Carbon Nanotubes as Optical Antennae

Light scattering from an array of aligned multiwall carbon nanotubes (MWCNTs) has previously been investigated, and shown to be consistent with that from an array of antennae. Two basic antenna effects have been demonstrated: 1) the polarization effect, which suppresses the response of an antenna when the electric field of the incoming radiation is polarized perpendicular to the dipole antenna axis, and 2) the antenna-length effect, which maximizes the antenna response when the antenna length is a multiple of the radiation half wavelength in the medium surrounding the antenna. In these previous experiments a random nanotube array was chosen to eliminate the intertube diffraction effects. In this communication, we provide compelling evidence of the antenna action of an MWCNT, by demonstrating that its directional radiation characteristics are in an excellent and quantitative agreement with conventional radio antenna theory and simulations. According to conventional radio antenna theory, a simple “thin” wire antenna (a metallic rod of diameter d and length l >> d) maximizes its response to a wavelength k when l = mk/2, where m is a positive integer. Thus, an antenna acts as a resonator of the external electromagnetic radiation. An antenna is a complex boundary value problem; it is a resonator for both the external fields, and the currents at the antenna surface. In a long radiating antenna, a periodic pattern of current distribution is excited along the antenna, synchronized with the pattern of fields outside. The current pattern consists of segments, with the current direction alternating from segment to segment. Thus, a long antenna can be viewed as an antenna array consisting of smaller, coherently driven antennae (segments) in series. Therefore, the resulting radiation pattern, as a function of the angle with respect to the antenna axis, consists of lobes of constructive interference, separated by radiation minima due to destructive interference. Consider a simple antenna as shown in Figure 1a. The radiation pattern produced by this antenna is rotationally symmetric about the z axis. For a center-fed antenna, or one excited by an external wave propagating perpendicular to the antenna axis (i.e., with the glancing angle hi = 90°), the pattern is also symmetric with respect to the x–y plane. For an antenna excited by an incoming wave propagating at an angle (hi < 90°), the relative strengths of the radiation lobes are expected to shift towards the specular direction. This follows from a qualitative argument based on the single-photon scattering picture, and conservation laws for scattered photons from an antenna. Since such scattering is elastic, the energy of each scattering photon x (where is the reduced Planck constant and x is the angular frequency) and its total momentum k = ki= ks (where k is the wave number, ki is the incident wave vector, and ks is the scattered wave vector) must be conserved. Due to the cylindrical symmetry, K, the length of the momentum vector component perpendicular to the antenna, must also be conserved. Thus, the momentum components parallel to the antenna for the incoming, and scattered photons, k (s) and k (i) respectively, satisfy the following condition k (i) = k 2 – K = k (s), or finally k (s) = ±k (i). This immediately leads to a formula for the angle of scattering hs = 180° – hi, since for a “thin” antenna with diameter d << l, the back scattering is suppressed, and therefore the negative sign is unlikely. Thus, scattering is dominated by the specular reflection. We have confirmed this effect, by measuring the scattered microwave radiation from a simple wire antenna; the forward radiation was about one order of magnitude more intense than for the backward scattered wave. To complete the preliminary antenna studies, we performed computer simulations of the detailed antenna response to an external plane wave. Figure 1b shows a polar coordinate plot of the radiation pattern (field intensity versus h), in the y–z plane, from a thin antenna (d = 0.001l) with l = 7k. The incoming wave of fixed wavelength k, struck the antenna at different incidence angles hi = 30°, 45°, and 60°. This produced radiation patterns dominated by lobes at hs = 180 – hi = 150°, 135°, and 120°, respectively: the scattering was dominated by the specular reflection with respect to the 90° line, in agreement with the simple analysis above. Due to cylindrical symmetry in the x–y plane, the response was mirror-image symmetric about the z axis in the x–z plane. The dependence of C O M M U N IC A IO N