We investigate the effects of Rashba spin-orbit interaction on the optical absorption coefficients and refractive index changes associated with transitions between the first two lower-lying electronic levels in double quantum wire. The wire system represented by a symmetric, double quartic-well confinement potential is subjected to a perpendicular magnetic field. The analytical expressions of the linear and third-order nonlinear optical absorption coefficients and refractive index changes are obtained by using the compact density matrix formalism and iterative scheme. Optical properties are investigated as a function of structural parameter, magnetic field, Rashba spin-orbit interaction and photon energies. Numerical results reveal that competing effects between spin-orbit interaction and magnetic field modify strongly the optical properties and can be altered by these parameters. (C) 2016 Elsevier Ltd. All rights reserved.