics, 2nd ed. (Artech House, Norwood, MA).

] is a prominent technique in electromagnetics research and has led to the observation of many novel phenomena in resonator structures [12

12. A. Taflove and S. C. Hagness, Computational Electrodynamics, 2nd ed. (Artech House, Norwood, MA).

], photonic crystals [13

13. J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals, Molding the Flow of Light. (Princeton Univ. Press, Princeton N. J., 1995).

, 14

14. S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, “Refraction in media with a negative refractive index,” Phys. Rev. Lett. 90,107402 (2003). [CrossRef] [PubMed]

, 15

15. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65,201104 (2002). [CrossRef]

] and negative index metamaterials [16

16. R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64,056625 (2001). [CrossRef]

]. Recently, this method has been also employed for the study of metallic nanostructures, such as silver nanoshells or nanoshell dimers [17

17. C. Oubre and P. Nordlander, “Finite-difference time-domain studies of the optical properties of nanoshell dimers,” J. Phys. Chem. B 109,10042–10051 (2005). [CrossRef]

, 18

18. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridizaton in nanoparticle dimers,” Nano Lett. 4,899–903 (2004). [CrossRef]

], plasmonic nanoguides [6

6. S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67,205402 (2003). [CrossRef]

, 19

19. P. B. Catrysse, H. Shin, and S. H. Fan, “Propagating modes in subwavelength cylindrical holes,” J. Vac. Sci. Technol. B 23,2675–2678 (2005). [CrossRef]

] and plasmonic super-lenses [20

20. H. Shin and S. H. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96,073907 (2006). [CrossRef] [PubMed]

, 21

21. P. G. Kik, S. A. Maier, and H. A. Atwater, “Image resolution of surface-plasmon-mediated near-field focusing with planar metal films in three dimensions using finite-linewidth dipole sources,” Phys. Rev. B 69,045418 (2004). [CrossRef]

]. Challener et al. [22

22. W. Challener, I. Sendur, and C. Peng, “Scattered field formulation of finite difference time domain for a focused light beam in dense media with lossy materials,” Opt. Express 11,3160–3170 (2003).http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-23-3160. [CrossRef] [PubMed]

] investigated solid spherical silver particles with the FDTD technique and made a comparison with the respective Mie theory. Nevertheless, their study focused only on specific cases, involving either off-resonance near-fields or larger sub-micron sized particles. However, many of the aforementioned applications can benefit from the high-field values present in the vicinity of metallic nanosized particles, when excited on-resonance. Mie resonances for smaller sized metallic spheres typically have smaller linewidth and thus larger quality factors. This implies, that these cases would be comparatively intricate to model numerically [23

23. S. Foteinopoulou and C. M. Soukoulis, “Theoretical investigation of one-dimensional cavities in two-dimensional photonic crystals,” IEEE J. Quantum Electron. 38,844–849 (2002). [CrossRef]

]. Accordingly, it is rather important to briefly review the validity and limitations of the FDTD method for such cases by comparison with rigorous Mie calculations [1

1. R. Ruppin, “Spherical and cylindrical surface polaritons in solids,” in Electromagnetic Surface Modes, pp.345–398(John Wiley & Sons, Belfast, 1982).

, 24

24. G. Mie, “Beitrage zur optik trüber medien, spellzien kolloïdaler metallosungen,” Ann. Physik 25,377 (1908). [CrossRef]

, 25

25. M. Born and E. Wolf, Principles of Optics, 2nd ed. (Macmillan Co., New-York1964).

]. In this way, one can evaluate the applicability of this numerical approach to other more complicated nanoparticle-based structures.

We present an outline of the FDTD method used in all the simulations in Sec. 2. To ascertain the suitability of the FDTD method we model in Sec. 3 different silver spheres with radii ranging from 25nm-75nm, and compare the near field enhancement spectrum, and snapshots of the field distribution with Mie-theory calculations [25

25. M. Born and E. Wolf, Principles of Optics, 2nd ed. (Macmillan Co., New-York1964).

]. Subsequently, we explore the possibility to manipulate the polarization of the enhanced local field. We consider dimers and quadrumer structure under different illumination and orientations and present our results and conclusions in Sec. 4. Afterward, we research self-similar nanosphere arrays and find that these can convert a diffraction-limited Gaussian beam into a subwavelength focus with size ~ λ0/10, with λ0 being the vacuum wavelength. We demonstrate two different types of nanolens designs in Sec. 5. Lastly, we present our conclusions in Sec. 6.

2. The Finite difference time domain method in plasmonic structures

Typically, the FDTD technique relies on the solution of Maxwell’s equation on a staggered grid lattice with leapfrog stepping in time (Yee algorithm [12

12. A. Taflove and S. C. Hagness, Computational Electrodynamics, 2nd ed. (Artech House, Norwood, MA).

, 26

26. K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, FL, 1993).

]). Although this method can incorporate trivially any dielectric medium, the same is not true for a dispersive material, because of the frequency dependence of the dielectric permittivity. Different schemes have been adopted thus far to handle dispersive materials in FDTD [12

12. A. Taflove and S. C. Hagness, Computational Electrodynamics, 2nd ed. (Artech House, Norwood, MA).

, 27

27. J. L. Young and R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag. 43,61–77 (2001). [CrossRef]

]. We employ in this work the Auxiliary Differential Equation (ADE) method [12

12. A. Taflove and S. C. Hagness, Computational Electrodynamics, 2nd ed. (Artech House, Norwood, MA).

, 27

27. J. L. Young and R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag. 43,61–77 (2001). [CrossRef]

, 28

28. S. A. Cummer, “An analysis of new and existing FDTD methods for isotropic cold plasma and a method for improving their accuracy,” IEEE Trans. Antennas Propag. 45,392–400 (1997). [CrossRef]

