Nanofocusing properties of a tip in the form of a dielectric tapered fiber with metal apertureless coating and dielectric nanocladding can be tuned within a wide spectral range by choice of cladding permittivity. The silica core of diameter decreasing from 2 μm to 5 nm in apex is covered with a silver layer and has a 5 nm dielectric cladding. Internal illumination with a radially polarized Laguerre-Gauss beam guided in fiber is used. In body-of-revolution finite-difference time-domain simulations we find that with an increase of the refractive index of nanocladdings the maximum enhancement occurs for increasingly longer wavelengths.
©2009 Optical Society of America
Progress in nano-optics is connected with increasing interest in the underestimated role, up to not long ago, of evanescent fields and surface plasmon-polaritons (SPPs) in imaging and energy guiding along metal nanostructures . Local electromagnetic field enhancement due to SPPs decides about resolution of nanoscale investigations of biomedical and chemical molecules and surface enhanced Raman scattering. This progress is conditioned by the development of several nanotechnologies that allow fabrication of metal and dielectric nanostructures as well as patterning, etching and drilling techniques with nanometer accuracy. The use of evanescent waves decides that the classical diffraction limit of resolution to about half a wavelength does not restrict scanning near-field and tunneling optical microscopes . To a great extent it is possible, due to advantageous use of SPPs in light transmission and technical means, to concentrate optical energy to nanometer size spots [1–3]. Efforts to develop easy to fabricate nanotips for scanning near-field optical microscopes (SNOMs) continue since the mid-eighties of the previous century . In near-field microscopy the narrower is the confinement of scanning light the better is the resolution. For SNOMs with aperture probes a practical limit of the resolution is the sum of the diameter of the aperture of a tapered-fiber metal-coated tip and twice the skin depth of the metal coating, what corresponds to light penetration into metal layers on both sides of the aperture. Understanding of charge densities and current distributions on the metal rim of the aperture of a tip  suggested that a way to improve resolution of scanning microscopes is possible due to enhancement of energy throughput of aperture probes. Several methods aiming at this were recently proposed, e.g [6–8]. Another approach to SNOM resolution improvement is the use of apertureless metallic or metal-coated tips for nanofocusing of light proposed by Novotny et al. , which with efficient light coupling may offer better resolution.
Vigorous progress in nanotip design and fabrication has been done in the last decade [10–19]. Babadjanyan et al.  predicted theoretically, using a simple conical model of a tapered wire, that the wavelength of plasmons approaching the tip apex decreases and electric field density increases. A more realistic model, where a tip is defined by its length, taper angle and radius of its spherical apex, in which nanofocusing depends additionally on polarization, angle of incidence and wavelength of external illumination was considered by Sun and Shen . An innovative idea to efficiently generate plasmons at the metal surface of tips was proposed by Bouhelier et al. . They proposed a tapered-fiber metal-coated probe with internal radially polarized illumination to couple light to plasmons, what corresponds to a flat Kretschmann configuration transformed to a conical symmetry. The idea of a tapered-fiber metal-coated tip, where energy transfers from optical modes guided in the fiber to SPP modes guided on outer metal surface, was further analyzed by Janunts et al. . A thorough study of optical-to-plasmon mode coupling, energy dissipation in metal, radiation losses and their dependence on tapered fiber and metal coating geometrical parameters was published by Ding et al. . Optimum energy coupling from radially polarized waveguide modes in tapered fiber to SPP modes on the outer surface of a metalized probe achieved 10% . Lack of sound theoretical models to describe nanofocusing of plasmons frequently limited the scope of investigations to precise simulations performed with different methods such as for example finite element method (FEM) [15–18] and body-of-revolution finite difference time domain (BOR FDTD) . In FEM simulations Issa and Guckenberger  observed existence of optimal taper angles for maximum field enhancements recorded 1 nm behind the tip apex. Chen and Zhan  proposed radially polarized internal illumination of silver coated tip combined with a glass solid immersion lens. Using external illumination, Baida and Belkhir  presented a sophisticated set-up where a doughnut shape beam with radial polarization impinges onto metal tip from all sides.
