28 November 1997 Ž . Chemical Physics Letters 280 1997 66–72 Large third-order optical nonlinearities of C -derived nanotubes 60 in infrared Rui-Hua Xie a,1 , Jie Jiang b a Chemical Physics Theory Group, Department of Chemistry, UniÕersity of Toronto, Toronto, Ontario M5S 3H6, Canada b Department of Physics, Nanjing UniÕersity, Nanjing, Jiangsu 210093, China Received 1 July 1997; in final form 22 August 1997 Abstract Garito and coworkers have suggested a mechanism to dramatically increase third-order optical nonlinearities of linear w Ž . x p-electron-conjugated molecules. Very recently, Marder and coworkers Science 276 1997 1233 have tested these ideas experimentally and have got large third-order optical nonlinearities in polarized carotenoids. In this Letter, our theoretical calculations predict that large third-order optical nonlinearities in C -derived nanotubes could be obtained in the infrared, 60 which implies that carbon nanotubes are also important nonlinear optical materials in photonic applications. q 1997 Elsevier Science B.V. 1. Introduction Ž Over the past ten years, the fullerenes C n s n . 60,70, etc , a new class of carbon materials, have been extensively studied, both theoretically and ex- w x perimentally 1–5 . With the further studies of C 60 and C , it was soon realized that carbon nanotube 70 w x 1,6,7 , a new member of the intriguing class of carbon materials, could be synthesized. These nan- otubes have cylindrical shapes, and their cylinder surfaces have honeycomb-lattice patterns just as in a two-dimensional graphite planes. Up to now, some wx work has been done on their geometric structures 8 , w x electronic structures 7,9 , and magnetic properties w x 10 , including nonlinear optical properties of C 60 w x and C 2–5,11–14 . 70 Recently, researchers’ interest has been attracted 1 E-mail: rhxie@tikva.chem.utoronto.ca by a kind of nanotubes with the smallest available w x diameter 6,7 , where the geometric effects are pre- dicted to be the largest. Two examples are armchair w x Ž. and zigzag nanotubes derived from C 7,15 : i 60 cutting a C molecule into two parts along its 60 equatorial line and then inserting one row of five armchair hexagons, one obtains C ; more generally, 70 if adding i rows of armchair hexagons, one then obtains a C molecule which would be in a 60qi=10 Ž form of a monolayer graphene tube armchair nan- .Ž. otube ; ii similarly, by cutting the C molecule in 60 half to a threefold axis along the zigzag edges, a perfect fit can be made to a single-layer cylindrical sheath consisting of i rows of nine zigzag hexagons, and one further gets a C molecule which is 60qi=18 Ž also in a form of a monolayer graphene tube zigzag . nanotube . All these nanotubes have diameter of about 0.7 nm, and are of scientific interest as carbon w x fibers 1,7 , which are today commercially important for their extraordinary high modulus and strength. 0009-2614r97r$17.00 q 1997 Elsevier Science B.V. All rights reserved. Ž . PII S0009-2614 97 01068-3