]. The later scheme dependents on the particular material dispersion relation, but is much more efficient in memory requirements in comparison with recursive convolution methods [27

27. J. L. Young and R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag. 43,61–77 (2001). [CrossRef]

]. We use the Drude model, to represent the dispersive dielectric response , ε(ω), of the silver particles–i.e.,

ε(ω)=εωp2ω(ω+iΓD).
(1)

The Drude model parameters in Eq. (1), namely the core dielectric constant, ε, plasma frequency, ω, and the intrinsic damping parameter, ΓD, are obtained by fitting on the Johnson and Christy [29

29. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6,4370–4379 (1972). [CrossRef]

] optical bulk experimental data for the frequency region of interest. Thus, we obtain ε = 4.785, ωp = 14.385 ∙ 1015 rad/sec, and ΓD = 7.95 ∙ 1013 rad/sec.

The ADE method in dispersive media, relies on the Fourier transform of an associated polarization current,

JP=ε0χe(ω)E(ω),
(2)

with ε0 being the vacuum permittivity, from frequency to time domain. In our case, χe(ω) represents the electric susceptibility of the Drude medium. Then for propagation inside a Drude-material domain the relevant Eqs. are [27, 28]:

tE=1ε0ε(×HJP)
(3)

and

tJP+ΓDJP=ε0ωp2E.
(4)

Equations (3) and (4) along with the third of Maxwell’s equations (Ampere’s law) are dis-cretized on a three dimensional (3D) staggered grid lattice according to the Yee-algorithm. The resulting numerical scheme provides the evolution in space and time of the fields in the dispersive part of the computational domain. We alert the reader at this point regarding the sign convention in Eq. (2). It corresponds to fields varying in time with exp(-jωt), and requires a positive sign for ΓD. All relevant signs should be modified accordingly, when fields vary in time as exp(jωt). We note, just like in FDTD modeling of dielectric structures, the computational domain is terminated with an absorbing boundary, to avoid any spurious back-reflections. In all the calculations that will be presented in the following, the silver nanoparticles are embedded in a glass matrix with refractive index, n, equal to 1.60. We therefore adopt a modified MUR absorbing boundary[12

12. A. Taflove and S. C. Hagness, Computational Electrodynamics, 2nd ed. (Artech House, Norwood, MA).

] based on an Enquist-Majda equation[12

12. A. Taflove and S. C. Hagness, Computational Electrodynamics, 2nd ed. (Artech House, Norwood, MA).

] for a phase velocity equal to c/n, – with c being the velocity of light.

3. FDTD modeling of single silver spheres: Comparison with Mie theory

Fig. 1. Spectral response of the normalized near-field enhancement at the center of the nanoparticle. The plane of illumination and polarization of the source are shown in the upper panel. The dotted lines represent the FDTD results, while the solid lines the corresponding Mie calculations. The solid circles represent Mie calculations, where the actual tabulated Johnson and Christy data [29] are used for the dielectric function of silver. In the inset, we also show the on-resonance field distribution for two different nanoparticle sizes, –with radius 25 nm and 50 nm respectively– as indicated with the arrows.

We study the electromagnetic excitations on a single silver spherical particle with radius ranging from 25nm to 75nm, embedded in a glass medium. For this purpose, we perform FDTD simulations and will compare the results with corresponding Mie theory [25

25. M. Born and E. Wolf, Principles of Optics, 2nd ed. (Macmillan Co., New-York1964).

]. We adopt a cubic Yee cell with a side equal to 1 nm, and a time step dt=1.54∙10-18 sec, bounded by the Courant condition [12

12. A. Taflove and S. C. Hagness, Computational Electrodynamics, 2nd ed. (Artech House, Norwood, MA).

, 27

27. J. L. Young and R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag. 43,61–77 (2001). [CrossRef]

]. The particle is illuminated with a source with a Gaussian profile on the xy plane and electric field polarized along the x-direction, as indicated in the upper part of Fig. 1. A wide beam waist is chosen to emulate a plane wave propagating along the z-direction.

We concentrate on the near-field enhancement in the center of the nanoparticles. For this calculation we launch a pulsed signal in time, with central vacuum wavelength, λ0= 476.2 nm and width, σt= 1.395 λ0/c, in order to span the frequency area around the first Mie resonance of the silver nanospheres. Subsequently, we observe the evolution of the x-component of the electric field in the center of the particle, and apply a Fast Fourier Transform (FFT) [30

30. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge University, Cambridge, 1989).

] on the respective time series. This procedure yields the spectral dependence for the magnitude of the x-component of the electric field. The later quantity is normalized appropriately with the help of a second simulation run without the silver particle. We note at this point, it suffices to examine only the electric field parallel to the incident polarization, because at the center of the silver sphere the other electric field components are zero (or negligible in the FDTD). In this manner, we acquire the respective near-field enhancement at the silver sphere center, which is shown versus the free space wavelength with the dotted lines in Fig. 1. The solid lines represent the corresponding Mie calculations, when the Drude model [Eq. (1)] is used to describe the silver permittivity function. For comparison, we also show the expected Mie result of the enhancement when the actual values from the Johnson and Christy [29

29. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6,4370–4379 (1972). [CrossRef]

] tabulated data are used for the dielectric function of silver.