Here, we present a novel SNOM probe in the form of a dielectric tapered fiber with metal apertureless coating and dielectric nanocladding. Internal illumination with a radially polarized Laguerre-Gauss beam guided in the fiber core efficiently couples optical energy to plasmons. Lack of external far-field illumination eliminates background bias which usually reduces signal-to-noise ratio. Due to different dielectrics on both metal interfaces asymmetric plasmon modes are generated and the tip has extreme nanofocusing properties. When refractive index of the dielectric cladding increases from unity (air), the enhancement is observed at increasingly longer wavelengths. In BOR-FDTD simulations we assess that achievable intensity enhancement is better than with an apertureless metallized fiber. The nanocladding adds new functionality of a probe, increase of cladding permittivity causes a red-shift of maximum concentration.
2. Apertureless nanotip
We introduce a novel structure of an apertureless tip: a tapered dielectric fiber with metal coating and dielectric nanocladding (DMD). Figure 1 shows schematically and not to scale such a tip: a dielectric core of radius r is tapered at α = 20° half-angle, has a silver coating of thickness d, and a very thin w = 5 nm outer dielectric layer. Photon to plasmon coupling occurs in the tapered part, where metal is sandwiched between two dielectrics. In this region asymmetric plasmon modes are generated at both interfaces. At a certain core diameter the core mode ceases, but the plasmon at the outer metal surface and polariton in the cladding propagate towards the apex. Their wavelength and velocity decrease and evanescent field concentration increases.
The role of the outer dielectric nanocladding is twofold. Chemically, it protects against oxidation of silver, which is used for its low loss plasmon propagation. Electromagnetically, it modifies the coupling conditions of light modes propagating in the core to SPP modes at the metal-nanocladding interface. The spectral location of maximum enhancement at the tip apex can be tuned by choosing the value of nanocladding dielectric constant. Moreover, it decreases the plasmon wavelength, what increases the optical distance over which plasmons accumulate and in effect enhances evanescent field concentration. Efficient coupling of internal illumination to outer silver-dielectric interface is due to Laguerre-Gauss mode with radial polarization guided in the fiber core [20–22].
Existence of asymmetric modes supported by a thin and flat metal layer with substrate and superstrate with different dielectric constants was considered by several authors, e.g. [23,24]. Recently, enhanced nanofocusing due to asymmetric field distribution in different dielectrics on both sides of the metal layer was observed in flat tapered waveguides .
3. Simulation method
BOR FDTD simulations using in-house code are made for silica fiber core (nc = 1.45), silver coating and dielectric cladding with various dielectric constants. An optical fiber of 2 μm diameter is tapered at a half-angle of 20° chosen as an example. Then, a silver layer thickness of thickness d and of a 5 nm radius at the apex are applied to the outside of the dielectric core. The resulting tip is a classical apertureless SNOM probe introduced earlier , onto which a 5 nm dielectric layer of different permittivities ε is applied. In simulations we consider the effect of this layer on superfocusing at the tip apex. Moreover, we investigate how energy enhancement changes depending on the permittivity of this new layer.
The apertureless probe is a conical structure of cylindrical symmetry, thus numerical body-of-revolution methods are used in these investigations. We employ the FDTD algorithm to calculate the fields inside and around the structure using a uniform mesh of spatial discretization Δr = 0.5 nm and time discretization Δt = Δr/2c, where c is the speed of light in vacuum. The dielectric cladding is assumed to be dispersionless with a refractive index from unity to 1.8 (ε = 3.24). This shows gradual changes to the focusing fields at the tip apex. Silver is modeled using Drude dispersion with parameters equal ε ∞ = 3.70, ω p = 13673 THz and Γ = 27.35 THz . The excitation signal is a radially polarized, cylindrically symmetric Laguerre-Gauss beam. Its radial electric field profile is proportional to , where the beam has maximum intensity at radius R.
