Excitation of four coherent phonon modes of different symmetries has been realized in copper metaborate CuB$_2$O$_4$ via impulsive stimulated Raman scattering (ISRS). Phonons were detected by monitoring changes in the linear optical birefringence using the balanced-detection (BD) technique. We compare the results of BD-ISRS experiment to the polarized spontaneous Raman scattering spectra. We show that the agreement between the two sets of data obtained by these allied techniques in a wide phonon frequencies range of 4-14 THz can be achieved by rigorously taking into account the symmetry of the phonon modes, and the corresponding excitation and detection selection rules. It is also important to account for the difference between incoherent and coherent phonons in terms of their contributions to the Raman scattering process. This comparative analysis highlights the importance of the ratio between the frequency of a particular mode, and the pump and probe spectral widths. We demonstrate analytically that the pump and probe pulse durations of 90 and 50 fs, respectively, used in our experiments, limit the highest frequency of the excited and detected coherent phonon modes to 12 THz, and define their relative amplitudes.
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