In this paper, we have proposed a directional coupler formed by two non-identical single-mode fibers and derived the closed-form equation of the transaction power of the directional coupler. To find the coupling coefficient of the directional coupler, we have derived the analytical closed-form equations for the phased and the non-phase matched condition under various types of index fiber. Moreover, it also shows the effect of coupling length with coupling coefficient for different fiber indexes with the variation of the operating wavelength. Next, with the help of different tables and a graphical representation, the coupling coefficient variation is shown with operating wavelength for step-index, triangular index and parabolic index under single-mode optical fiber for the directional coupler. The mathematical solution shows that the efficiency of the coupling coefficient has been enhanced with corresponding unconditional frequency and waveguide parameters under every index type of the single-mode optical fibers.