Figure 1 attests an excellent agreement for the resonant wavelength of the near-field enhancement spectrum between Mie theory and the FDTD. We also observe generally a very good agreement for the corresponding peak height. We notice, that the FDTD peak-heights are consistently a little lower than the respective Mie theory ones. This small difference, which is more pronounced for the smaller particles, is caused by the staircase that approximates the spherical surface of the nanoparticle in the Cartesian numerical grid. It is not surprising that this staircase effect is stronger for the smaller spheres. We see these are characterized by a relatively higher-quality-factor resonance, which would be more sensitive to structural and simulation parameters [23

23. S. Foteinopoulou and C. M. Soukoulis, “Theoretical investigation of one-dimensional cavities in two-dimensional photonic crystals,” IEEE J. Quantum Electron. 38,844–849 (2002). [CrossRef]

]. It is expected, that small imperfections in the surface of experimentally realizable nanoparticles could lead to a similar type of effect. For the same reason, for small to moderate particle sizes (radius ranging between 25 nm and 50 nm), frequencies approaching the second Mie resonance should be avoided. As these typically involve a large quality factor, they would pose much higher demands in spatial discretization and consequently in cpu memory requirements. Put it differently, the proper mesh size in FDTD modeling of metallic nanoparticles is dictated not only by the relevant frequency but also by the quality factor of their characteristic resonances.

We also compared the snapshots of the electric field, for the silver spheres of different sizes. These are sampled at a certain moment after steady state is reached. In each case the nanoparticle is excited with a quasi-monochromatic wave [14

14. S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, “Refraction in media with a negative refractive index,” Phys. Rev. Lett. 90,107402 (2003). [CrossRef] [PubMed]

], with frequency set to be close to the respective Mie-resonance. We depict the x-component of the electric field, on the xy plane in the inset of Fig. 1, for two characteristic sphere sizes. The left panel displays the results from FDTD, while the right panel the results from Mie theory [25

25. M. Born and E. Wolf, Principles of Optics, 2nd ed. (Macmillan Co., New-York1964).

]. In order to make the comparison between FDTD and Mie theory, a phase factor multiplies the Mie calculated fields. In this way, the two fields (from FDTD and Mie theory) are compared at the same time instant of the full periodic cycle. We observe an excellent agreement in the electric field patterns, especially for the larger particle sizes.

Accordingly, we reviewed the parameters and restrictions for the reliable modeling of silver nanospheres by the FDTD technique. We will use these particles as the fundamental building blocks to construct composite structures which can exhibit new interesting phenomena, such as polarization selective enhancement and nano-lensing. Verification of this type of phenomena with an ab-initio method, like the FDTD, is of outmost important. Since the retardation effects of the EM field are taken into account, the calculated results provide solid grounds for the possibility of realization of the reported phenomena.

4. Field enhancement in multimer nanosphere-based configurations

Therefore, we utilize multimers comprising of silver spheres with radius equal to 50 nm, and investigate whether such structures can produce an enhancement which is comparable to that of a smaller sphere with 25 nm radius. We note in passing, that other works have explored the possibility of achieving high enhancement with dimer configurations of nanorods [32

32. J. Kottmann and O. Martin, “Plasmon resonant coupling in metallic nanowires,” Opt. Express 8,655–663 (2001).http://www.opticsinfobase.org/abstract.cfm?URI=oe-8-12-655. [CrossRef] [PubMed]

, 34

34. J. P. Kottman and O.J.F. Martin, “Retardation-induced plasmon resonances in coupled nanoparticles,” Opt. Lett. 26,1096 (2001). [CrossRef]

] or nanospheres [33

33. H. Xu, E. J. Bjerneld, M. Kall, and L. Borjensson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman Scattering,” Phs. Rev. Lett. 21,4357–4360 (1999). [CrossRef]

, 35

35. E. Hao and Schatz G. C., “Electromagnetic fields around silver nanoparticles and dimers,” J. Chem. Phys. 120,357 (2004). [CrossRef] [PubMed]

]. Nevertheless, polarization manipulation of the enhanced field is not discussed in any of the aforementioned works. In our subsequent study we explore the conditions of illumination, as well as the configuration and orientation of the silver sphere multimers that would lead to an enhancement with controlled polarization. We concentrate on the frequency range between 480nm and 1400nm, where Mie theory and FDTD show a very good agreement for the near field surrounding a 50 nm-radius silver sphere. In order to span this frequency region two different pulsed measurements,– centered at λ 0 = 909.1 nm, and λ 0 = 588.3 nm respectively–, are performed in the FDTD simulation. The spectra are always obtained with FFT [30

30. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge University, Cambridge, 1989).

], from the time sequence representing the evolution of the electric field at a certain detector point. We stress, that whenever we refer to near-field intensity enhancement in this section, we mean the intensity of the electric field normalized by its respective value in the absence of the metallic nanoparticles.

Fig. 2. Spectral response of the near field intensity enhancement in the vicinity of touching dimers. The top panel indicates the position of the detectors where the field is monitored. The vertical axis represents the z direction, i.e. the illumination direction for case (a) and the y-direction, i.e., the normal to both the illumination direction and exciting field polarization, for case (b). The color of the plotted lines matches the color of the specified detector.

