A new modality for probing ultrafast phenomena that relies on radially or azimuthally polarized probe pulses is presented. First, we describe the principle and then theoretically analyze the signals expected for different types of pump-induced nonlinearities. Last, we experimentally verify the methodology by probing a pump-induced Kerr gate with a time-delayed radially polarized probe pulse. In general, we find excellent agreement between the simulated and measured results.