4. Optical intensity distribution at the nanofocus region
We analyze dependence of concentration of energy at the apex on permittivity values of the nanocladding for a fixed silver layer thickness d = = 40 nm. Figure 2 presents spectral plots of intensity enhancement normalized to the maximum intensity of incident light (Fig. 2(a)) and to intensity enhancement achievable without cladding (Fig. 2(b)), where existence of a subnanometer silver oxide layer is neglected. The nanocladding permittivity tangibly affects the resonant wavelength for which maximum intensity enhancement is observed. For a metal-coated tapered-fiber apertureless probe the best enhancement of 104 is observed for wavelength λ = 420 nm. Jumps of the nanocladding refractive index by 0.1 shift the resonant wavelength by 25 nm. Thus it is possible to shift the resonance to longer wavelengths. Moreover, probes with nanocladding offer allover greater enhancements than those without. For example, it is possible to have intensity enhancement exceeding 103 in the whole analyzed visible range from 420 nm to 650 nm using n = 1.8. Naturally, the use of dielectrics with higher n is possible under the condition, that they are transparent. The important role of nanocladding is illustrated in Fig. 2(b), where plots of intensity enhancement normalized with respect to that possible for classical apertureless probes in air are shown. For a range of nanocladding refractive index values the intensity enhancement gain reaching two orders of magnitude is possible for wavelengths 530-630 nm.
Figure 3 shows how enhancement of the field at apexes depends on thickness d of the silver layer sandwiched between the dielectrics. For a given permittivity of the nanocladding maximum enhancement is observed at the same wavelengths for all d values. However, optimum layer thickness changes with illumination wavelength.
In biology and chemistry for molecular detection applications it is useful to have high intensity enhancement in narrow spectral ranges and volumes comparable with the size of molecules. Therefore, apart from ways to achieve concentration, methods of tuning light frequency in order to match maximums enhancement plots in Fig. 2(a) are of interest. To this end special care is taken in choosing permittivities of cladding materials with high transmissivity in the spectral region of interest. The second factor is a search for linear-to-radial polarization converters working together with tunable polychromatic sources . Additional tuning may be available through the use of nanocladding materials with an optical absorption edge, e.g . Moreover, small corrections of absorption edge spectral positiondepend on film thickness. In addition, it can be seen in Fig. 2(a), that for nanocladdings of ε > 2.56 the lowest intensity enhancement is 103 for wavelengths greater than 425 nm. This opens a possibility to use DMD probes with broadband light sources.
We illustrate how the dielectric nanocladding affects focusing properties with electric energy density plots. Figure 4 presents three apertureless probes, one without and two with nanocladding, for those wavelengths for which maximum energy concentration is achieved. The silver coated tip without cladding is an idealization because we neglect inevitable existence of a nontransparent Ag2O layer. In all cases the electric energy density enhancement is similar and reaches 105 of the incident one. In previous studies [e.g. 15], electric energy density enhancement was controlled by adjusting the taper angle. Here, for a fixed taper angle we accomplish this with different nanocladding permittivities, however, the method is valid for various taper angles. The use of cladding only marginally affects the full-width at half-maximum (FWHM) of the electric field at the apex, as it is indicated in Fig. 4 caption.
We have proposed a new apertureless SNOM probe structure. A dielectric tapered fiber is coated with a thin silver layer and has a dielectric nanocladding. Both metal and dielectric coatings are continuous including the apex. Internal illumination with a radially polarized Laguerre-Gauss beam guided in the fiber core allows better signal-to-noise ratio than possible with external far-field sources. The role of the dielectric nanocladding is to influence spectral characteristics of apertureless SNOM probes.
The permittivity constant and thickness of dielectric nanocladding are new parameters that influence the focusing properties of apertureless SNOM tips, in addition to taper angle and wavelength considered before. Thus, for a given taper angle defined by a technological process it is possible to tune the maximum enhancement wavelength by choosing the nanocladding dielectric constant value. This novel concept is illustrated with BOR-FDTD simulations for core refractive index 1.45 and those of nanocladding from the range 1.0-1.8.
This research was sponsored by Polish Ministry of Science and Higher Education grants # N N507 445534. The authors are partners in COST Actions MP 0702 and MP 0803. Numerical computations were performed in the Interdisciplinary Centre for Mathematical and Computational Modelling (ICM), University of Warsaw, grant number G33-7.
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