We also calculate the intensity enhancement in the entire 3D space for selected frequencies. For this purpose, we excite the touching dimer with a quasi-monochromatic Gaussian source at a certain free space wavelength, λ 0. The illumination conditions are otherwise the same as in Fig. 2. In each case, two simulations runs are necessary to obtain the intensity enhancement, I. Specifically,

I(x,y,z)=12ε0εglasst0t0+TEx2(x,y,z,t)+Ey2(x,y,z,t)+Ez2(x,y,z,t)12ε0εglasst0t0+TE0x2(x,y,z,t)+E0y2(x,y,z,t)+E0z2(x,y,z,t),
(5)

where, ε 0 is the vacuum permittivity and εglass is the relative permittivity of glass. The summation yielding the time-averaged value of the intensity starts at time t 0, after steady state is reached, and completes after an entire cycle of period, T. The denominator represents the time averaged intensity obtained in a run without the presence of the dimers,- needed for normalization. We illustrate the intensity enhancement distribution both on an xy plane cutting through the middle of the dimers (top panel of Fig. 3), and in the entire 3D space (middle panel of Fig. 3). The excitations wavelengths we have selected correspond to the two peaks of Fig. 2, - at 1136 nm and 625 nm respectively-, and the in-between valley, at 833 nm. The 3D plots depicted in the middle panel for the same wavelengths are iso-intensity plots. The green surfaces, enclose the space in the outer neighborhood of the dimers where the normalized intensity enhancement exceeds the value of 10. Conversely, the red surfaces enclose the space in the outer part of the dimers where the normalized intensity enhancement exceeds the value of 100. It is interesting to observe, that in all cases the interstitial region between the two spheres is characterized by a high enhancement factor. However, the area this enhancement covers is quite larger for the wavelengths corresponding to the peaks of the spectrum, and especially for case with λ 0 = 1136 nm. For comparison, we also plot the intensity enhancement for a silver nanosphere with 25 nm radius, as calculated from Mie theory, in the bottom panel of Fig. 3. The left-bottom graph represents an excitation on-resonance, while the other two adjacent graphs represent red-shifted excitation wavelengths away from the resonance. For the single 25nm-radius silver particle, we observe a significant enhancement only for the resonant wavelength. Even the later though, does not surpass the enhancement values we found in the dimers comprising of the larger spheres. Evidently, single particles exhibit rather a frequency selective enhancement while dimers produce a more broadband response.

Fig. 3. Normalized time averaged intensity plots for three different excitation wavelengths: λ 0=1136 nm (left panel), 833 nm (middle panel) and 625 nm (right panel). In each case we see the intensity on the xy- plane slicing through the middle of the dimer, as well as in the entire 3D space. The 3D plots display two iso-intensity surfaces, representing an enhancement value of 100 (red) and 10 (green) respectively. For comparison in the bottom panel we show the intensity enhancement around a single silver sphere with 25 nm radius, on and off- resonance
Fig. 4. Intensity enhancement for a dimer illuminated as shown in the upper schematics, at the indicated detector point. The contributions of the different components of the electric field to the total intensity enhancement are shown separately. It is clear, the predominant contribution comes from the field along the wave vector (orange vector), which is perpendicular to the illumination plane. In other words, the enhanced field became orthogonal to the driving field. Thus, we observed a depolarized enhancement phenomenon.

We flip now the dimer and orient it’s axis along the y-direction, i.e. perpendicularly to both the polarization of the incident field and it’s wave vector, k. In this configuration we did not observe any significant intensity enhancement. We rotate once more the dimer and make it parallel to the wave vector of the driving field, and witness a rather striking effect. While the electric field parallel to the exciting field is weak, the electric field along the illumination direction, z-, is very strong. In other words, the enhanced fields are “almost” completely depolarized in respect to the incident fields. This can be seen in Fig. 4, where we plot the spectral response of the different field components sampled at the point indicated in the upper panel. The solid black, dashed red, and solid green curves represent the contributions to the intensity enhancement corresponding to the x-, y- and z- component of the electric field respectively. In logarithmic scale we see that the contribution from the z- component of the electric field is almost two orders of magnitude more than the contribution from the x- component and more than seven orders of magnitude more than the contribution from the y-component.

Fig. 5. Iso-surfaces representing an intensity enhancement value of 100 (red) and 10 (green) for quadrumers lying on the illuminating plane (top panel), or normally to the illuminating plane (bottom panel). We show the total enhancement [left: in (a) and (c)] and the enhancement corresponding to the major contributing field component, which is along x for case (b) and along z for case (d).

As dimers lead to a larger enhancement than the one stemming from the constituent spheres, it becomes an obvious choice to also explore configurations with more particles. For this reason, we considered touching quadrumers, for different orientations in respect to the illuminating field. We did not find an increased enhancement and overall their behavior is somewhat similar to that of the dimers. This is not surprising, as the high-field values seem confined in the two-sphere interstitial region. In other words, quadrumers act like two non-interacting dimers put together. It is not obvious to determine which are the parting dimers, as this depends on the particular illumination conditions. In the quadrumer structures we also found cases with polarized and depolarized enhancement. We show two such examples in Fig. 5. In the top panel the quadrumer lies on the plane of illumination (xy-plane). In the bottom panel the quadrumers lie on the yz plane and are thus perpendicular to the polarization of the incident source. To evaluate the quality of the polarized or depolarized enhancement we show the iso-intensity surfaces, both for the total intensity (left-panel) and only the contribution from the predominant field component (right-panel). The predominant field component is along the field of the incident source for the case of the quadrumers lying on the xy-plane, i.e. we have polarized enhancement. Conversely, the predominant field component is along the wave vector of the incident source for the case of the quadrumers lying on the yz-plane, i.e. we have depolarized enhancement. Notice the remarkable agreement between the predominant and total intensity enhancement for the case of polarized enhancement [Figs. 5 (a) and 5(b)]. For the yz-quadrumer configuration we find almost complete depolarization in the interstitial region, but we observe some enhancement in the outer sphere region coming from fields parallel to the incident source. The later intensities are though by far smaller than the values in the interstitial regions. This means that for practical purposes we can say that the enhancement is depolarized in such a case.

