Real-time optics and spectroscopy simulations ideally provide results at update rates of 120 Hz or more without any noticeable delay between changing input parameters and the calculated results. Such calculations require models of sufficient speed yet adequate level of detail in the physical approximations to contain the essential features of the simulated phenomena. We discuss a representation of femtosecond laser pulses in which fast phase oscillations due to carrier frequency and due to spatial propagation are separated out and amplitude modulations due to Gaussian beam propagation are also separated and treated explicitly. We derive simplified expressions for the spatial modulations of laser beams. Further, we derive visibility and beam-overlap factors describing multi-pulse interference. We obtain simplified expressions for radius and curvature of nonlinear signal beams in the case of fundamental beams with different convergence, different beam waist, and imperfect mutual overlap. The described model is implemented in the virtual-reality laser laboratory simulation "femtoPro," but the derived equations can be used independently for other applications.
