Abstract

We demonstrate analytically and numerically that the detection of the spectral response of a single spherical Au nanoantenna allows one to map very small (down to 5·10−4 RIU) variations of the refractive index of an optically transparent sample. Spectral shift of the dipole local plasmon resonance wavelength of the nanoantenna and the spectral sensitivity of the method developed was estimated by using simple analytical quasi-static model. A pointed scanning probe based on fiber microaxicon with the Au spherical nanoantenna attached to its tip was proposed to realize the RI mapping method. Finite-difference time-domain numerical simulations of the spectral properties of the proposed probe are in good agreement with the theoretical quasi-electrostatic estimations for a radius of the nanoantenna not exceeding the skin depth of Au.

© 2014 Optical Society of America

1. Introduction

The state-of-the-art development and fabrication level of various nanodevices imposes stringent requirements on the microscopic analysis methods of their critical dimensions, chemical composition, topography and local optical properties [1]. The analysis of the structural and topographical sample properties can be efficiently implemented by using atomic force (AFM) and scanning electron microscopy (SEM) methods, while detecting small changes in refractive index (RI), which fully determines the local chemical composition and optical properties of the sample, is usually based on the interaction of the sample surface with a light field localized at nanoscale [2].

Light radiation is difficult to focus on the sample under study by means of far-field optics due to the fundamental diffraction limit. Optical nanoantennas exhibit higher performance in light control and localization at nanoscale [2], thus giving opportunities for practical applications of optical manipulation for nano-objects [3], nanolithography [4], excitation and detection of single-molecule fluorescence at 20-nm resolution [5], as well as subwavelength RI microscopy [6]. In the letter case the development of such a superresolution technique for refractometric studying of the optically transparent samples opens up broad prospective for novel practical applications in integrated optics for the characterization of various nanophotonic devices recorded in the photosensitive materials, in microbiology for nonfluorescent study of the biological samples, etc.

To control the “nanoantenna - sample” distance as well as to simultaneously map the local RI changes, the nanoantenna should be placed at the extremity of the scanning probe. With the aperture-type scanning near-field optical microscopy such a nanoantenna typically represents a localized light source, fabricated in the form of the through nanosized aperture on the end of a tapered optical fiber coated with an opaque metal film [7]. The described approach is widely used in subwavelength optical microscopy of different samples with a lateral resolution down to 50 nm, however, the low throughput of the nanoaperture greatly limits the sensitivity of a-SNOM in RI mapping at nanoscale. The use of resonant apertures with higher throughput (bowtie apertures [4,8], C-shaped apertures [9], and apertures surrounded by concentric grooves [10]) can improve the lateral resolution of the a-SNOM (down to 20 nm), however, is not able to provide the significant sensitivity increase in detecting small RI changes (12-% intensity signal change at extremely high RI variation Δn~2 refractive index units (RIU) [6]).

With the scattering-type near-field optical microscopy (s-SNOM) the metal tip of the AFM cantilever placed in the focal spot of the laser source and focused the radiation due to the “lighting rod effect” serves us such nanoantenna [11]. The radiation localized near the tip of such a “probe-like” nanoantenna is scattered owing to its interaction with the sample surface. The scattered signal intensity varies with the topographic and local optical properties of the surface [11] or even sub-surface [12] of the samples, which provides to s-SNOM with the possibility to detect sample chemical composition. However, the extended focal spot irradiated the tip adds the background contribution to the nanoantenna signal. This problem is solved by detection of nonlinear processes or by modulation techniques [13], which greatly complicate the practical realization of high-resolution refractometers based on the s-SNOM. Furthermore, in some applications the presence of the broad focal spot on the sample surface is highly undesirable [5]. It also should be noted that the metalized cantilever tip can be approximately considered us pointed nanoantenna owing to its infinite size does not support geometrical resonances [5]. Recently to avoid this drawback resonant probes (also referred to as “pointed probes”) based on the dipole or monopole nanoantennas were proposed and mapping and enhancement of the single-molecule fluorescence with a lateral resolution down to 20 nm were demonstrated [14,15]. However, the scattered radiation intensity from the resonant nanoantenna, as for the case of a-SNOM with resonant apertures, weakly dependents on the sample RI local changes preventing the usage of the nonfluorescent methods in studying the optically transparent samples.

It is known that the use of spectrally-based signal processing techniques in SNOM systems, instead of amplitude ones, can increase the sensitivity of these systems [16]. Similar approach based on the detection of the nanoantenna’s spectral response rather than the scattered signal intensity seems to increase the sensitivity of the SNOM methods as well as provides them with the possibility to detect small RI changes of the optically transparent samples. Such an approach could be based on the fact that the metal nanoparticles have a pronounced spectral dependence of the local plasmon resonance (LPR) on the surrounding media RI [17]. Therefore, the metal nanoparticle placed at the extremity of the scanning probe can act as the pointed nanoantenna. The detection of the spectral response of this nanoantenna can provide the high-precision mapping of RI changes of the optically transparent samples. In this paper, by detecting the spectral response of the simplest nanoantenna - spherical Au nanoparticle placed at the extremity of the transparent dielectric probe fabricated in the form of a fiber microaxicon (FMA), we will theoretically demonstrate the possibility of mapping the extremely small RI variations (down to 5·10−4 RIU under ideal conditions) with the lateral resolution comparable to the nanoantenna diameter. We will show that the use of the FMA as a scanning probe provides an efficient excitation of dipole LPR in the nanoantenna by the diffraction-limited focal spot as well as the collection of the nanoantenna signal. The results of numerical simulations based on the 3D finite-difference time-domain (FDTD) method are in good agreement with the theoretical quasi-electrostatic estimations for the radius of the nanoantenna not exceeding the skin depth of Au.