Fig. 6. Outline of different cases studied in this section. The spectral response as well as the type of enhancement, - polarized or depolarized-, is briefly described for each case.

We outline all cases that we studied for dimers and quadrumers in Fig. 6. We always kept the illuminating plane to be the xy plane, yielding a propagating wave with wave vector along z. The polarization of the incident source is along the x-axis. Then, the dimer and quadrumer structures are rotated in different ways, to encompass all possible relations between their orientation and illumination. The peaks of their spectral response are determined from several detectors placed in the vicinity of the contact points. From Fig. 6 we deduce that enhancement occurs when the nano-composite has a structural direction either along the incident field, or along the wave vector of the incident field. Hence, we observe field enhancement with quadrumers for any conditions, and no enhancement for dimers along the y-direction. We get depolarized enhancement if the nano-particle composite has no structural direction along the direction of the illuminating field. Otherwise, the enhancement is mostly highly polarized, especially if in addition the nano-composite does not also share a structural direction with the direction of the incident field wave vector. Moreover we found that a really broadband enhancement, – beginning from the near-infrared all the way to the visible–, occurs for the arrangements that have a structural direction along the driving electric field (E). To resume, we have found a way to predict and control the polarization of the enhanced local field, which can be a key factor for SERS based detection methods [31

31. P. G. Etchegoin, C. Galloway, and E. C. Le Ru, “Polarization-depedent effects in surface-enhanced Raman scattering (SERS),” Phys. Chem. Chem. Phys. 8,2624–2628 (2006). [CrossRef] [PubMed]

].

We note in passing, that non-local effects [38

38. R. Fuchs and F. Claro, “Multipolar response of small metallic spheres: Nonlocal Theory,” Phys. Rev. B 35,3722 (1987). [CrossRef]

] have not been taken into account in the calculations. The latter may impact the enhancement factors of the cases with a dimer or quadrumer axis along the incident field. However, we do not expect these would affect our conclusions regarding the polarization dependence of the local enhanced field, on the specific relations between structure orientation and illuminating field. Actually, we checked that these conclusions survive even for a small (2 nm) interparticle distance where it is known that non-local effects are really minor [35

35. E. Hao and Schatz G. C., “Electromagnetic fields around silver nanoparticles and dimers,” J. Chem. Phys. 120,357 (2004). [CrossRef] [PubMed]

].

5. Nanoparticle based lens

Fig. 7. (a). (1.55 MB) Self-similar silver nanosphere array acting as a nanolens. A Gaussian source polarized perpendicularly to the array axis is converted into foci with spot size about one tenth the vacuum wavelength, λ 0. [Media 1] (b) The time averaged intensity in source (black lines) and focus plane (red lines). The dotted lines represent the total intensity, while the solid lines represent the contribution from the component of the field parallel to the incident source polarization.

Indeed, the self-similar nanosphere array of Fig. 7 does exhibit an interesting conversion of a diffraction limited Gaussian beam into two subwavelength foci, thus acting as a nanolens. We attribute this effect to a near-field interaction between the Mie plasmons of the individual particles. Despite the interesting nature of this phenomenon, there is a certain disadvantage to this design. Due to the location of the foci in the array, it is rather hard to use them subsequently to excite a plasmonic device [6

6. S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67,205402 (2003). [CrossRef]

, 40

40. A. Karalis, E. Lidorikis,, M. Ibanescu, J. D. Joannopoulos, and M. Soljacic, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95,063901 (2005). [CrossRef] [PubMed]

, 41

41. P. B. Catrysse, G. Veronis, H. Shin, J. T. Shen, and S. Fan, “Guided modes supported by plasmonic films with a periodic arrangement of subwavelength slits,” Appl. Phys. Lett. 88,031101 (2006). [CrossRef]

, 42

42. R. Zia, M. D. Selker, and M. L. Brongersma, “Leaky and bound modes of surface plasmon waveguides,” Phys. Rev. B 71,165431 (2005). [CrossRef]

] or as a source for subwavelength lithographic patterning [45

45. F. Dhili, R. Bachelot, A. Rumyantseva, G. Lerondel, and P. Royer, “Nanoparticle photosensitive polymers using local field enhancement at the end of apertureless SNOM tips,” J. Microsc. 209,214–222 (2003). [CrossRef]

]. Therefore, in the following we investigate for an alternative nanolens design, which would lead to a subwavelength focus in a more functional location for these type of applications.

Fig. 8. (a). (2.064 MB) Another design of a self-similar-silver-nanosphere-array nanolens. A Gaussian source polarized parallelly to the array axis is converted into a subwavelength focus with size of the order of one tenth the vacuum wavelength, λ 0. [Media 2] (b) The time averaged intensity in source (black lines) and focus (red lines) plane are also shown. The dotted lines represent the total intensity, while the solid lines represent the contribution from the component of the field parallel to the incident source polarization.

6. Conclusions

Acknowledgments

References and links

1.

R. Ruppin, “Spherical and cylindrical surface polaritons in solids,” in Electromagnetic Surface Modes, pp.345–398(John Wiley & Sons, Belfast, 1982).

2.

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82,257–259 (2003). [CrossRef]

3.

S. Schultz, D. R. Smith, J. J. Mock, and David A. Schultz,“Single-target molecule detection with nonbleaching multicolor immunolabels,” Proc. Nat. Acad. Sci. 97,996–1001 (2000). [CrossRef] [PubMed]

4.

T. D. Corrigan, S. H. Guo, H. Szmacinski, and R. J. Phaneuf, “Systematic study of the size and spacing dependence of Ag nanoparticle enhanced fluorescence using electron-beam lithography,” Appl. Phys. Lett. 88,101112 (2006). [CrossRef]

5.

