We report a theory of optical generation and detection of the propagating spin waves in antiferromagnetic materials relevant for ultrafast pump-probe experiments. We derive and solve the equations of motion for antiferromagnetic spins in response to the light-induced effective magnetic field in the linear regime. Different forms of the excitation and the properties of the generated spin waves are analyzed. We theoretically show the selective detection of the spin waves by the magneto-optical Kerr effect. The developed formalism is readily applicable to inform future experiments on antiferromagnetic optomagnonics.