2. Theoretical estimations

To estimate the LPR spectral response of the spherical nanoantenna placed in the close proximity with the optically transparent sample surface we use a quasi-electrostatic theory. It is known that the impact of an electromagnetic wave with an electric field amplitude E on the spherical Au nanoparticles with a radius a and a dielectric permittivity εAu and a permeability μ = 1, surrounded by a transparent homogeneous dielectric medium with the dielectric permittivity εm = 1 leads to its polarization with a dipole moment

p=4πa3ε0εAu1εAu+2E.
We further assume a semi-infinite medium with a plane boundary and the dielectric permittivity εm and permeability the μ = 1 placed at a distance d = z0–a from the nanoantenna’s center (Fig. 1(a)). The incident electromagnetic field is assumed to be polarized in the direction perpendicular (s-polarization) to the medium surface (Fig. 1(a)).

 

Fig. 1 (a) Spherical Au nanoantenna illuminated by the s-polarized plane wave and its image dipole located at a distance d in the semi-infinite homogeneous medium with the dielectric permittivity εm; (b) Equivalent dielectric medium polarized by uniform electric field; (c) Sketch of the FMA with the attached Au nanoantenna.

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In this case, the polarized nanoantenna will induce surface charges in the medium. The electromagnetic field of these surface charges can be described by an equivalent field of an image dipole [18] with dipole moment pekv = αp, α = (εm-1)/(εm + 1), located inside the medium at a distance 2z0 from the nanoantenna’s center (Fig. 1(a)). This field will affect the nanoantenna in turn. In this case, we can show that the dipole moment of the nanoantenna will affect only the longitudinal component (directed along the z-axis in Fig. 1(a)) generated by the reflected component of the dipole electric field, which can be written as:

Eekv=14a3z03αεAu-1εAu+2E.
On the other hand, the Eekv can be expressed in term of the field-related charges in the equivalent medium (Fig. 1(b)) polarized by the E field and surrounded the nanoantenna from all sides [18]
Eekv=εekv12εekv+1E.
where εekv is the dielectric permittivity of the equivalent medium. By equating the Eqs. (2) and (3) we can found that the relationship between the εekv and the dielectric permittivity εm of the semi-infinite medium located at the distance z0 can be expressed by the following equation
εekv=a3(εm1)4z03(εm+1)(εAu1)+(εAu+2)4a3(εm1)4z03(εm+1)εAu.
The spectral dependence of the dielectric permittivity of the Au nanoantenna is assumed to follow the Drude-Lorentz model [18]:
εAu(λ)=ε1λp2(1/λ2+i/γpλ),
where ε is a high-frequency limit dielectric constant, λp - plasma wavelength, and γr - damping parameter. By neglecting the εekv dispersion, assuming (εm - 1) <<1 and using the known equation for the dipole LPR of small spherical nanoparticles [7]
Re(2εekv+εAu)=0,
we can obtain from Eq. (4) the simple equation describing the relationship between the dipole LPR wavelength λSP of the spherical Au nanoantenna and the dielectric permittivity of semi-infinite medium εm:
λSP=λmedia1(λmedia)2(λvak)2(λvak)2(134a3z031(nm2+1)),
where nm=εm; λmedia and λvak are the dipole LPR wavelengths of the spherical Au nanoparticle in the homogeneous dielectric medium with εm and in vacuo respectively.

The λmedia and λvak values can be obtained by applying the Eq. (6) to the Eq. (5). Note that in general Eq. (5) gives quite good approximation for Au dispersion curve in the visible spectral range. However, the use of such expression to determine exact λmedia and λvak values are quite approximate, which leads to the incorrect estimates of λSP value in turn. Therefore, to carefully estimate the λmedia and λvak values we used a modified Drude-Lorentz model [19]:

εAu(λ)=ε1λp2(1/λ2+i/γpλ)+m=1,2Amλm[eiφm(1/λm1/λi/γm)+eiφm(1/λm+1/λ+i/γm)],
where the first and the second terms represent the classic Drude model, while the following terms take into account interband transitions in visible and near-infrared spectral regions (λm - interband transition wavelength, γm - interband transition broadening expressed in wavelength, Am and Φm - dimensionless critical points amplitude and phase [19], respectively). The following equation allows one to describe the spectral dependence of the dielectric permittivity of Au, that best fits the experimentally measured values for bulk material [20], thereby gives more accurate estimations for λmediaand λvak. By repeating the aforementioned calculations for p-polarized exiting field (Fig. 1(a)), we can obtain
λSP=λmedia1(λmedia)2(λvak)2(λvak)2(138a3z031(nm2+1)).
Figures 2(a)-(b) show the dependencies of the relative dipole LPR wavelength λSPSP0SP0 - dipole LPR wavelength of the nanoantenna in vacuo) of the nanoantenna on the semi-infinite medium RI nm (curves 1-5), calculated for different “nanoantenna-medium” distances d and incident field polarizations in accordance with the Eqs. (7) and (9) respectively.

 

Fig. 2 (a-b) Relative dipole LPR wavelength λSPSP0 (λSP0 - dipole LPR wavelength in vacuo) of the nanoantenna as a function of the semi-infinite medium RI nm calculated for s- (a) and p-polarized (b) incident electric field and different “nanoantenna-medium” distances d. (c) Slope Sλ = sp/dnm of the λSP(nm) curves calculated near nm = 1.35 as a function of the “nanoantenna-sample” distance d.

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The λSPSP0(nm) dependencies calculated for the nanoantenna fully surrounded by the homogeneous dielectric medium [21] are also presented in the Fig. 2(a) and 2(b) (dashed curves). As seen, the change in the RI leads to a detectable red-shift of the dipole LPR wavelength in comparison with the λSP0, with the shift value being strongly depended on the incident field polarization as well as the “nanoantenna-media” distance d. Nevertheless, even for nanoantenna located in a close proximity to the surface the spectral shift is significantly lower than for the nanoantenna fully surrounded by this dielectric media (dashed curves in Figs. 2(a) and 2(b)). Figure 2(c) shows the dependence of a linear section slope Sλ = sp/dnm of the λSP(nm) curve calculated near nm = 1.35 on the “nanoantenna-media” distance d. As seen, the maximum spectral sensitivity Sλ ~19 nm/RIU is expectedly achieved at d = 0 and s-polarized excitation field owing to the distribution character of the energy density maxima in the nanoantenna near-field [22,23]. At the same time the Sλ value is only 4 times lesser than the sensitivity of the nanoantenna fully surrounded by the medium. In accordance with the resolution of modern optical spectrum analyzers estimated by using the Rayleigh criterion (no worse than 0.02 nm) [24], the method proposed can detect the RI changes ~10−3 RIU. However, by taking into account the existing state-of-the-art methods of optical spectra processing based on detection of the spectral peak “center of gravity”, we can expect an increase in the resolution of the method at least by an order of magnitude (down to 10−4 RIU).

