Polarization-dependent optical properties of the open (N, N) carbon tubules C4N+2NnH4N (N = 5-8 and n = 0-11) are studied in low energy region with the CNDO/S-TDA calculations. It is shown that the low-lying excitation energies periodically decrease with n but not with N, irrespective of polarization directions. The N- and n-dependences of the oscillator strengths are also discussed. (C) 2004 Elsevier B.V. All rights reserved.