Carbon nanotubes as probes for scanning near-field optical microscopy
Scanning near-field optical microscopy (SNOM)1 is a powerful technique that allows imaging and characterization of a single nano-object or molecule with a resolution far exceeding the diffraction limit of light. SNOM exploits near fields, which are nonpropagating electromagnetic fields that exist only in the vicinity of their source. Usually, the SNOM probe is placed close to the object being imaged. Both the probe and the object are illuminated by light. The near-field interaction between the two leads to an electromagnetic response that is very different from their individual responses in isolation. The resolution capability of the microscope and the information about the composite probe-object structure obtained by analysis of the scattered signal depends crucially on the size and material of the probe.
Among the different types of SNOM probes, plasmonic nanoantennas are of great interest2,3 because of their ability to efficiently couple the nonpropagating near fields and the freely propagating light from the illumination source. Recently, we theoretically predicted4,5 that metallic carbon nanotubes (CNTs) can also act as nanoantennas. The resonance frequencies of a metallic CNT nanoantenna vary from the terahertz (THz) to the near-IR (NIR) regimes, depending on the length of the CNTs. Although we and others have already shown the potential of CNTs as SNOM tips in the visible regime,6,7 and we have obtained 30nm resolution,6 the influence of the antenna resonances on the operating characteristics of the near-field optical microscope have not been investigated. Yet, this influence could be crucial for SNOM.
A first step in delineating the influence requires understanding the peculiarities of the near-field interaction between a metallic single-wall CNT (SWNT) nanoantenna and the object under investigation. We considered8 a harmonically oscillating electric dipole of moment 
as the object and studied the scattering of this dipole's near field by an SWNT. Here 
and ν are the amplitude and frequency of oscillation, and i is an imaginary unit. Though simple, this model contains all the essential physics involved in the probe-object interaction and can be relatively easily extended to more general cases.
To describe the strength of the coupling of the electric dipole to the metallic SWNT, we calculated8 the electric current induced on the SWNT surface by the near field of the electric dipole placed in the vicinity of the SWNT edge and polarized along the SWNT axis (see Figure 1). Both the distribution of the current along the SWNT axis—see Figure 1(a)—and the average magnitude of the current strongly depend on the frequency ν. Particularly, we observe more than one order of magnitude enhancement of the induced current at the frequencies of antenna resonances in the SWNT: see Figure 1(b).4 This means that the scattered signal will be maximized at these frequencies, making them preferable for SNOM using SWNT tips. The resonance frequencies can be adjusted by varying the length of the SWNT.
) placed on the SWNT axis at a distance zs=10nm from the closer edge of the SWNT. 
debye. : Electric dipole moment amplitude. ν: Frequency of electric dipole oscillation. (a) The current distribution 
along the SWNT axis z. Due to the electrically small diameter (~1nm) of the SWNT, the current is uniform along the SWNT circumference. (b) Frequency dependence of the average current 
dz. dz: Differential. pA: Picoampere. THz: Terahertz. To investigate the resolution that can be obtained using a metallic SWNT probe, we calculated8 the strength of the electric field 
, radiated by the system comprising two oscillating electric dipoles placed in the vicinity of a metallic SWNT at the observation point far away from the system (see Figure 2). The parameters of the SWNT and the dipoles are the same as in Figure 1. Figure 3 shows values calculated for the ratio 
at the observation point situated on the x axis, where 
is the electric field radiated at the observation point by a single electric dipole in the absence of the SWNT. When the observation point is far away, this ratio depends on the direction (but not on the magnitude) of the radial vector to the observation point. Figure 3 shows that in the close proximity of the SWNT, the strength of the field radiated by the dipoles in the far-field zone increases by more than two orders of magnitude. However, for interdipole separation <10nm, the images of the two dipoles merge and cannot be resolved separately: see Figure 3(a).
for different relative positions of the SWNT probe and the electric dipoles (see Figure 2), assuming that the separation between the SWNT and the xy plane is constant and equal to zc=5nm. Here is the electric field at an observation point located on the x axis radiated by the system of two electric dipoles and a metallic SWNT, whereas is the electric field at the same observation point due to only one isolated electric dipole placed in the coordinate system origin. The dipole oscillation frequency ν=2 .6THz, which is also the frequency of the first antenna resonance of the SWNT: brown arrow in Figure 1(b). The interdipole separation distance d equals 10nm in (a) and 20nm in (b). In summary, we have shown that antenna resonances play an important role in the operation of a scanning near-field optical microscope with a metallic SWNT probe. In particular, the coupling between the object (electric dipole) and the SWNT probe at a resonance frequency is considerably stronger than at frequencies away from the resonances. We estimate that the resolution limit that can be achieved using the SWNT probe is about 10nm. As a next step, we plan to apply the model to fluorescence microscopy, namely, to study the influence of the SWNT probe on the spontaneous decay of an excited state of a molecule.
We are grateful for the support of the International Bureau BMBF (Germany) under project BLR 08/001, the Belarus Republican Foundation for Fundamental Research under projects F09MC-009 and F09M-071, the European Commission Seventh Framework Programme CACOMEL project FP7-247007, a grant under a cooperative agreement between Lehigh University and NASA Goddard Space Flight Center, and the Charles Godfrey Binder Endowment at the Pennsylvania State University.
Andrei Nemilentsau is a scientific researcher. He received his MS in theoretical physics (2004) from BSU and his PhD in theoretical physics (2009) from the Institute of Physics, Belarus National Academy of Sciences, Minsk, Belarus. He is a Fellow of SPIE.
Gregory Slepyan is a principal researcher. He received his MS in radioengineering from the Institute of Radioengineering, Minsk, Belarus, his PhD in radiophysics from BSU, and his DSc in radiophysics from Kharkov State University, Kharkov, Ukraine.
Sergey Maksimenko is head of the Laboratory of Electrodynamics of Inhomogeneous Media. He received his MS in the physics of heat and mass transfer (1976) and his PhD in theoretical physics (1988) both from BSU, and his DSc in theoretical physics in 1996 from the Institute of Physics, Belarus National Academy of Sciences, Minsk, Belarus.
Akhlesh Lakhtakia is the Charles Godfrey Binder (Endowed) Professor of Engineering Science and Mechanics. He received his BTech and DSc degrees in electronic engineering from Banaras Hindu University and his MS and PhD in electrical engineering from the University of Utah. He is a Fellow of SPIE, the Optical Society of America, the American Association for the Advancement of Science, and the Institute of Physics (UK). He is the recipient of the 2010 SPIE Technical Achievement Award.
Slava V. Rotkin is the Frank J. Feigl Junior Faculty Scholar and an associate professor of physics. He received his MSc (Summa Cum Laude) in 1994 from the Electro-technical University and his PhD in 1997 from the Ioffe Institute (both in St. Petersburg, Russia).