3. FDTD analysis

As it was mentioned above at real experimental conditions the nanoantenna should be placed at the extremity of the scanning probe, which can excite the nanoantenna with minimized sample background illumination. Such a probe must be integrated into the standard feedback system of a scanning probe microscope, and thus provide an opportunity to move nanoantenna with high precision in a close proximity to the sample surface. We assume that the nanoantenna is located on tip of the fiber microaxicon (FMA) (Fig. 1(c)) fabricated at the flat endface of a standard step-index optical fiber (OF). The semi-infinite homogeneous media (referred to as “sample”) with a refractive index nm ranging in 1 - 1.7 RIU is placed at a distance d from the nanoantenna. Note that the FMA presence causes some difference of the geometry under consideration from the conditions described in the analytical estimations. Also it should be noted that the abovementioned quasi-static approximation holds true only for relatively small nanoantenna radius (i.e., at a<σ, where σ - the skin depth of Au).

In order to take into account the retardation effects inside the nanoantenna [23] at a>σ, and to assess the influence of the FMA on the spectral sensitivity of the developed method we use numerical simulation based on the 3D-FDTD method [25]. The FMA is assumed to have a full taper angle θ = 90°, the base diameter equals to the OF core diameter and axial symmetry along the OF optical axis (z axis in Fig. 1(c)). Such a microlens can focus the laser radiation into the diffraction-limited spot with a lateral size ~λ/2 and a focal depth ~0.3λ [26], providing a high excitation efficiency of the dipole LPR nanoantenna with the minimized background illumination as well as a possibility to collect the nanoantenna spectral signal. The following parameters were used to model the OF properties: fiber core diameter Dcore = 4.5 μm, cladding diameter Dclad = 125 μm and the numerical aperture NA = 0.14. The FMA is excited by a broadband p-polarized Gaussian source (its position is marked in Fig. 1(c)) with a central wavelength λs = 532 nm and spectral FWHM ΔλFWHM = 100 nm, providing the single-mode propagation regime in this spectral range at the abovementioned OF parameters. Perfectly matched layers are used as the boundary conditions. Mesh size of the computational cell equals to 1x1x1 nm3. Moreover, to increase the calculation accuracy an additional mesh covering the nanoantenna area with the cell size 0.2x0.2x0.2 nm3 is used.

Figure 3(a) shows the dependence of the relative dipole LPR wavelength λSPSP0 of the nanoantenna on the sample RI nm calculated for small nanoantenna radii (a<σ) and “nanoantenna-sample” distance d = 0. Note that the dipole LPR wavelength λSP0 is not constant and rises linearly [27] with the nanoantenna radius a (Fig. 3(b)), which is also consistent with the data presented in [22,23]. Therefore, to present the calculated and analytical curves on one plot the λSP value in each case is normalized to the correspondent λSP0 value determined at nm = 1. Figure 3(a) also shows the λSPSP0(nm) dependencies obtained using the analytical estimations for the s- (Eq. (7)) and p-polarized (Eq. (9)) radiation, as well as λSPSP0(nm) dependence, which corresponds to the well-known case of the nanoantenna fully surrounded by a homogeneous dielectric medium (black solid line in Fig. 3(a)). As seen, for a<25 nm the relative spectral shift λSPSP0 obtained using numerical simulations is in good agreement with the analytical estimations. Moreover, at low RI (1<nm<1.3) calculated and analytical curves rises almost linearly with nm. However, the λSPSP0 value for all calculated curves exceeds the analytical value estimated by using the Eq. (7) for the p-polarized radiation. This fact can be partly explained by the presence of the longitudinal component of the electromagnetic field directed along z axis (Fig. 1(c)) in the FMA focal spot excited the nanoantenna. Furthermore, the analysis of the data in Fig. 3(b) shows, than all calculated curves tend to increase the slope Sλ with the nm growth (in the range 1.3<nm<1.7), while the slope of the λSPSP0(nm) dependencies estimated by using the analytical Eqs. (7) and (9) demonstrates the decrease with nm growth. This mismatch between the calculated and analytical results can be explained by the fact that the assumption (εm - 1)<<1 made in analytical estimations does not hold true at the specified RI range. Moreover, to provide more accurate analytical estimation one should take into account the multiple reflections of the image dipole and nanoantenna that contribution increases with nm.

 

Fig. 3 (a) Relative dipole LPR wavelength λSPSP0 of the nanoantenna as a function of the sample RI nm calculated for different nanoantenna radii a. (b) Dependence of the dipole LPR wavelength λSP0 in vacuo on the nanoantenna radius a. (c) Normalized change in dipole LPR wavelength ∆λSP with an abrupt step-like spatial change of the sample’s RI from nm = 1.3 to 1.7 RIU calculated at d = 5 nm and nanoantenna radii а = 25 nm and 50 nm, with the estimated lateral resolution of the proposed method being 55 nm and 103 nm, respectively. (d) Far-field (solid curves) and near-field (dashed curves) scattering spectra of the nanoantenna calculated at a = 25 nm and different RI nm of the sample surface.

