The LOFAR radio telescope located in the north of the Netherlands offers a high density of omnidirectional radio antennas. The LOFAR key science project Cosmic Rays is therefore well suited for detailed studies of the radio signal from air showers, and has been measuring since mid-2011 at primary energies in the range of 10 17 to 10 18 eV. We present high-precision measurements of the polarization of the radio signals, and the shape of the radio wavefront from the lateral distribution of signal

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... arrival times. Polarization and timing of the incoming radio pulse are complementary observables to the lateral distribution of signal power. These are shown to provide additional information on the air shower geometry and on the contribution of different radio emission mechanisms, such as the geomagnetic and charge excess processes.