In optical fiber communication, usually, optical signals are communicated around 1.35 or 1.55 mm. All optical active and passive devices should operate in these wavelengths or in a bandwidth close to these wavelengths. In this paper, it is shown that the Fibonacciclass Γ°FCΓ°J; nΓΓ one-dimensional quasi-periodic dielectric stack for [1.2-2 mm] bandwidth duration shows superimposed Bragg Gratings behavior. Thus, a new method will be presented to approximate these structures with superimposed Bragg Gratings in this wavelength duration. For the approximated superimposed Gratings the number of Gratings, the index of refraction contrasts, number of layers and related period of Gratings are calculated in terms of original system parameters. The proposed idea will open applicable analytical methods for investigation of quasi crystals in optical communication. Also, using presented approach nature of light propagation and physical interactions through these structures can be better described. In this work, using simulation of original Fibonacci quasi structure some of important parameters are extracted. Then, all parameters for construction of the superimposed Bragg Gratings using basic relations in integrated optics and extracted information will be calculated. Finally, constructed model is simulated and compares with original case. We show that our constructed superimposed Bragg Gratings closely follows original curve.