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Figure 2(c) shows the dependencies of a linear section slope of the λSP(nm) curve estimated near nm = 1.35 Sλ = dλsp/dnm on the “nanoantenna-sample” distance d calculated for different nanoantenna radii a. As seen, despite some mismatch in the maximum values estimates at d = 0, the behavior of the calculated curves shows good agreement with the analytical results. It should be noted that the Sλ(d) dependence for the nanoantennas with the radius larger than the skin depth of Au has a similar behavior with both numerical calculations for the a<σ and the analytical estimations. However, with nanoantenna radii growth the slope of the λSPSP0(nm) dependence increases, exceeding the estimated value (Eq. (9)) at a>25 nm and reaching the maximum value Sλ~21 nm/RIU at a = 50 nm. Such behavior apparently can be explained by the increasing influence of the field retardation effect with the nanoantenna radius growth [32].

It also should be noted that the spectral FWHM of the dipole LPR is strongly increased with the nanoantenna radius [22] due to the higher-order (nondipole) plasmon modes excitation. Potentially it significantly complicates the spectral shift registration. To estimate the lateral resolution of the method developed, we simulated the case when the dipole LPR wavelength varies with a step-like spatial change of the sample surface RI. The results of the correspondent numerical calculations for nanoantennas with the radii a = 50 nm and a = 25 nm are shown in Fig. 3(c). As seen, the lateral resolution estimated as the difference between the 10-% and 90%-levels of the maximum signal improves with the nanoantenna radius decreasing and reaches ~55 nm, which approximately corresponds to the doubled nanoantenna radius. Summing up these facts, in spite of the spectral sensitivity increase with a, both the spectral LPR peak broadening and the lateral resolution worsening can reduce the positive effect of the large-radius nanoantennas. Thus, in our opinion, the use of the nanoantennas with a<50 nm is optimal in terms of the achieved lateral resolution and provided sensitivity (down to 5·10−4 RIU under ideal conditions). Obviously, the change in LPR spectral position associated with the “nanoantenna-sample” distance or the microroughness of the sample surface could lead to an error in evaluating the actual RI change, thus the stated spectral sensitivity can be lower. This error as well as possible artifacts in the RI map seems to be minimized by simultaneously scanning the topography and the RI of the sample surface using SNOM feedback system based on a standard tuning fork.

It should be noted that the spectral shift registration can be performed in the far-field by using the focusing optics as well as directly through the FMA. Figure 3(d) shows the calculated reflection spectra of the scattered nanoantenna radiation collected by the FMA. As seen, all the local maxima of the reflection spectrum (solid curves) are slightly blue-shifted [23,28] in comparison with the spectra calculated in the nanoantenna’s near-field (dashed curves). Nevertheless, the “far-field” λSPSP0(nm) dependence (not presented here) is similar to that of presented in the Fig. 3(a).

Finally, the use of the nanoantennas with an elongated geometrical shape (higher aspect ratio [29],) or specially designed resonant nanoantennas [30,31] can substantially increase the sensitivity of the developed method as well as provide better lateral resolution. These features as well as the experimental realization of the proposed probe will be discussed in our forthcoming paper.

4. Conclusions

In summary, in the paper we showed analytically and numerically that the use of spectral response detection of a single spherical Au nanoantenna allows one to map very small (down to 5·10−4 RIU under ideal conditions) variations of the RI of the optically transparent sample. Simple analytical quasi-static model allowed estimating the spectral shift of the nanoantenna dipole LPR wavelength and the spectral sensitivity of the method developed was presented. The pointed scanning probe based on fiber microaxicon with the Au spherical nanoantenna attached to its tip was proposed to realize the RI mapping. The finite-difference time-domain numerical simulations of the spectral properties of the proposed probe are in agreement with the theoretical quasi-electrostatic estimations for the radius of the nanoantenna, not exceeding the skin depth of Au.

The fabrication technique and the focusing properties of the FMAs are carefully studied [26,32]. The nanoantenna on the extremity of the microaxicon can be fabricated by using several developed experimental techniques: ion-beam milling, laser-induced femtosecond transfer [33], single Au nanoparticles scanning [34], etc. To precisely control the distance between the nanoantenna and the sample surface a standard SNOM feedback system based on a tuning fork can be used providing the possibility to simultaneously map the local RI changes and the topography of the sample under study. Spectral signal detection can be performed in the far field by using focusing lens as well as directly through the fiber probe, which significantly simplifies the optical signal system. The experimental realization of the probe proposed will be presented in our forthcoming paper.

Acknowledgments

The authors acknowledge partial support from Russian Foundation for Basic Research (Projects nos. 14-02-31323-mol_a, 14-02-00205-a).

References and links

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21. This curve was obtained by using the Eq. (8) and the condition (6).

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27. In accordance with our numerical simulations the presence of the microaxicon red-shifts the λSP0(a) dependence approximately on 20 nm in comparison with the single nanoparticles in vacuo.

