We consider, for the first time, optical specifications such as the nonlinear optical rectification (NOR), the second harmonic generation (SHG) and the third harmonic generation (THG) of quantum well (QW) that has the Rosen-Morse potential confinement and is generated by GaAs/GaAlAs heterostructure. To do this, QW structure is firstly asymmetrized by applying an external electric field, as 10 kV/cm. Therefore, the electric field-triggered (F = 10 kV/cm) Rosen-Morse QW (eftRMQW) is taken into consideration throughout the study. In this study, it is elucidated that how to control NOR, SHG and THG optical responses through monochromatic linearly polarized intense laser field (ILF). In order to be able to investigate the ILF effects, the time-dependent of ILF is removed to potential energy term of the wave equation by using Kramers-Henneberger (KH) and the dipole approximations, building the laser-dressed potential. Then, the bound state energies and the wave functions of eftRMQW are obtained using the diagonalization method within the effective mass approach and the parabolic approximation. The influences of the ILF and structural parameters of eftRMQW on NOR, SHG and THG coefficients are discussed in detail. The optimum of structure is ferreted out for devices design and applications that will consider eftRMQW, and for this optimum the alternative parameter analysis is carried out. (C) 2020 Elsevier B.V. All rights reserved.