K. Aslan, Z. Leonenko, J. R. Lakowicz, and C. D. Geddes, “Annealed silver-island films for applications in metal-enhanced fluorescence: Interpretation in terms of radiating plasmons,” J. Fluoresc. 15,643–654 (2005). [CrossRef] [PubMed]

6.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67,205402 (2003). [CrossRef]

7.

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. 23,1331–1333 (1998). [CrossRef]

8.

C. Girard and R. Quidant, “Nearfield optical transmittance of metal particle chain waveguides,” Opt. Express 12,6141–6146 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-25-6141. [CrossRef] [PubMed]

9.

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold Particle as a probe for apertureless SNOM,” J. Microsc. 202,72–76 (2001). [CrossRef] [PubMed]

10.

A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14,1557–1567 (2006).http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-4-1557. [CrossRef] [PubMed]

11.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature (London) 438,335–338 (2005). [CrossRef]

12.

A. Taflove and S. C. Hagness, Computational Electrodynamics, 2nd ed. (Artech House, Norwood, MA).

13.

J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals, Molding the Flow of Light. (Princeton Univ. Press, Princeton N. J., 1995).

14.

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, “Refraction in media with a negative refractive index,” Phys. Rev. Lett. 90,107402 (2003). [CrossRef] [PubMed]

15.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65,201104 (2002). [CrossRef]

16.

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64,056625 (2001). [CrossRef]

17.

C. Oubre and P. Nordlander, “Finite-difference time-domain studies of the optical properties of nanoshell dimers,” J. Phys. Chem. B 109,10042–10051 (2005). [CrossRef]

18.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridizaton in nanoparticle dimers,” Nano Lett. 4,899–903 (2004). [CrossRef]

19.

P. B. Catrysse, H. Shin, and S. H. Fan, “Propagating modes in subwavelength cylindrical holes,” J. Vac. Sci. Technol. B 23,2675–2678 (2005). [CrossRef]

20.

H. Shin and S. H. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96,073907 (2006). [CrossRef] [PubMed]

21.

P. G. Kik, S. A. Maier, and H. A. Atwater, “Image resolution of surface-plasmon-mediated near-field focusing with planar metal films in three dimensions using finite-linewidth dipole sources,” Phys. Rev. B 69,045418 (2004). [CrossRef]

22.

W. Challener, I. Sendur, and C. Peng, “Scattered field formulation of finite difference time domain for a focused light beam in dense media with lossy materials,” Opt. Express 11,3160–3170 (2003).http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-23-3160. [CrossRef] [PubMed]

23.

S. Foteinopoulou and C. M. Soukoulis, “Theoretical investigation of one-dimensional cavities in two-dimensional photonic crystals,” IEEE J. Quantum Electron. 38,844–849 (2002). [CrossRef]

24.

G. Mie, “Beitrage zur optik trüber medien, spellzien kolloïdaler metallosungen,” Ann. Physik 25,377 (1908). [CrossRef]

25.

M. Born and E. Wolf, Principles of Optics, 2nd ed. (Macmillan Co., New-York1964).

26.

K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, FL, 1993).

27.

J. L. Young and R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag. 43,61–77 (2001). [CrossRef]

28.

S. A. Cummer, “An analysis of new and existing FDTD methods for isotropic cold plasma and a method for improving their accuracy,” IEEE Trans. Antennas Propag. 45,392–400 (1997). [CrossRef]

29.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6,4370–4379 (1972). [CrossRef]

30.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge University, Cambridge, 1989).

31.

P. G. Etchegoin, C. Galloway, and E. C. Le Ru, “Polarization-depedent effects in surface-enhanced Raman scattering (SERS),” Phys. Chem. Chem. Phys. 8,2624–2628 (2006). [CrossRef] [PubMed]

32.

J. Kottmann and O. Martin, “Plasmon resonant coupling in metallic nanowires,” Opt. Express 8,655–663 (2001).http://www.opticsinfobase.org/abstract.cfm?URI=oe-8-12-655. [CrossRef] [PubMed]

33.

H. Xu, E. J. Bjerneld, M. Kall, and L. Borjensson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman Scattering,” Phs. Rev. Lett. 21,4357–4360 (1999). [CrossRef]

34.

J. P. Kottman and O.J.F. Martin, “Retardation-induced plasmon resonances in coupled nanoparticles,” Opt. Lett. 26,1096 (2001). [CrossRef]

35.

E. Hao and Schatz G. C., “Electromagnetic fields around silver nanoparticles and dimers,” J. Chem. Phys. 120,357 (2004). [CrossRef] [PubMed]

36.

S. Enoch, R. Quidant, and Goncal Badenes, “Optical sensing based on plasmon coupling in nanoparticle arrays,” Opt. Express 12,3422–3427 (2004).http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-15-3422. [CrossRef] [PubMed]

37.

I. Romero, J. Aizpurua, G. W. Bryant, and F.J.Garcia de Abajo, “Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers,” Opt. Express 14,9988–9999 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-9988. [CrossRef] [PubMed]

38.

R. Fuchs and F. Claro, “Multipolar response of small metallic spheres: Nonlocal Theory,” Phys. Rev. B 35,3722 (1987). [CrossRef]

39.

J. Kottmann, O. Martin, D. Smith, and S. Schultz, “Spectral response of plasmon resonant nanoparticles with a non-regular shape,” Opt. Express 6,213–219 (2000).http://www.opticsinfobase.org/abstract.cfm?URI=oe-6-11-213. [CrossRef] [PubMed]

40.

