In the present work, we are interested for an isolated and self-assembled InAs/InP quantum dots with a dome cross-section. We have tried to study the electronic and optical properties in the quantum dot by using an efficient and simple method. This numerical method is based on the coordinate transformation and the finite difference method (FDM). The influence of the parameters introduced in the mathematical function, is studied on the size, the shape and the number of the quantum dot. The electron, and heavy hole energy levels as well as their interband transition energies are also investigated. The linear, third-order nonlinear and total interband optical absorption coefficients and refractive index changes are investigated as a function of photon energy with varying height dot (H) and the incident optical intensity (I). The analytical expressions of these optical properties are obtained by using the compact-density matrix formalism.