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References

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  1. A. J. Huber, D. Kazantsev, F. Keilmann, J. Wittborn, R. Hillenbrand, “Simultaneous ir material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. 19(17), 2209–2212 (2007).
    [CrossRef]
  2. P. Bharadwaj, B. Deutsch, L. Novotny, “Optical antennas,” Adv. Opt. Photon 1(3), 438–483 (2009).
    [CrossRef]
  3. L. Novotny, R. X. Bian, X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).
    [CrossRef]
  4. A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
    [CrossRef] [PubMed]
  5. T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7(1), 28–33 (2007).
    [CrossRef] [PubMed]
  6. T. Lee, E. Lee, S. Oh, J. W. Hahn, “Imaging heterogeneous nanostructures with a plasmonic resonant ridge aperture,” Nanotechnology 24(14), 145502 (2013).
    [CrossRef] [PubMed]
  7. L. Novotny and B. Hecht, Principles of Nano-Optics, (Cambridge University Press, 2006).
  8. M. Mivelle, T. S. van Zanten, L. Neumann, N. F. van Hulst, M. F. Garcia-Parajo, “Ultrabright bowtie nanoaperture antenna probes studied by single molecule fluorescence,” Nano Lett. 12(11), 5972–5978 (2012).
    [CrossRef] [PubMed]
  9. L. Wang, E. X. Jin, S. M. Uppuluri, X. Xu, “Contact optical nanolithography using nanoscale C-shaped apertures,” Opt. Express 14(21), 9902–9908 (2006).
    [CrossRef] [PubMed]
  10. T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26(24), 1972–1974 (2001).
    [CrossRef] [PubMed]
  11. T. Taubner, R. Hillenbrand, F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85(21), 5064 (2004).
    [CrossRef]
  12. T. Taubner, F. Keilmann, R. Hillenbrand, “Nanoscale-resolved subsurface imaging by scattering-type near-field optical microscopy,” Opt. Express 13(22), 8893–8899 (2005).
    [CrossRef] [PubMed]
  13. E. J. Sánchez, L. Novotny, X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82(20), 4014–4017 (1999).
    [CrossRef]
  14. F. Huth, A. Chuvilin, M. Schnell, I. Amenabar, R. Krutokhvostov, S. Lopatin, R. Hillenbrand, “Resonant antenna probes for tip-enhanced infrared near-field microscopy,” Nano Lett. 13(3), 1065–1072 (2013).
    [CrossRef] [PubMed]
  15. L. Neumann, J. van ’t Oever, N. F. van Hulst, “A resonant scanning dipole-antenna probe for enhanced nanoscale imaging,” Nano Lett. 13(11), 5070–5074 (2013).
    [CrossRef] [PubMed]
  16. Y. N. Kulchin, O. B. Vitrik, A. A. Kuchmizhak, E. V. Pustovalov, A. V. Nepomnyashchii, “Cavity-based Fabry-Perot probe with protruding subwavelength aperture,” Opt. Lett. 36(19), 3945–3947 (2011).
    [CrossRef] [PubMed]
  17. K.-S. Lee, M.-A. El-Sayed, “Gold and silver nanoparticles in sensing and imaging: sensitivity of plasmon response to size, shape, and metal composition,” J. Phys. Chem. B 110(39), 19220–19225 (2006).
    [CrossRef] [PubMed]
  18. M. Born and E. Wolf, The Principles of Optics (Pergamon Press, 1964).
  19. P. G. Etchegoin, E. C. Le Ru, M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
    [CrossRef] [PubMed]
  20. P. B. Johnson, R. W. Christy, “Optical-constants of noble-metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]
  21. This curve was obtained by using the Eq. (8) and the condition (6).
  22. K. L. Kelly, E. Coronado, L. L. Zhao, G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
    [CrossRef]
  23. G. W. Bryant, F. J. García de Abajo, J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett. 8(2), 631–636 (2008).
    [CrossRef] [PubMed]
  24. www.yokogawa.com .
  25. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
  26. A. A. Kuchmizhak, S. O. Gurbatov, A. A. Nepomniaschii, O. B. Vitrik, Yu. N. Kulchin, “High-quality fiber microaxicons fabricated by a modified chemical etching method for laser focusing and generation of Bessel-like beams,” Appl. Opt. 53(5), 937–943 (2014).
    [CrossRef] [PubMed]
  27. In accordance with our numerical simulations the presence of the microaxicon red-shifts the λSP0(a) dependence approximately on 20 nm in comparison with the single nanoparticles in vacuo.
  28. B. M. Ross, L. P. Lee, “Comparison of near- and far-field measures for plasmon resonance of metallic nanoparticles,” Opt. Lett. 34(7), 896–898 (2009).
    [CrossRef] [PubMed]
  29. K. M. Mayer, J. H. Hafner, “Localized surface plasmon resonance sensors,” Chem. Rev. 111(6), 3828–3857 (2011).
    [CrossRef] [PubMed]
  30. Z. Pan, J. Guo, “Enhanced optical absorption and electric field resonance in diabolo metal bar optical antennas,” Opt. Express 21(26), 32491–32500 (2013).
    [CrossRef] [PubMed]
  31. T. Grosjean, M. Mivelle, F. I. Baida, G. W. Burr, U. C. Fischer, “Diabolo nanoantenna for enhancing and confining the magnetic optical field,” Nano Lett. 11(3), 1009–1013 (2011).
    [CrossRef] [PubMed]
  32. T. Grosjean, S. S. Saleh, M. A. Suarez, I. A. Ibrahim, V. Piquerey, D. Charraut, P. Sandoz, “Fiber microaxicons fabricated by a polishing technique for the generation of Bessel-like beams,” Appl. Opt. 46(33), 8061–8067 (2007).
    [CrossRef] [PubMed]
  33. A. I. Kuznetsov, R. Kiyan, B. N. Chichkov, “Laser fabrication of 2D and 3D metal nanoparticle structures and arrays,” Opt. Express 18(20), 21198–21203 (2010).
    [CrossRef] [PubMed]
  34. P. Anger, P. Bharadwaj, L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
    [CrossRef] [PubMed]

2014 (1)

2013 (4)

Z. Pan, J. Guo, “Enhanced optical absorption and electric field resonance in diabolo metal bar optical antennas,” Opt. Express 21(26), 32491–32500 (2013).
[CrossRef] [PubMed]

T. Lee, E. Lee, S. Oh, J. W. Hahn, “Imaging heterogeneous nanostructures with a plasmonic resonant ridge aperture,” Nanotechnology 24(14), 145502 (2013).
[CrossRef] [PubMed]

F. Huth, A. Chuvilin, M. Schnell, I. Amenabar, R. Krutokhvostov, S. Lopatin, R. Hillenbrand, “Resonant antenna probes for tip-enhanced infrared near-field microscopy,” Nano Lett. 13(3), 1065–1072 (2013).
[CrossRef] [PubMed]

L. Neumann, J. van ’t Oever, N. F. van Hulst, “A resonant scanning dipole-antenna probe for enhanced nanoscale imaging,” Nano Lett. 13(11), 5070–5074 (2013).
[CrossRef] [PubMed]

2012 (1)

M. Mivelle, T. S. van Zanten, L. Neumann, N. F. van Hulst, M. F. Garcia-Parajo, “Ultrabright bowtie nanoaperture antenna probes studied by single molecule fluorescence,” Nano Lett. 12(11), 5972–5978 (2012).
[CrossRef] [PubMed]

2011 (3)

