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A detailed investigation of various physical contributions to the refractive index change due to injection of free carriers and their effect on the wavelength tuning in a three-section InGaAsP/InP semiconductor tunable laser diode (TLD) is carried out using Crosslight PICS3D software. A comprehensive numerical model of a TLD is presented with the wavelength tuning based on a simultaneous consideration of optical and free carrier transport phenomena. The main difference of our study from most of the previous works is that the investigation is applied to the operating multisection active device rather than to a device with a predetermined refractive index change used as the input parameter. The only inputs in our model are the injection currents at the contacts of each section. We have demonstrated possibility of 30 nm discontinuous and 15 nm continuous tuning in the optimized TLD. We study the influence of design parameters, such as the coupling coefficient κ and Bragg section length L, on the tuning performance of the Bragg section of the TLD. The tuning performance of the TLD depends strongly on the mutual positions of the peak gain wavelength and the Bragg wavelength at the beginning of the tuning. The tuning range is strongly affected by the material composition of the Bragg grating. We found that wavelength tuning saturation may take place in typical devices in spite of the continuing change of the effective refractive index with the current injection. It is shown that with careful design optimization and selection of κ and L, the saturation effect can be completely eliminated and the tuning range of the TLD can be increased up to two to three times.