Effect of light polarization on the electromagnetically induced transparency and birefringence in a cylindrical quantum dot with spin–orbit interaction

•(Ec)min is less for x-polarization than z-polarization.•Absorption and refractive index depend on the length of quantum dot for z-polarization.•Absorption and refractive index depend on the radius of quantum dot for x-polarization.•Transparency window and FWHM do no depend on the size of quantum dot.•By increasing Rabi frequency, transparency window is increased.

In this paper electromagnetically induced transparency of GaAs cylindrical QD with parabolic potential and spin–orbit interaction are investigated by solving Schrödinger equation in effective mass and using perturbation method. Eigenfunctions and eigenvalues of this system are obtained. Effect of light polarization and dimensions of cylindrical QD are investigated finally.