Y. N. Kulchin, O. B. Vitrik, A. A. Kuchmizhak, E. V. Pustovalov, A. V. Nepomnyashchii, “Cavity-based Fabry-Perot probe with protruding subwavelength aperture,” Opt. Lett. 36(19), 3945–3947 (2011).
[CrossRef] [PubMed]

T. Grosjean, M. Mivelle, F. I. Baida, G. W. Burr, U. C. Fischer, “Diabolo nanoantenna for enhancing and confining the magnetic optical field,” Nano Lett. 11(3), 1009–1013 (2011).
[CrossRef] [PubMed]

K. M. Mayer, J. H. Hafner, “Localized surface plasmon resonance sensors,” Chem. Rev. 111(6), 3828–3857 (2011).
[CrossRef] [PubMed]

2010 (1)

2009 (2)

2008 (1)

G. W. Bryant, F. J. García de Abajo, J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett. 8(2), 631–636 (2008).
[CrossRef] [PubMed]

2007 (3)

T. Grosjean, S. S. Saleh, M. A. Suarez, I. A. Ibrahim, V. Piquerey, D. Charraut, P. Sandoz, “Fiber microaxicons fabricated by a polishing technique for the generation of Bessel-like beams,” Appl. Opt. 46(33), 8061–8067 (2007).
[CrossRef] [PubMed]

A. J. Huber, D. Kazantsev, F. Keilmann, J. Wittborn, R. Hillenbrand, “Simultaneous ir material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. 19(17), 2209–2212 (2007).
[CrossRef]

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7(1), 28–33 (2007).
[CrossRef] [PubMed]

2006 (5)

K.-S. Lee, M.-A. El-Sayed, “Gold and silver nanoparticles in sensing and imaging: sensitivity of plasmon response to size, shape, and metal composition,” J. Phys. Chem. B 110(39), 19220–19225 (2006).
[CrossRef] [PubMed]

P. G. Etchegoin, E. C. Le Ru, M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[CrossRef] [PubMed]

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
[CrossRef] [PubMed]

L. Wang, E. X. Jin, S. M. Uppuluri, X. Xu, “Contact optical nanolithography using nanoscale C-shaped apertures,” Opt. Express 14(21), 9902–9908 (2006).
[CrossRef] [PubMed]

P. Anger, P. Bharadwaj, L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

T. Taubner, R. Hillenbrand, F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85(21), 5064 (2004).
[CrossRef]

2003 (1)

K. L. Kelly, E. Coronado, L. L. Zhao, G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
[CrossRef]

2001 (1)

1999 (1)

E. J. Sánchez, L. Novotny, X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82(20), 4014–4017 (1999).
[CrossRef]

1997 (1)

L. Novotny, R. X. Bian, X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).
[CrossRef]

1972 (1)

P. B. Johnson, R. W. Christy, “Optical-constants of noble-metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Aizpurua, J.

G. W. Bryant, F. J. García de Abajo, J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett. 8(2), 631–636 (2008).
[CrossRef] [PubMed]

Amenabar, I.

F. Huth, A. Chuvilin, M. Schnell, I. Amenabar, R. Krutokhvostov, S. Lopatin, R. Hillenbrand, “Resonant antenna probes for tip-enhanced infrared near-field microscopy,” Nano Lett. 13(3), 1065–1072 (2013).
[CrossRef] [PubMed]

Anger, P.

P. Anger, P. Bharadwaj, L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[CrossRef] [PubMed]

Baida, F. I.

T. Grosjean, M. Mivelle, F. I. Baida, G. W. Burr, U. C. Fischer, “Diabolo nanoantenna for enhancing and confining the magnetic optical field,” Nano Lett. 11(3), 1009–1013 (2011).
[CrossRef] [PubMed]

Bharadwaj, P.

P. Bharadwaj, B. Deutsch, L. Novotny, “Optical antennas,” Adv. Opt. Photon 1(3), 438–483 (2009).
[CrossRef]

P. Anger, P. Bharadwaj, L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[CrossRef] [PubMed]

Bian, R. X.

L. Novotny, R. X. Bian, X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).
[CrossRef]

Bryant, G. W.

G. W. Bryant, F. J. García de Abajo, J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett. 8(2), 631–636 (2008).
[CrossRef] [PubMed]

Burr, G. W.

T. Grosjean, M. Mivelle, F. I. Baida, G. W. Burr, U. C. Fischer, “Diabolo nanoantenna for enhancing and confining the magnetic optical field,” Nano Lett. 11(3), 1009–1013 (2011).
[CrossRef] [PubMed]

Charraut, D.

Chichkov, B. N.

Christy, R. W.

P. B. Johnson, R. W. Christy, “Optical-constants of noble-metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Chuvilin, A.

F. Huth, A. Chuvilin, M. Schnell, I. Amenabar, R. Krutokhvostov, S. Lopatin, R. Hillenbrand, “Resonant antenna probes for tip-enhanced infrared near-field microscopy,” Nano Lett. 13(3), 1065–1072 (2013).
[CrossRef] [PubMed]

Conley, N. R.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
[CrossRef] [PubMed]

Coronado, E.

K. L. Kelly, E. Coronado, L. L. Zhao, G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
[CrossRef]

Deutsch, B.

P. Bharadwaj, B. Deutsch, L. Novotny, “Optical antennas,” Adv. Opt. Photon 1(3), 438–483 (2009).
[CrossRef]

Ebbesen, T. W.

El-Sayed, M.-A.

K.-S. Lee, M.-A. El-Sayed, “Gold and silver nanoparticles in sensing and imaging: sensitivity of plasmon response to size, shape, and metal composition,” J. Phys. Chem. B 110(39), 19220–19225 (2006).
[CrossRef] [PubMed]

Etchegoin, P. G.

P. G. Etchegoin, E. C. Le Ru, M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[CrossRef] [PubMed]

Fischer, U. C.

