The optical properties of carbon nanotubes are highly relevant for materials science. The way carbon nanotubes interact with electromagnetic radiation is unique in many respects, as evidenced by their peculiar absorption, photoluminescence (fluorescence), and Raman spectra. Carbon nanotubes are unique "one-dimensional" materials, whose hollow fibers (tubes) have a unique and highly ordered atomic and electronic structure, and can be made in a wide range of dimension. The diameter typically varies from 0.4 to 40 nm (i.e., a range of ~100 times). However, the length can reach 55.5 cm (21.9 in), implying a length-to-diameter ratio as high as 132,000,000:1; which is unequaled by any other material. Consequently, all the electronic, optical, electrochemical and mechanical properties of the carbon nanotubes are extremely anisotropic (directionally dependent) and tunable. Applications of carbon nanotubes in optics and photonics are still less developed than in other fields. Some properties that may lead to practical use include tuneability and wavelength selectivity. Potential applications that have been demonstrated include light emitting diodes (LEDs), bolometers and optoelectronic memory. Apart from direct applications, the optical properties of carbon nanotubes can be very useful in their manufacture and application to other fields. Spectroscopic methods offer the possibility of quick and non-destructive characterization of relatively large amounts of carbon nanotubes, yielding detailed measurements of non-tubular carbon content, tube type and chirality, structural defects, and many other properties that are relevant to those other applications.
Geometric structure
Chiral angle A single-walled carbon nanotube (SWNT or SWCNT) can be envisioned as strip of a graphene molecule (a single sheet of graphite) rolled and joined into a cylinder. The structure of the nanotube can be characterized by the width of the diameter d of the tube and the angle (θ) of the strip relative to the main symmetry axes of the hexagonal graphene lattice. This angle, which varies from 0 to 30 degrees, is called the "chiral angle" of the tube and varies dependent on the conditions of nanotube growth.
(n, m) notation
The nanotube structure can be described by two integer indices (n,m) that describe the width and direction of that hypothetical strip as coordinates in a fundamental reference frame of the graphene lattice. If the atoms around any 6-member ring of the graphene are numbered sequentially from 1 to 6, the two vectors u and v of that frame are the displacements from atom 1 to atoms 3 and 5, respectively. Those two vectors have the same length, and their directions are 60 degrees apart. The vector w = n u + m v is then interpreted as the circumference of the unrolled tube on the graphene lattice; it relates each point A1 on one edge of the strip to the point A2 on the other edge that will be identified with it as the strip is rolled up. The chiral angle α is then the angle between u and w. The pairs (n, m) that describe distinct tube structures are those with 0 ≤ m ≤ n and n > 0. All geometric properties of the tube, such as diameter, chiral angle, and symmetries, can be computed from these indices. The type also determines the electronic structure of the tube. Specifically, the tube behaves like a metal if m − n is a multiple of 3, and like a semiconductor otherwise. Thus, across the available indices, one third of SWNTs are metallic, and two thirds are semiconducting. Truly metallic carbon nanotubes with minimal to nonexistent band gap have been defined only as those where n = m.
Zigzag and armchair tubes Tubes of type (n, m) with n = m (chiral angle = 30°) are called "armchair" and those with m = 0 (chiral angle = 0°) "zigzag". All other chiral angles produce what are known as chiral nanotubes.
Electronic structure The optical properties of carbon nanotubes are largely determined by their unique electronic structure. The rolling up of the graphene lattice affects that structure in ways that depend strongly on the geometric structure type (n, m).
Van Hove singularities
A characteristic feature of one-dimensional crystals is that their distribution of density of states (DOS) is not a continuous function of energy, but it descends gradually and then increases in a discontinuous spike. These sharp peaks are called Van Hove singularities. In contrast, three-dimensional (bulk) materials have continuous DOS. Van Hove singularities result in the following optical properties of carbon nanotubes:
Optical transitions occur between the v1 − c1, v2 − c2, etc., states of semiconducting or metallic nanotubes and are traditionally labeled as S11, S22, M11, etc., or, if the "conductivity" of the tube is unknown or unimportant, as E11, E22, etc. Crossover transitions c1 − v2, c2 − v1, etc., are dipole-forbidden and thus are extremely weak, but they were possibly observed using cross-polarized optical geometry. The energies between the Van Hove singularities depend on the nanotube structure. Thus by varying this structure, one can tune the optoelectronic properties of carbon nanotube. Such fine tuning has been experimentally demonstrated using UV illumination of polymer-dispersed CNTs. Optical transitions are rather sharp (~10 meV) and strong. Consequently, it is relatively easy to selectively excite nanotubes having certain (n, m) indices, as well as to detect optical signals from individual nanotubes.
Kataura plot
The band structure of carbon nanotubes having certain (n, m) indexes can be calculated. A theoretical graph based on these calculations was designed in 1999 by Hiromichi Kataura to rationalize experimental findings. A Kataura plot relates the nanotube diameter and its bandgap energies for all nanotubes in a diameter range. The oscillating shape of every branch of the Kataura plot reflects the intrinsic strong dependence of the SWNT properties on the (n, m) index rather than on its diameter.
Optical properties
Optical absorption
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