Gallium phosphide is an important indirect band gap material with variety of applications in optics ranging from LEDs to applications in GaP/Si based solar cells. We investigated GaP using ultrafast, pump-probe coherent acoustic phonon spectroscopy (time-domain Brillouin scattering). We measured the dependence of the amplitude of the differential reflectivity as modulated by coherent acoustic phonons (CAPs) as a function of laser probe energy and found that the amplitude of the coherent phonon oscillations varies non-monotonically near the direct gap transition at the $\Gamma$ point. A theoretical model is developed which quantitatively explains the experimental data and shows that one can use coherent phonon spectroscopy to provide detailed information about the electronic structure, the dielectric function and optical transitions in indirect band gap materials. Our calculations show that the modelling of experimental results is extremely sensitive to the wavelength dependent dielectric function and its derivatives.