T. Grosjean, M. Mivelle, F. I. Baida, G. W. Burr, U. C. Fischer, “Diabolo nanoantenna for enhancing and confining the magnetic optical field,” Nano Lett. 11(3), 1009–1013 (2011).
[CrossRef] [PubMed]

Fromm, D. P.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
[CrossRef] [PubMed]

García de Abajo, F. J.

G. W. Bryant, F. J. García de Abajo, J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett. 8(2), 631–636 (2008).
[CrossRef] [PubMed]

Garcia-Parajo, M. F.

M. Mivelle, T. S. van Zanten, L. Neumann, N. F. van Hulst, M. F. Garcia-Parajo, “Ultrabright bowtie nanoaperture antenna probes studied by single molecule fluorescence,” Nano Lett. 12(11), 5972–5978 (2012).
[CrossRef] [PubMed]

Grosjean, T.

T. Grosjean, M. Mivelle, F. I. Baida, G. W. Burr, U. C. Fischer, “Diabolo nanoantenna for enhancing and confining the magnetic optical field,” Nano Lett. 11(3), 1009–1013 (2011).
[CrossRef] [PubMed]

T. Grosjean, S. S. Saleh, M. A. Suarez, I. A. Ibrahim, V. Piquerey, D. Charraut, P. Sandoz, “Fiber microaxicons fabricated by a polishing technique for the generation of Bessel-like beams,” Appl. Opt. 46(33), 8061–8067 (2007).
[CrossRef] [PubMed]

Guo, J.

Gurbatov, S. O.

Hafner, J. H.

K. M. Mayer, J. H. Hafner, “Localized surface plasmon resonance sensors,” Chem. Rev. 111(6), 3828–3857 (2011).
[CrossRef] [PubMed]

Hahn, J. W.

T. Lee, E. Lee, S. Oh, J. W. Hahn, “Imaging heterogeneous nanostructures with a plasmonic resonant ridge aperture,” Nanotechnology 24(14), 145502 (2013).
[CrossRef] [PubMed]

Hillenbrand, R.

F. Huth, A. Chuvilin, M. Schnell, I. Amenabar, R. Krutokhvostov, S. Lopatin, R. Hillenbrand, “Resonant antenna probes for tip-enhanced infrared near-field microscopy,” Nano Lett. 13(3), 1065–1072 (2013).
[CrossRef] [PubMed]

A. J. Huber, D. Kazantsev, F. Keilmann, J. Wittborn, R. Hillenbrand, “Simultaneous ir material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. 19(17), 2209–2212 (2007).
[CrossRef]

T. Taubner, F. Keilmann, R. Hillenbrand, “Nanoscale-resolved subsurface imaging by scattering-type near-field optical microscopy,” Opt. Express 13(22), 8893–8899 (2005).
[CrossRef] [PubMed]

T. Taubner, R. Hillenbrand, F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85(21), 5064 (2004).
[CrossRef]

Huber, A. J.

A. J. Huber, D. Kazantsev, F. Keilmann, J. Wittborn, R. Hillenbrand, “Simultaneous ir material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. 19(17), 2209–2212 (2007).
[CrossRef]

Huth, F.

F. Huth, A. Chuvilin, M. Schnell, I. Amenabar, R. Krutokhvostov, S. Lopatin, R. Hillenbrand, “Resonant antenna probes for tip-enhanced infrared near-field microscopy,” Nano Lett. 13(3), 1065–1072 (2013).
[CrossRef] [PubMed]

Ibrahim, I. A.

Jin, E. X.

Johnson, P. B.

P. B. Johnson, R. W. Christy, “Optical-constants of noble-metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kazantsev, D.

A. J. Huber, D. Kazantsev, F. Keilmann, J. Wittborn, R. Hillenbrand, “Simultaneous ir material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. 19(17), 2209–2212 (2007).
[CrossRef]

Keilmann, F.

A. J. Huber, D. Kazantsev, F. Keilmann, J. Wittborn, R. Hillenbrand, “Simultaneous ir material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. 19(17), 2209–2212 (2007).
[CrossRef]

T. Taubner, F. Keilmann, R. Hillenbrand, “Nanoscale-resolved subsurface imaging by scattering-type near-field optical microscopy,” Opt. Express 13(22), 8893–8899 (2005).
[CrossRef] [PubMed]

T. Taubner, R. Hillenbrand, F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85(21), 5064 (2004).
[CrossRef]

Kelly, K. L.

K. L. Kelly, E. Coronado, L. L. Zhao, G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
[CrossRef]

Kino, G. S.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
[CrossRef] [PubMed]

Kiyan, R.

Krutokhvostov, R.

F. Huth, A. Chuvilin, M. Schnell, I. Amenabar, R. Krutokhvostov, S. Lopatin, R. Hillenbrand, “Resonant antenna probes for tip-enhanced infrared near-field microscopy,” Nano Lett. 13(3), 1065–1072 (2013).
[CrossRef] [PubMed]

Kuchmizhak, A. A.

Kuipers, L.

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7(1), 28–33 (2007).
[CrossRef] [PubMed]

Kulchin, Y. N.

Kulchin, Yu. N.

Kuznetsov, A. I.

Le Ru, E. C.

P. G. Etchegoin, E. C. Le Ru, M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[CrossRef] [PubMed]

Lee, E.

T. Lee, E. Lee, S. Oh, J. W. Hahn, “Imaging heterogeneous nanostructures with a plasmonic resonant ridge aperture,” Nanotechnology 24(14), 145502 (2013).
[CrossRef] [PubMed]

Lee, K.-S.

K.-S. Lee, M.-A. El-Sayed, “Gold and silver nanoparticles in sensing and imaging: sensitivity of plasmon response to size, shape, and metal composition,” J. Phys. Chem. B 110(39), 19220–19225 (2006).
[CrossRef] [PubMed]

Lee, L. P.

Lee, T.

T. Lee, E. Lee, S. Oh, J. W. Hahn, “Imaging heterogeneous nanostructures with a plasmonic resonant ridge aperture,” Nanotechnology 24(14), 145502 (2013).
[CrossRef] [PubMed]

Lezec, H. J.

Linke, R. A.

Lopatin, S.