A. Karalis, E. Lidorikis,, M. Ibanescu, J. D. Joannopoulos, and M. Soljacic, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95,063901 (2005). [CrossRef] [PubMed]

41.

P. B. Catrysse, G. Veronis, H. Shin, J. T. Shen, and S. Fan, “Guided modes supported by plasmonic films with a periodic arrangement of subwavelength slits,” Appl. Phys. Lett. 88,031101 (2006). [CrossRef]

42.

R. Zia, M. D. Selker, and M. L. Brongersma, “Leaky and bound modes of surface plasmon waveguides,” Phys. Rev. B 71,165431 (2005). [CrossRef]

43.

K. Li, M. I. Stockman, and D. J. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett. 91,227402 (2003). [CrossRef] [PubMed]

44.

S. E. Sburlan, L. A. Blanco, and M. Nieto-Vesperinas, “Plasmon excitation in sets of nanoscale cylinders and spheres,” Phys. Rev. B 73,035403 (2006). [CrossRef]

45.

F. Dhili, R. Bachelot, A. Rumyantseva, G. Lerondel, and P. Royer, “Nanoparticle photosensitive polymers using local field enhancement at the end of apertureless SNOM tips,” J. Microsc. 209,214–222 (2003). [CrossRef]

46.

A. Hohenau, H. Ditlbacher, B. Lamprecht, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Electron beam lithography, a helpful tool for nanooptics,” in press Micro. Eng.

47.

R. Fikri, “Modelling of the apertureless near-field scanning optical microscope with the finite element method,” Ph. D. thesis, Université de Technologie de Troyes (2003).

48.

P. G. Kik, S. A. Maier, and H. A. Atwater, “Plasmon printing - a new approach to near-field lithography,” Mat. Res. Soc. Symp. Proc.705, Y3.6 (2002).

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.2110) Physical optics : Electromagnetic optics
(260.3910) Physical optics : Metal optics
(290.4020) Scattering : Mie theory
(290.5850) Scattering : Scattering, particles

ToC Category:
Optics at Surfaces

History
Original Manuscript: October 9, 2006
Revised Manuscript: February 19, 2007
Manuscript Accepted: March 20, 2007
Published: April 2, 2007

Virtual Issues
Vol. 2, Iss. 5 Virtual Journal for Biomedical Optics

Citation
S. Foteinopoulou, J. P. Vigneron, and C. Vandenbem, "Optical near-field excitations on plasmonic nanoparticle-based structures," Opt. Express 15, 4253-4267 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-7-4253


