Resonant second-harmonic generation in monosized and aligned single-walled carbon nanotubes

Abstract

The magnitude and spectral response of second-harmonic generation ͑SHG͒ from 0.4 nm single-walled carbon nanotubes ͑CNTs͒ in the channels of AlPO 4 -5 zeolite is reported. The second harmonics ͑SH͒ was found to be polarized perpendicular to the tube axis and maximized by an excitation polarization at 45°to the tube axis. A SH resonance peak at 2 eV was observed, which corresponds to the lowest-energy excitonic state in chiral ͑4,2͒ CNTs. The second-order optical susceptibility ͑2͒ of the system was determined to be 10 −6 esu, which agrees with the large ͑2͒ predicted for small diameter CNTs. These experimental results suggest that SHG can be used to characterize the symmetry and chirality of CNTs.

Measurement of optical second-harmonic generation from an individual single-walled carbon nanotube

“…SHG has been observed from thin films of SWCNTs [18,19,23], and from an ensemble of SWCNTs trapped in zeolites [24]. The latter result was associated with chirality, and a large second-order susceptibility on the order of 400 pm V −1 , predicted theoretically [17,25], was experimentally confirmed.…”

“…This is about 50 times higher than the measured signal of 77 counts s −1 . Note, however, that the maximum second-order susceptibility is found at excitation energies resonant with the electronic level structure of the CNT [24,25], and the measured signal scales quadratically with susceptibility. The difference between our experiment and the estimate could therefore be due to measuring off resonance, rendering the effective susceptibility to be about 57 pm V −1 for our particular tube.…”

“…We first estimate the expected SHG signal strength by assuming that the second-order susceptibility of CNTs is equal to 400 pm V −1 , as reported from measurements on an ensemble of SWCNTs trapped in zeolites [24]. (See appendix for calculation details.)…”

Probing microporous materials with second-harmonic generation

“…Apart from the traditional Kurtz powder measurements (see Section 4) [17], also polarization dependent measurements on single zeolite crystals [18,19] and oriented zeolite films [9,20,21] were performed, confirming the alignment of the adsorbed molecules along the pore direction. Similarly spectral and polarization dependent SHG measurements were done on single walled carbon nanotubes (SWCNT) inside AlPO 4 -5 single crystals to confirm that they are chiral (4,2) SWCNTs [23]. Herance et al showed that the efficiency of guest molecules to generate SHG depends on the pore dimensionality of the interconnected pore system as follows: 1D > 2D > 3D [24].…”

Communications: Ab initio second-order nonlinear optics in solids

“…6,7 Their interest is rapidly growing because of their sensitivity to space symmetry violations, and nowadays SHG and SFG are also used for characterizing systems such as nanocrystal interfaces 8 or as a probe for molecular chirality in polymers 9 and nanotubes. 10 In these processes, the interaction of matter with light is described by the macroscopic second-order susceptibility ͑2͒ . This quantity takes into account the many-body interactions among the electrons of the system: the variation of the screening fields on the microscopic scale, i.e., crystal local-field effects, 11 and the electron-hole interaction, i.e., excitonic effects, 12 as real and/or virtual excitations are created in the process.…”