F. Huth, A. Chuvilin, M. Schnell, I. Amenabar, R. Krutokhvostov, S. Lopatin, R. Hillenbrand, “Resonant antenna probes for tip-enhanced infrared near-field microscopy,” Nano Lett. 13(3), 1065–1072 (2013).
[CrossRef] [PubMed]

Mayer, K. M.

K. M. Mayer, J. H. Hafner, “Localized surface plasmon resonance sensors,” Chem. Rev. 111(6), 3828–3857 (2011).
[CrossRef] [PubMed]

Meyer, M.

P. G. Etchegoin, E. C. Le Ru, M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[CrossRef] [PubMed]

Mivelle, M.

M. Mivelle, T. S. van Zanten, L. Neumann, N. F. van Hulst, M. F. Garcia-Parajo, “Ultrabright bowtie nanoaperture antenna probes studied by single molecule fluorescence,” Nano Lett. 12(11), 5972–5978 (2012).
[CrossRef] [PubMed]

T. Grosjean, M. Mivelle, F. I. Baida, G. W. Burr, U. C. Fischer, “Diabolo nanoantenna for enhancing and confining the magnetic optical field,” Nano Lett. 11(3), 1009–1013 (2011).
[CrossRef] [PubMed]

Moerland, R. J.

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7(1), 28–33 (2007).
[CrossRef] [PubMed]

Moerner, W. E.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
[CrossRef] [PubMed]

Nepomniaschii, A. A.

Nepomnyashchii, A. V.

Neumann, L.

L. Neumann, J. van ’t Oever, N. F. van Hulst, “A resonant scanning dipole-antenna probe for enhanced nanoscale imaging,” Nano Lett. 13(11), 5070–5074 (2013).
[CrossRef] [PubMed]

M. Mivelle, T. S. van Zanten, L. Neumann, N. F. van Hulst, M. F. Garcia-Parajo, “Ultrabright bowtie nanoaperture antenna probes studied by single molecule fluorescence,” Nano Lett. 12(11), 5972–5978 (2012).
[CrossRef] [PubMed]

Novotny, L.

P. Bharadwaj, B. Deutsch, L. Novotny, “Optical antennas,” Adv. Opt. Photon 1(3), 438–483 (2009).
[CrossRef]

P. Anger, P. Bharadwaj, L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[CrossRef] [PubMed]

E. J. Sánchez, L. Novotny, X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82(20), 4014–4017 (1999).
[CrossRef]

L. Novotny, R. X. Bian, X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).
[CrossRef]

Oh, S.

T. Lee, E. Lee, S. Oh, J. W. Hahn, “Imaging heterogeneous nanostructures with a plasmonic resonant ridge aperture,” Nanotechnology 24(14), 145502 (2013).
[CrossRef] [PubMed]

Pan, Z.

Pellerin, K. M.

Piquerey, V.

Pustovalov, E. V.

Ross, B. M.

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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

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Other (6)

In accordance with our numerical simulations the presence of the microaxicon red-shifts the λSP0(a) dependence approximately on 20 nm in comparison with the single nanoparticles in vacuo.

www.yokogawa.com .

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This curve was obtained by using the Eq. (8) and the condition (6).

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Figures (3)

Fig. 1
Fig. 1

(a) Spherical Au nanoantenna illuminated by the s-polarized plane wave and its image dipole located at a distance d in the semi-infinite homogeneous medium with the dielectric permittivity εm; (b) Equivalent dielectric medium polarized by uniform electric field; (c) Sketch of the FMA with the attached Au nanoantenna.

Fig. 2
Fig. 2

(a-b) Relative dipole LPR wavelength λSPSP0 (λSP0 - dipole LPR wavelength in vacuo) of the nanoantenna as a function of the semi-infinite medium RI nm calculated for s- (a) and p-polarized (b) incident electric field and different “nanoantenna-medium” distances d. (c) Slope Sλ = sp/dnm of the λSP(nm) curves calculated near nm = 1.35 as a function of the “nanoantenna-sample” distance d.

Fig. 3
Fig. 3

(a) Relative dipole LPR wavelength λSPSP0 of the nanoantenna as a function of the sample RI nm calculated for different nanoantenna radii a. (b) Dependence of the dipole LPR wavelength λSP0 in vacuo on the nanoantenna radius a. (c) Normalized change in dipole LPR wavelength ∆λSP with an abrupt step-like spatial change of the sample’s RI from nm = 1.3 to 1.7 RIU calculated at d = 5 nm and nanoantenna radii а = 25 nm and 50 nm, with the estimated lateral resolution of the proposed method being 55 nm and 103 nm, respectively. (d) Far-field (solid curves) and near-field (dashed curves) scattering spectra of the nanoantenna calculated at a = 25 nm and different RI nm of the sample surface.

Equations (9)

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p=4π a 3 ε 0 ε Au 1 ε Au +2 E.
E ekv = 1 4 a 3 z 0 3 α ε Au -1 ε Au +2 E.
E ekv = ε ekv 1 2 ε ekv +1 E.
ε ekv = a 3 ( ε m 1) 4 z 0 3 ( ε m +1) ( ε Au 1)+( ε Au +2) 4 a 3 ( ε m 1) 4 z 0 3 ( ε m +1) ε Au .
ε Au (λ)= ε 1 λ p 2 (1/ λ 2 +i/ γ p λ) ,
Re(2 ε ekv + ε Au )=0,
λ SP = λ media 1 ( λ media ) 2 ( λ vak ) 2 ( λ vak ) 2 (1 3 4 a 3 z 0 3 1 ( n m 2 +1) ) ,
ε Au (λ)= ε 1 λ p 2 (1/ λ 2 +i/ γ p λ) + m=1,2 A m λ m [ e i φ m (1/ λ m 1/λi/ γ m ) + e i φ m (1/ λ m +1/λ+i/ γ m ) ] ,
λ SP = λ media 1 ( λ media ) 2 ( λ vak ) 2 ( λ vak ) 2 (1 3 8 a 3 z 0 3 1 ( n m 2 +1) ) .

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