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. Ruppin, "Spherical and cylindrical surface polaritons in solids," in Electromagnetic Surface Modes, pp. 345-398 (John Wiley & Sons, Belfast, 1982).
  2. J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West and N. J. Halas, "Surface enhanced Raman effect via the nanoshell geometry," Appl. Phys. Lett. 82, 257-259 (2003). [CrossRef]
  3. S. Schultz, D. R. Smith, J. J. Mock, and DavidA. Schultz,"Single-target molecule detection with nonbleaching multicolor immunolabels," Proc. Nat. Acad. Sci. 97, 996-1001 (2000). [CrossRef] [PubMed]
  4. T. D. Corrigan, S. H. Guo, H. Szmacinski, and R. J. Phaneuf, "Systematic study of the size and spacing dependence of Ag nanoparticle enhanced fluorescence using electron-beam lithography," Appl. Phys. Lett. 88, 101112 (2006). [CrossRef]
  5. K. Aslan, Z. Leonenko, J. R. Lakowicz, and C. D. Geddes, "Annealed silver-island films for applications in metal-enhanced fluorescence: Interpretation in terms of radiating plasmons," J. Fluoresc. 15, 643-654 (2005). [CrossRef] [PubMed]
  6. S. A. Maier, P. G. Kik and H. A. Atwater, "Optical pulse propagation in metal nanoparticle chain waveguides," Phys. Rev. B 67, 205402 (2003). [CrossRef]
  7. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333 (1998). [CrossRef]
  8. C. Girard and R. Quidant, "Nearfield optical transmittance of metal particle chain waveguides," Opt. Express 12, 6141-6146 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-25-6141. [CrossRef] [PubMed]
  9. T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, "A single gold Particle as a probe for apertureless SNOM," J. Microsc. 202, 72-76 (2001). [CrossRef] [PubMed]
  10. A. Alù, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," Opt. Express 14, 1557-1567 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-4-1557. [CrossRef] [PubMed]
  11. A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature (London) 438, 335-338 (2005). [CrossRef]
  12. A. Taflove and S. C. Hagness, Computational Electrodynamics, 2nd ed. (Artech House, Norwood, MA).
  13. J.D. Joannopoulos, R.D. Meade and J.N. Winn, Photonic Crystals, Molding the Flow of Light. (Princeton Univ. Press, Princeton N. J., 1995).
  14. S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a negative refractive index," Phys. Rev. Lett. 90, 107402 (2003). [CrossRef] [PubMed]
  15. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002). [CrossRef]
  16. R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001). [CrossRef]
  17. C. Oubre and P. Nordlander, "Finite-difference time-domain studies of the optical properties of nanoshell dimers," J. Phys. Chem. B 109, 10042-10051 (2005). [CrossRef]
  18. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, "Plasmon hybridizaton in nanoparticle dimers," Nano Lett. 4, 899-903 (2004). [CrossRef]
  19. P. B. Catrysse, H. Shin, and S. H. Fan, "Propagating modes in subwavelength cylindrical holes," J. Vac. Sci. Technol. B 23, 2675-2678 (2005). [CrossRef]
  20. H. Shin and S. H. Fan, "All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure," Phys. Rev. Lett. 96, 073907 (2006). [CrossRef] [PubMed]
  21. P. G. Kik, S. A. Maier and H. A. Atwater, "Image resolution of surface-plasmon-mediated near-field focusing with planar metal films in three dimensions using finite-linewidth dipole sources," Phys. Rev. B 69, 045418 (2004). [CrossRef]
  22. W. Challener, I. Sendur, and C. Peng, "Scattered field formulation of finite difference time domain for a focused light beam in dense media with lossy materials," Opt. Express 11, 3160-3170 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-23-3160. [CrossRef] [PubMed]
  23. S. Foteinopoulou and C. M. Soukoulis, "Theoretical investigation of one-dimensional cavities in two-dimensional photonic crystals," IEEE J. Quantum Electron. 38, 844-849 (2002). [CrossRef]
  24. G. Mie, "Beitrage zur optik trüber medien, spellzien kolloïdaler metallosungen," Ann. Physik 25, 377 (1908). [CrossRef]
  25. M. Born and E. Wolf, Principles of Optics, 2nd ed. (Macmillan Co., New-York, 1964).
  26. K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, FL, 1993).
  27. J. L. Young and R. O. Nelson, "A summary and systematic analysis of FDTD algorithms for linearly dispersive media," IEEE Antennas Propag. Mag. 43, 61-77 (2001). [CrossRef]
  28. S. A. Cummer, "An analysis of new and existing FDTD methods for isotropic cold plasma and a method for improving their accuracy," IEEE Trans. Antennas Propag. 45, 392-400 (1997). [CrossRef]
  29. P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972). [CrossRef]
  30. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge University, Cambridge, 1989).
  31. P. G. Etchegoin, C. Galloway, and E. C. Le Ru, "Polarization-depedent effects in surface-enhanced Raman scattering (SERS)," Phys. Chem. Chem. Phys. 8, 2624-2628 (2006). [CrossRef] [PubMed]
  32. J. Kottmann and O. Martin, "Plasmon resonant coupling in metallic nanowires," Opt. Express 8, 655-663 (2001). http://www.opticsinfobase.org/abstract.cfm?URI=oe-8-12-655. [CrossRef] [PubMed]
  33. H. Xu, E. J. Bjerneld, M. Kall and L. Borjensson, "Spectroscopy of single hemoglobin molecules by surface enhanced Raman Scattering," Phs. Rev. Lett. 21, 4357-4360 (1999). [CrossRef]
  34. J. P. Kottman and O.J.F. Martin, "Retardation-induced plasmon resonances in coupled nanoparticles," Opt. Lett. 26, 1096 (2001). [CrossRef]
  35. E. Hao and G. C. Schatz, "Electromagnetic fields around silver nanoparticles and dimers," J. Chem. Phys. 120, 357 (2004). [CrossRef] [PubMed]
  36. 3. S. Enoch, R. Quidant and G. Badenes, "Optical sensing based on plasmon coupling in nanoparticle arrays," Opt. Express 12, 3422-3427 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-15-3422. [CrossRef] [PubMed]
  37. I. Romero, J. Aizpurua, G. W. Bryant and F.J. Garcia de Abajo, "Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers," Opt. Express 14, 9988-9999 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-9988. [CrossRef] [PubMed]
  38. R. Fuchs and F. Claro, "Multipolar response of small metallic spheres: Nonlocal Theory," Phys. Rev. B 35, 3722 (1987). [CrossRef]
  39. J. Kottmann, O. Martin, D. Smith, and S. Schultz, "Spectral response of plasmon resonant nanoparticles with a non-regular shape," Opt. Express 6, 213-219 (2000). http://www.opticsinfobase.org/abstract.cfm?URI=oe-6-11-213. [CrossRef] [PubMed]
  40. A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos and M. Soljacic, "Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air," Phys. Rev. Lett. 95, 063901 (2005). [CrossRef] [PubMed]
  41. P. B. Catrysse, G. Veronis, H. Shin, J. T. Shen, S. Fan, "Guided modes supported by plasmonic films with a periodic arrangement of subwavelength slits," Appl. Phys. Lett. 88, 031101 (2006). [CrossRef]
  42. R. Zia, M. D. Selker and M. L. Brongersma, "Leaky and bound modes of surface plasmon waveguides," Phys. Rev. B 71, 165431 (2005). [CrossRef]
  43. K. Li, M. I. Stockman, and D. J. Bergman, "Self-similar chain of metal nanospheres as an efficient nanolens," Phys. Rev. Lett. 91, 227402 (2003). [CrossRef] [PubMed]
  44. S. E. Sburlan, L. A. Blanco and M. Nieto-Vesperinas, "Plasmon excitation in sets of nanoscale cylinders and spheres," Phys. Rev. B 73, 035403 (2006). [CrossRef]
  45. F. Dhili, R. Bachelot, A. Rumyantseva, G. Lerondel, and P. Royer, "Nanoparticle photosensitive polymers using local field enhancement at the end of apertureless SNOM tips," J. Microsc. 209, 214-222 (2003). [CrossRef]
  46. A. Hohenau, H. Ditlbacher, B. Lamprecht, J. R. Krenn, A. Leitner and F. R. Aussenegg, "Electron beam lithography, a helpful tool for nanooptics," in press Micro. Eng.
  47. R. Fikri, "Modelling of the apertureless near-field scanning optical microscope with the finite element method," Ph. D. thesis, Universit de Technologie de Troyes (2003).
  48. P. G. Kik, S. A. Maier, and H. A. Atwater, "Plasmon printing - a new approach to near-field lithography," Mat. Res. Soc. Symp. Proc. 705, Y3.6 (2002).

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