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We propose to include a Bragg-wavelength-detuned (BWD) layer in a portion of the cavity of an index-coupled distributed feedback (DFB) laser to overcome the mode degeneracy problem. The new two-section DFB (TSDFB) lasers are experimentally demonstrated to have comparable device dimension and output characteristics as conventional DFB lasers but have much better spectral stability. High side-mode suppression ratio can be obtained over a wide range of current injection and temperature conditions when the laser is coated with anti-reflection coatings on both output facets. Wavelength tuning over 5.4 nm can be obtained by adjusting the heatsink temperature and levering the bias currents. With excellent mode stability, the TSDFB lasers are demonstrated to perform wavelength conversion with large extinction ratio, high conversion efficiency, and waveform reshaping capability. The wavelength conversion can cover 30-THz of input frequency that matches the frequency grid of the dense wavelength division multiplexing systems. Penalty-free conversion is also demonstrated.