Dear Muhammad,

May i came late to this question. The phase is strictly speaking is used for sinusoidal waves rather than pulses. For pulses you can define delay time instead of the phase. If the medium is not dispersive then it will preserve the pulse shape. If it is dispersive the shape of the pulse will change.For visible light communication the dispersion will not be cause by the difference in the refractive index for the different wavelengths contained in the light but it will be caused by multi path effect.So, in principle you can use any source of white light.

You can check this theory by using both sources in your experiment.

Best wishes